Paul Johnson, Steven Durlauf and Jonathan Temple 1145contaminated by short-run dynamics. These problems are likely to be even more
serious in developing countries, where large slumps or crises are not uncommon,
and output may deviate for long periods from any previous structural trend. As
Pritchett (2000a) emphasizes, output often behaves very differently in developing
countries compared to Organization for Economic Cooperation and Development
(OECD) member countries, and a major collapse in output is not a rare event. There
may be no underlying trend in the sense commonly understood, and conventional
time series methods should be applied with caution.
The problem of short-run output instability extends further. It is easy to construct
examples where the difference between observed output and potential output is
correlated with variables that move up and down at high frequencies, with inflation
being one obvious example (Temple, 2000a). At a minimum, this means that any
time series or panel data analysis should distinguish carefully between short-run
and long-run effects.
Nevertheless, despite these problems, there are some hypotheses for which time
series variation may be informative. Jones (1995) and Kocherlakota and Yi (1997)
show how time series models might be used to discriminate between different
growth theories. More specifically, they develop a statistical test of endogenous
growth models based on regressing growth on lagged growth and a lagged policy
variable (or the lagged investment rate, as in Jones). Exogenous growth models
predict that the coefficients on the lagged policy variable should sum to zero, indi-
cating no long-run growth effect of permanent changes in this variable. In contrast,
some endogenous growth models would imply that the sum of coefficients should
be non-zero. A simple time series regression then provides a direct test. More for-
mally, as in Jones (1995), for a given countryione can investigate a dynamic
relationship for the growth rateγi,t, where:
γi,t=A(L)γi,t− 1 +B(L)zi,t+εi,t, (24.30)wherezis the policy variable or growth determinant of interest, andA(L)andB(L)
are lag polynomials assumed to be compatible with stationarity. The hypothesis of
interest is whetherB( 1 ) =0. If the sum of the coefficients in the lag polynomial
B(L)is significantly different from zero, this implies that a permanent change in
the variablezwill affect the growth rate indefinitely. As Jones (1995) explicitly dis-
cusses, this test is best seen as indicating whether a policy change affects growth
over a long horizon, rather than firmly identifying or rejecting the presence of a
long-run growth effect in the theoretical sense of that term. The theoretical con-
ditions under which policy variables affect the long-run growth rate are strict,
and many endogenous growth models are best seen as new theories of potentially
sizeable level effects.^17
A related idea is that of Granger causality, where the hypothesis of interest would
be the explanatory power of lags ofZi,tforγi,tconditional on lagged values ofγi,t.
Blomstrom, Lipsey and Zejan (1996) carry out Granger causality tests for invest-
ment and growth using panel data with five-year sub-periods. They find strong
evidence that lagged growth rates have explanatory power for investment rates,