8.1 A Linear Convergence Equation
- {b, bse, bstan, bpval} =
linreg(x, y)
- estimates coefficients for a linear regression problem from data
x and y and calculates the ANOVA table
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Following Mankiw, Romer, and Weil (1992), Temple (1998) estimates a linear
conditional convergence regression, or
growth regression using data for 78
countries and covering the period 1960-1985, that is of the form:
where
is a normally distributed error term reflecting a
country-specific shock. The dependent variable is the log difference of
output per working-age person over the period. The first four independent
variables (
) are respectively the logarithm of average
shares of real equipment and real nonequipment investment in real output,
the logarithm of the average percentage of the working-age population that
is in secondary school for the period 1960-85, and the logarithm of the
annual average growth rate of the working-age population plus an exogenous
rate of technological progress and a depreciation rate, both of them being
constant across countries.
These variables reflect differences in factor
accumulation across countries and are expected to control for growth
differences in equilibrium. The fifth variable (
) is the logarithm of
output per working-age person at the beginning of the period, and is
expected to capture the Neoclassical convergence effect due to diminishing
returns to reproducible factors, that tends to favor poorer countries. The
last four exogenous variables (
) are dummies for
respectively sub-Saharan Africa, Latin America and the Caribbean, East Asia,
and the industrialized countries of the OECD plus Israel. These variables
allow us to control for differences in efficiency, variation of which has
been found to be essentially intercontinental.
To estimate such a multiple linear regression, we first read the data Temple (1998)
analyzed and that are stored in temple.dat
and define both
the independent and the dependent variables.
z=read("temple.dat")
x=z[,2:10]
y=z[,1]
Second, we load the stats
quantlib and use the following XploRe
code that computes the linear regression of y on x, and stores
the values of the estimated parameters as well as their respective standard
error,
-statistic, and
-value.
library("stats")
{b,bse,bstan,bpval}=linreg (x,y)
This quantlet also provides as an output the following ANOVA (ANalysis Of
VAriance) table that allows us to infer:
- that the model as it is
specified allows us to explain about 80% of the variance exhibited in the
annual average growth rate of income per working-age person over the period
- that the coefficient on the initial level of income per working-age
person (
) is significantly negative; that is, there is a tendency for
poor countries to grow faster on average than rich countries
- that the
social returns to equipment investment in developing countries are very high
(see also Temple; 1998)
- that the variable reflecting the
accumulation of human capital, in contrast to previous results, is not
significantly different from 0, etc.
A N O V A SS df MSS F-test P-value
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Regression 10.957 9 1.217 33.397 0.0000
Residuals 2.479 68 0.036
Total Variation 13.436 77 0.174
Multiple R = 0.90305
R^2 = 0.81550
Adjusted R^2 = 0.79108
Standard Error = 0.19093
PARAMETERS Beta SE StandB t-test P-value
_________________________________________________________________
b[ 0,]= 4.2059 0.7425 0.0000 5.664 0.0000
b[ 1,]= 0.2522 0.0354 0.5934 7.122 0.0000
b[ 2,]= 0.3448 0.0635 0.3966 5.426 0.0000
b[ 3,]= 0.0674 0.0533 0.1364 1.263 0.2108
b[ 4,]= -0.4411 0.2480 -0.1476 -1.778 0.0798
b[ 5,]= -0.3981 0.0543 -0.8488 -7.330 0.0000
b[ 6,]= -0.2038 0.0828 -0.2178 -2.461 0.0164
b[ 7,]= 0.0642 0.0810 0.0676 0.793 0.4303
b[ 8,]= 0.3910 0.1175 0.2078 3.328 0.0014
b[ 9,]= 0.1611 0.1177 0.1747 1.368 0.1757