Shall we take Solow seriously?? Empirics of growth Ania Nicińska Agnieszka Postępska Paweł Zaboklicki

Original & augmented models: Solow Assuming neoclassical production function steady state level of capital per capita is determined by saving and population growth rates Mankiw, Romer &Weil Yes – predicted directions of influence are consistent with the data… but…we need to add accumulation of human capital to get the right magnitudes but…we need to add accumulation of human capital to get the right magnitudes

Why? For any given rate of human capital accumulation higher saving or lower population growth leads to a higher level of income and thus a higher level of human capital. Omitting human capital accumulation causes bias if correlated with saving and population growth rates.

We will prove that… Including a proxy for human capital as an additional explanatory variable in the regression equation leads to magnitudes predicted by Solow. The augmented model accounts for about 80% of the cross country variation in income!!!!

So…after all Solow was right – he just forgot about some details… happens!!!! So…after all Solow was right – he just forgot about some details… happens!!!!

What about convergence??

We will prove that once accounting for the saving and population growth rate we observe convergence at roughly the rate that Solow predicted. We will prove that once accounting for the saving and population growth rate we observe convergence at roughly the rate that Solow predicted.

Data We used data from Barro and Lee data set. It contains different country set to the one used by authors so our results vary in magnitudes. However, the spirit remains unchanged!

Data cont. We have data from years for 121 countries divided into three groups: We have data from years for 121 countries divided into three groups: 1 – non-oil countries 2 – intermediate countries 3 – OECD countries The dataset includes real income, investments, population growth and proxy for human capital accumulation. The dataset includes real income, investments, population growth and proxy for human capital accumulation.

Basic model First, we will look at the results obtained from the basic model equation estimation, which takes the following form:

We want to investigate whether real income is higher in countries with higher saving rate and lower in countries with higher values of n+g+d. We want to investigate whether real income is higher in countries with higher saving rate and lower in countries with higher values of n+g+d.

We assume that g+d =0.05 is constant across countries, where g reflects the advancement of knowledge, which is not country specific. We assume that g+d =0.05 is constant across countries, where g reflects the advancement of knowledge, which is not country specific.

Results (OLS): gen lny=ln(gdp) gen lns=ln(inv) gen lnngd=ln(gpop +0.05) reg lny lns lnngd if group1==1 Source | SS df MS Number of obs = 566 Source | SS df MS Number of obs = F( 2, 563) = Model | Prob > F = Model | Prob > F = Residual | R-squared = Residual | R-squared = Adj R-squared = Total | Root MSE = Total | Root MSE = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lns | lns | lnngd | lnngd | _cons | _cons |

Results (panel): tis czas iis kraj xtreg lny lns lnngd if group1==1 Random-effects GLS regression Number of obs = 566 Group variable (i): kraj Number of groups = 97 R-sq: within = Obs per group: min = 2 between = avg = 5.8 between = avg = 5.8 overall = max = 6 overall = max = 6 Random effects u_i ~ Gaussian Wald chi2(2) = corr(u_i, X) = 0 (assumed) Prob > chi2 = lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] lns | lns | lnngd | lnngd | _cons | _cons | sigma_u | sigma_u | sigma_e | sigma_e | rho | (fraction of variance due to u_i) rho | (fraction of variance due to u_i)

Human capital the fraction of the eligible population (aged 12-17) enrolled in secondary school multiplied by the fraction of population at working-age that is of school age (15-17) for country j and time period i. assumed to be constant over time and equal to 0.05 for all countries

xtreg lny lns lnngd lnSCHOOL if group1== sigma_u | sigma_e | rho | (fraction of variance due Random-effects GLS regression Number of obs = 497 Group variable (i): kraj Number of groups = 86 R-sq: within = Obs per group: min = 1 between = avg = 5.8 overall = max = 6 Random effects u_i ~ Gaussian Wald chi2(3) = corr(u_i, X) = 0 (assumed) Prob > chi2 = lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] lns | lnngd | lnSCHOOL | _cons | to u_i) Introducing human capital

We reject Ho hypothesis and run fixed effect regression Hausman specification test ---- Coefficients ---- | Fixed Random lny | Effects Effects Difference lns | lnngd | lnSCHOOL | Test: Ho: difference in coefficients not systematic chi2( 3) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re) = Prob>chi2 = Hausman test

xtreg lny lns lnngd lnSCHOOL if group1==1, fe Fixed-effects (within) regression Number of obs = 497 Group variable (i): kraj Number of groups = 86 R-sq: within = Obs per group: min = 1 between = avg = 5.8 overall = max = 6 F(3,408) = corr(u_i, Xb) = Prob > F = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lns | lnngd | lnSCHOOL | _cons | sigma_u | sigma_e | rho | (fraction of variance due to u_i) F test that all u_i=0: F(85, 408) = Prob > F = Fixed effect regression

gen rhs1= lnngd-lns gen rhs2= lnSCHOOL-lns

xtreg lny rhs1 rhs2 if group1==1, fe Fixed-effects (within) regression Number of obs = 497 Group variable (i): kraj Number of groups = 86 R-sq: within = Obs per group: min = 1 between = avg = 5.8 overall = max = 6 F(2,409) = corr(u_i, Xb) = Prob > F = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] rhs1 | rhs2 | _cons | sigma_u | sigma_e | rho | (fraction of variance due to u_i) F test that all u_i=0: F(85, 409) = Prob > F = Restricted fixed effect regression

