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H. Ahumada and M. Cornejo
Disentangling Short- and Long-Run Effects of Climate
Change
For series with persistent behavior, both stationary or integrated, which do not change
much from period to period, it is possible to distinguish short-run and long-run effects.
For integrated variables, to obtain the long-run effects, we can test if the variables
are co-integrated. Co-integration implies the existence of a linear combination of variables which is stationary when the variables in the relationship are non-stationary
and integrated of equal order. Co-integrated variables are driven by the same persistent shocks, and, thus, those variables have a common stochastic trend, showing
a tendency to move together in the long run. As indicated by (Juselius 2006), in
multivariate co-integration analysis, all variables are represented as stochastic and
a shock to one variable is transmitted to all other variables via the dynamics of the
system until the system finds its new equilibrium position.
Once co-integration is found, an equilibrium correction model (ECM) can be
estimated. This model encompasses differenced variables as well as the deviations
from the long-run or co-integrated relationship for integrated variables as expressed
in Eq. (3). There are several advantages of this formulation associated not only with
avoiding multicollinearity typically present in time-series data but also allowing
a more intuitive interpretation of the estimates disentangling short- and long-run
effects.
Moreover, another advantage of using this approach is the invariance of the cointegration property to the extension of the information set (Juselius 2006). This
property implies that once co-integration is found among a set of variables, the cointegration results will remain valid if more variables are added to the partial system,
as the one we estimate below. In this sense, there would be no omitted variable effects
present for co-integration when adopting this specific-to-general strategy.
Because of that, for the Argentine case, we start by estimating a partial system through a vector autoregressive (VAR)
4 model between 1973 and 2015 among
soybean yields, global temperature anomalies, and CO 2 concentrations in the atmosphere. This climate system also controls for two variables
5 : La Niña events and the
number of days with maximum temperatures above 30
◦ C during the growing season
of the plant. Both variables negatively affect soybeans yields.
6
Therefore, there is evidence from the climate system that one long-run relationship
exists in which all variables adjust to reach the long-run equilibrium. Equation(2)
represents the long-run relationship when writting ln(yield) as the dependent variable.
4 A VAR model is a multivariate stochastic process model that can be used to capture the linear
interdependences among the variables analyzed in the system. It generalizes the time-series AR
model.
5 These variables, that we previously selected according to their statistical significance, were
included unrestrictedly in the system, that is, outside the co-integration vector.
6 The VAR model passes all diagnostic tests at traditional levels and included a linear trend in the
long run since the variables can co-integrate but may have different deterministic trends. These
results are not reported but can be obtained from the authors upon request.
H. Ahumada and M. Cornejo
Disentangling Short- and Long-Run Effects of Climate
Change
For series with persistent behavior, both stationary or integrated, which do not change
much from period to period, it is possible to distinguish short-run and long-run effects.
For integrated variables, to obtain the long-run effects, we can test if the variables
are co-integrated. Co-integration implies the existence of a linear combination of variables which is stationary when the variables in the relationship are non-stationary
and integrated of equal order. Co-integrated variables are driven by the same persistent shocks, and, thus, those variables have a common stochastic trend, showing
a tendency to move together in the long run. As indicated by (Juselius 2006), in
multivariate co-integration analysis, all variables are represented as stochastic and
a shock to one variable is transmitted to all other variables via the dynamics of the
system until the system finds its new equilibrium position.
Once co-integration is found, an equilibrium correction model (ECM) can be
estimated. This model encompasses differenced variables as well as the deviations
from the long-run or co-integrated relationship for integrated variables as expressed
in Eq. (3). There are several advantages of this formulation associated not only with
avoiding multicollinearity typically present in time-series data but also allowing
a more intuitive interpretation of the estimates disentangling short- and long-run
effects.
Moreover, another advantage of using this approach is the invariance of the cointegration property to the extension of the information set (Juselius 2006). This
property implies that once co-integration is found among a set of variables, the cointegration results will remain valid if more variables are added to the partial system,
as the one we estimate below. In this sense, there would be no omitted variable effects
present for co-integration when adopting this specific-to-general strategy.
Because of that, for the Argentine case, we start by estimating a partial system through a vector autoregressive (VAR)
4 model between 1973 and 2015 among
soybean yields, global temperature anomalies, and CO 2 concentrations in the atmosphere. This climate system also controls for two variables
5 : La Niña events and the
number of days with maximum temperatures above 30
◦ C during the growing season
of the plant. Both variables negatively affect soybeans yields.
6
Therefore, there is evidence from the climate system that one long-run relationship
exists in which all variables adjust to reach the long-run equilibrium. Equation(2)
represents the long-run relationship when writting ln(yield) as the dependent variable.
4 A VAR model is a multivariate stochastic process model that can be used to capture the linear
interdependences among the variables analyzed in the system. It generalizes the time-series AR
model.
5 These variables, that we previously selected according to their statistical significance, were
included unrestrictedly in the system, that is, outside the co-integration vector.
6 The VAR model passes all diagnostic tests at traditional levels and included a linear trend in the
long run since the variables can co-integrate but may have different deterministic trends. These
results are not reported but can be obtained from the authors upon request.