Palgrave Handbook of Econometrics: Applied Econometrics

1126 The Methods of Growth Econometrics

Assuming that the rates of technical progress and convergence are constant across
countries allows (24.4) to be rewritten as:

γi=g−βlogyiE,∞−βlogAi,0+βlogyi,0, (24.5)

with the key implication of a negative relationship between initial levels of output
and subsequent growth in a cross-section of countries, over any time period. The
mechanism is diminishing returns to capital: a country further below its balanced
growth path will tend to grow more quickly, other things equal, because a given
rate of investment has a larger effect on the growth rates of capital and output.

24.3.2 Cross-country growth regressions

The typical cross-country growth regression, the foundation of the empirical
growth literature, is motivated by adding a random error termυito (24.5), giving:

γi=g−βlogyEi,∞−βlogAi,0+βlogyi,0+υi. (24.6)

Operationalization of (24.6) requires empirical analogues for logyEi,∞and logAi,0.
Mankiw, Romer and Weil (1992) do this by assuming that aggregate out-
put is described by a three-factor Cobb–Douglas production functionYi,t =

Kiα,tHiφ,t

(

Ai,tLi,t

) 1 −α−φ

, whereKi,tdenotes physical capital andHi,tdenotes human

capital, assumed to follow the accumulation equationsK ̇i,t=sK,iYi,t−δKi,tand
H ̇i,t=sH,iYi,t−δHi,t, respectively, whereδdenotes the depreciation rate andsK,i
andsH,iare the respective (time-invariant) saving rates for physical and human
capital and dots above variables denote time derivatives. These assumptions imply
that the steady-state value of output per effective worker is:

yEi,∞=

⎛

⎝

sαK,isφH,i

(

ni+g+δ

)α+φ

⎞

⎠

1

1 −α−φ

, (24.7)

giving a cross-country growth regression of the form:

γi=g+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−βlogAi,0+υi. (24.8)

Mankiwet al.argue that initial efficiencyAi,0should be interpreted as reflect-
ing not just technology, which they assume to be constant across countries, but
also country-specific influences such as resource endowments, climate and insti-
tutions, assumed to vary randomly in the sense that logAi,0=logA+ei, where