. reg lny lnY60 if group1==1 Source | SS df MS Number of obs = F( 1, 544) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lnY60 | _cons | Convergence

Controlling for saving and population growth. xtreg lny lnY60 lns lnngd if group1==1 Random-effects GLS regression Number of obs = 540 Random-effects GLS regression Number of obs = 540 Group variable (i): kraj Number of groups = 91 Group variable (i): kraj Number of groups = 91 R-sq: within = Obs per group: min = 5 R-sq: within = Obs per group: min = 5 between = avg = 5.9 between = avg = 5.9 overall = max = 6 overall = max = 6 Random effects u_i ~ Gaussian Wald chi2(3) = Random effects u_i ~ Gaussian Wald chi2(3) = corr(u_i, X) = 0 (assumed) Prob > chi2 = corr(u_i, X) = 0 (assumed) Prob > chi2 = lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] lny | Coef. Std. Err. z P>|z| [95% Conf. Interval] lnY60 | lnY60 | lns | lns | lnngd | lnngd | _cons | _cons | sigma_u | sigma_u | sigma_e | sigma_e | rho | (fraction of variance due to u_i) rho | (fraction of variance due to u_i)

Hausman test. xthausman Hausman specification test Hausman specification test ---- Coefficients Coefficients ---- | Fixed Random | Fixed Random lny | Effects Effects Difference lny | Effects Effects Difference lns | lns | lnngd | lnngd | Test: Ho: difference in coefficients not systematic Test: Ho: difference in coefficients not systematic chi2( 2) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re) chi2( 2) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re) = = Prob>chi2 = Prob>chi2 =

Controlling for saving and population growth. xtreg lny lnY60 lns lnngd if group1==1, fe Fixed-effects (within) regression Number of obs = 540 Fixed-effects (within) regression Number of obs = 540 Group variable (i): kraj Number of groups = 91 Group variable (i): kraj Number of groups = 91 R-sq: within = Obs per group: min = 5 R-sq: within = Obs per group: min = 5 between = avg = 5.9 between = avg = 5.9 overall = max = 6 overall = max = 6 F(2,447) = F(2,447) = corr(u_i, Xb) = Prob > F = corr(u_i, Xb) = Prob > F = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lnY60 | (dropped) lnY60 | (dropped) lns | lns | lnngd | lnngd | _cons | _cons | sigma_u | sigma_u | sigma_e | sigma_e | rho | (fraction of variance due to u_i) rho | (fraction of variance due to u_i) F test that all u_i=0: F(90, 447) = Prob > F = F test that all u_i=0: F(90, 447) = Prob > F =

Controlling for saving and population growth. reg lny lnY60 lns lnngd if group1==1 Source | SS df MS Number of obs = 540 Source | SS df MS Number of obs = F( 3, 536) = F( 3, 536) = Model | Prob > F = Model | Prob > F = Residual | R-squared = Residual | R-squared = Adj R-squared = Adj R-squared = Total | Root MSE = Total | Root MSE = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lnY60 | lnY60 | lns | lns | lnngd | lnngd | _cons | _cons |

Controlling for human capital. reg lny lnY60 lns lnngd lnSCHOOL if group1==1 Source | SS df MS Number of obs = 471 Source | SS df MS Number of obs = F( 4, 466) = F( 4, 466) = Model | Prob > F = Model | Prob > F = Residual | R-squared = Residual | R-squared = Adj R-squared = Adj R-squared = Total | Root MSE =.5022 Total | Root MSE = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lnY60 | lnY60 | lns | lns | lnngd | lnngd | lnSCHOOL | lnSCHOOL | _cons | _cons |

Restricted regression. reg lny lnY60 rhs1 rhs2 if group1==1 Source | SS df MS Number of obs = 471 Source | SS df MS Number of obs = F( 3, 467) = F( 3, 467) = Model | Prob > F = Model | Prob > F = Residual | R-squared = Residual | R-squared = Adj R-squared = Adj R-squared = Total | Root MSE =.5037 Total | Root MSE = lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lny | Coef. Std. Err. t P>|t| [95% Conf. Interval] lnY60 | lnY60 | rhs1 | rhs1 | rhs2 | rhs2 | _cons | _cons |

Conclusions: We proved that augmented Solow model describes growth well, both in directions of influence and magnitudes. We also showed that convergence do happen in reality once we compare similar countries in terms of population growth and saving rates.

Cook book procedure for a research project: Begin as soon as possible: data sets are ‘like a box of chocolates – you never know what you’re gonna get’ Be patient: ‘read me’ files can be tricky Attend STATA classes and learn programming or become a ‘copy/paste’ master Make friends – there is a huge difference between knowing how to do something & doing it.

So…& so it is – just like Solow said it should be… GOOD LUCK!!!!!!