MAY 2009202
AEA PAPERS AND PROCEEDINGS
degree of adaptation over the long-run to aver-
age temperature levels, potentially offsetting
the short-run temperature effects. The param-
eter φ ∈ ( 0, 1) captures the rate of convergence.
We further assume that all countries start, in
antiquity at time zero, with the same level of
per capita income, logy
i
(0) = c for all i. Note
that since equation (2) applies to all countries,
including country *, E[logy
*
(t)] = c + (g + (γ +
ρ)
__
T
*
)t.
Integrating the differential equation (2) with
the initial condition and taking expectations, we
have
(3) E[logy
i
(t)] = E[logy
*
(t)]
+
γ + ρ
_____
φ
(
__
T
i
− T
*
)(1 − e
−φt
).
(This derivation is shown formally in the online
Appendix.) Therefore, in the long run, as t → ∞,
the cross-sectional relationship between income
and temperature is
(4)
dE[logy
i
]
_______
d
__
T
i
=
γ + ρ
_____
φ
.
Equation (4) is an equation with four unknowns,
and we have estimates for three of them. The
left-hand side of (4) is the cross-sectional regres-
sion parameter in the regression of income on
temperature, i.e., β = −0.085 in a cross-country
context and β = −0.012 in a within-country
context (see Table 2). As discussed above, the
short-run growth coefcient is approximately γ
= −0.011 (DJO 2008). The convergence param-
eter, much analyzed in the growth literature, is
typically estimated in the cross-country context
in the range φ ∈ [0.02, 0.10] (Barro and Sala-
i-Martin 1995; Francesco Caselli, Gerardo
Esquivel, and Fernando Lefort 1996).
A. The Convergence Mechanism
We rst consider turning off the adapta-
tion channel (setting ρ = 0 in (4)) to examine
the implications of convergence alone. In this
setting, reconciling the short-run and long-
run temperature effects is achieved when φ =
γ/β. In a cross-country context, this requires φ
= 0.129(i.e., −0.011/−0.085), which appears
somewhat high given estimates in the literature.
At a within-country level, we have no panel esti-
mate of the short-run growth effect γ . If one
applies the cross-country estimate of γ , then we
require φ = 0.917 (i.e., −0.011/−0.012). While
it is reasonable that convergence rates might be
substantially higher in a within-country context,
this estimate appears extremely high.
7
These
calculations suggest that adaptation is likely to
be important in reconciling the data.
B. The Adaptation Mechanism
Over the long run, areas may adapt to difcult
geographic conditions. Technologies, skills, and
physical capital can all be tailored to a given cli-
matic regime. Moreover, population can react,
either through fertility, death rates, or migra-
tion, thus altering the local per capita intensity
of the factors of production.
We now relax the strong assumption of no
adaptation (ρ = 0), and instead estimate ρ using
our ndings for β and γ , and a chosen con-
vergence rate, φ. Rearranging (4) shows that ρ
= βφ − γ . In the cross-country context, tak-
ing a middle-of-the-road convergence rate of φ
= 0.06 yields an estimate of ρ = 0.0059. This
suggests that 54 percent of the short-run effect
is offset in the long run, so that the long-run
growth rate effect of being 1 degree C warmer is
γ + ρ = −0.0051, or half of 1 percentage point
per annum.
In the within-country context, there is more
uncertainty, both because the short-run within-
country growth effect has not been estimated
in panel data and because the convergence rate
may be greater. If we apply the country-level
panel estimate of γ = −0.011 and take the
upper-bound cross-country convergence esti-
mate of φ = 0.10 internally, we nd ρ = 0.0098,
so that 89 percent of the short-run growth effect
is offset within countries. Thus, if the short-run
growth estimate were the same within countries
as between countries, there would be an even
larger role for adaptation within countries than
between countries.
8
7
For example, in developed countries (United States,
Japan, Europe) Barro and Sala-i-Martin estimate within-
country convergence coefcients of approximately
0.02–0.03.
8
For example, prices can offset productivity shocks. If
markets are more integrated within than across countries,
the price adaptation mechanism may offset the effects of
temperature differences more completely within countries.