Palgrave Handbook of Econometrics: Applied Econometrics

Paul Johnson, Steven Durlauf and Jonathan Temple 1127

eiis a country-specific shock that is distributed independently of the explanatory
variables.^2 Substitution into (24.8) and definingεi=υi−βeigives the regression:

γi=g−βlogA+βlogyi,0+β

α+φ

1 −α−φ

log

(

ni+g+δ

)

−β

α

1 −α−φ

logsK,i−β

φ

1 −α−φ

logsH,i+εi. (24.9)

Note an appealing feature of this regression: although the role of initial income
is predicated on diminishing returns to capital, the regression can be estimated
without using capital stock data. The measurement of capital stocks, especially for
developing countries, is fraught with problems, as discussed in Pritchett (2000b).
The specification derived by Mankiwet al.(1992) neatly sidesteps some of these
problems.
After assuming thatg+δ=.05 (based on data from the US and other economies),
Mankiwet al.use data from 98 countries over the period 1960–85 to obtain esti-
mates ofβˆ=−.299 (implying an estimatedλof 0.0142),αˆ=.48 andφˆ=.23. They
are unable to reject the parameter restriction, implicit in (24.9), that the final three
slope coefficients sum to zero.
There are many extensions to this “augmented” Solow model that can be char-
acterized as adding control variables,Zi, to the regression and understood as
modeling heterogeneneity in the level of technology at a given instant. In effect,
thegi−βlogAi,0terms in (24.4) are replaced withg−βlogA+πZi−βei, giving
the regression:

γi=g−βlogA+βlogyi,0+β

α+φ

1 −α−φ

log

(

ni+g+δ

)

−β

α

1 −α−φ

logsK,i−β

φ

1 −α−φ

logsH,i+πZi+εi. (24.10)

Note that (24.10) does not identify whether theZiare correlated with steady-state
growthgior the initial technology termAi,0, so a believer in a common long-
run growth rate will not be dissuaded by the finding that particular choices ofZi
help predict growth beyond the Solow regressors. The attribution of the predictive
content ofZito technology levels versus steady-state growth must largely depend
on a researcher’s prior beliefs about the long-run process driving the diffusion of
technology. It seems plausible, however, that the controlsZimay sometimes be
associated with differences in efficiency growthgi, rather than simply explaining
differences in initial technology levels. Even if all countries have the same rate of
technical progress in the long run, that assumption is somewhat implausible over
a sample period as short as 20 or 30 years.
The canonical growth regression can be understood as a version of (24.10) in
which the embedded parameter restrictions are ignored. A generic representation
of the regression is:

γi=βlogyi,0+ψXi+πZi+εi, (24.11)