8.1 A Linear Convergence Equation


{b, bse, bstan, bpval} = 16165 linreg (x, y)
estimates coefficients for a linear regression problem from data x and y and calculates the ANOVA table

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:

$\displaystyle Y_{i}=\beta _{0}+\beta _{1}X_{i1}+\beta _{2}X_{i2}+...+\beta
_{9}X_{i9}+\epsilon _{i}$

where $ \epsilon _{i}$ 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 ( $ X_{1},...,X_{4}$) 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 ($ X_{5}$) 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 ( $ X_{6},...,X_{9}$) 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, $ t$-statistic, and $ p$-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:

A  N  O  V  A               SS     df    MSS     F-test   P-value
_________________________________________________________________
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