Shall we take Solow seriously??

1
Shall we take Solow seriously??

• Empirics of growth
• Ania Nicinska
• Agnieszka Postepska
• Pawel Zaboklicki

2
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
• butwe need to add accumulation of human capital
  to get the right magnitudes

3
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.

4
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!!!!

5

• Soafter all Solow was right he just forgot
  about some details happens!!!!

6
What about convergence??
7

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

8
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!

9
Data cont.

• We have data from years 1960-1985 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.

10
Basic model

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

11

• We want to investigate whether real income is
  higher in countries with higher saving rate and
  lower in countries with higher values of ngd.

12

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

13
Results (OLS)

• gen lnyln(gdp)
• gen lnsln(inv)
• gen lnngdln(gpop 0.05)
• reg lny lns lnngd if group11
• Source SS df MS
  Number of obs 566
• -------------------------------------------
  F( 2, 563) 333.72
• Model 324.412641 2 162.20632
  Prob gt F 0.0000
• Residual 273.650411 563 .486057568
  R-squared 0.5424
• -------------------------------------------
  Adj R-squared 0.5408
• Total 598.063052 565 1.05851868
  Root MSE .69718
• --------------------------------------------------
  ----------------------------
• lny Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• lns .7575753 .0404936 18.71
  0.000 .6780384 .8371122
• lnngd -2.186215 .1768619 -12.36
  0.000 -2.533605 -1.838825
• _cons 3.342269 .4937159 6.77
  0.000 2.372519 4.312019

14
Results (panel)

• tis czas
• iis kraj
• xtreg lny lns lnngd if group11
• Random-effects GLS regression
  Number of obs 566
• Group variable (i) kraj
  Number of groups 97
• R-sq within 0.0849
  Obs per group min 2
• between 0.6024
  avg 5.8
• overall 0.5421
  max 6
• Random effects u_i Gaussian
  Wald chi2(2) 111.65
• corr(u_i, X) 0 (assumed)
  Prob gt chi2 0.0000
• --------------------------------------------------
  ----------------------------
• lny Coef. Std. Err. z
  Pgtz 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• lns .3205264 .0401647 7.98
  0.000 .2418049 .3992478

15
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
16
(No Transcript)
17
Introducing human capital
xtreg lny lns lnngd lnSCHOOL if
group11 4.17918 5.703551 ------------------
--------------------------------------------------
--------- sigma_u .48950053 sigma_e
.23470675 rho .81307219
(fraction of variance due Random-effects GLS
regression Number of obs
497 Group variable (i) kraj
Number of groups 86 R-sq
within 0.3090 Obs per
group min 1 between 0.7432
avg
5.8 overall 0.7029
max 6 Random effects
u_i Gaussian Wald chi2(3)
363.77 corr(u_i, X) 0 (assumed)
Prob gt chi2
0.0000 ------------------------------------------
------------------------------------ lny
Coef. Std. Err. z Pgtz 95
Conf. Interval ---------------------------------
--------------------------------------------
lns .3002022 .0389558 7.71 0.000
.2238503 .3765542 lnngd -1.038666
.1443974 -7.19 0.000 -1.32168
-.7556523 lnSCHOOL .2845598 .021147
13.46 0.000 .2431125 .3260071
_cons 4.941366 .3888772 12.71 0.000 to
u_i) ---------------------------------------------
--------------------------------- .
18
Hausman test
Hausman specification test ----
Coefficients ---- Fixed
Random lny Effects Effects
Difference ------------------------------------
------------------ lns .2198654
.3002022 -.0803368 lnngd
-.8024757 -1.038666 .2361903
lnSCHOOL .2400482 .2845598
-.0445116 Test Ho difference in
coefficients not systematic
chi2( 3) (b-B)'S(-1)(b-B), S (S_fe -
S_re) 165.07
Probgtchi2 0.0000
We reject Ho hypothesis and run fixed effect
regression
19
Fixed effect regression
xtreg lny lns lnngd lnSCHOOL if group11,
fe Fixed-effects (within) regression
Number of obs 497 Group variable
(i) kraj Number of groups
86 R-sq within 0.3099
Obs per group min 1
between 0.7441
avg 5.8 overall 0.7026
max
6
F(3,408) 61.07 corr(u_i, Xb)
0.5936 Prob gt F
0.0000 -------------------------------------
-----------------------------------------
lny Coef. Std. Err. t Pgtt
95 Conf. Interval ----------------------------
-------------------------------------------------
lns .2198654 .0420508 5.23
0.000 .1372021 .3025288 lnngd
-.8024757 .1530299 -5.24 0.000
-1.103301 -.5016503 lnSCHOOL .2400482
.0222506 10.79 0.000 .1963082
.2837883 _cons 5.511256 .4062469
13.57 0.000 4.712658 6.309854 -----------
-------------------------------------------------
----------------- sigma_u .6270438
sigma_e .23470675 rho .87711176
(fraction of variance due to u_i) ----------------
--------------------------------------------------
------------ F test that all u_i0 F(85,
408) 27.03 Prob gt F 0.0000
20
gen rhs1 lnngd-lns gen rhs2 lnSCHOOL-lns
21
Restricted fixed effect regression
xtreg lny rhs1 rhs2 if group11,
fe Fixed-effects (within) regression
Number of obs 497 Group variable
(i) kraj Number of groups
86 R-sq within 0.3023
Obs per group min 1
between 0.7273
avg 5.8 overall 0.6850
max
6
F(2,409) 88.61 corr(u_i, Xb)
0.5756 Prob gt F
0.0000 -------------------------------------
-----------------------------------------
lny Coef. Std. Err. t Pgtt
95 Conf. Interval ----------------------------
-------------------------------------------------
rhs1 -.4935334 .0456002 -10.82
0.000 -.5831734 -.4038934 rhs2
.2524585 .021553 11.71 0.000 .2100899
.294827 _cons 6.339631 .1076709
58.88 0.000 6.127974
6.551289 ----------------------------------------
-------------------------------------
sigma_u .63733151 sigma_e .23570005
rho .87968598 (fraction of variance
due to u_i) --------------------------------------
---------------------------------------- F test
that all u_i0 F(85, 409) 28.91
Prob gt F 0.0000
22
Convergence
. reg lny lnY60 if group11
Source SS df MS
Number of obs 546 -------------------
------------------------ F( 1, 544)
522.06 Model 294.766441 1
294.766441 Prob gt F 0.0000
Residual 307.152329 544 .564618253
R-squared 0.4897
-------------------------------------------
Adj R-squared 0.4888 Total
601.918771 545 1.10443811 Root MSE
.75141 -----------------------
--------------------------------------------------
----- lny Coef. Std. Err.
t Pgtt 95 Conf. Interval
-------------------------------------------------
---------------------------- lnY60
.0003215 .0000141 22.85 0.000
.0002938 .0003491 _cons
6.902612 .0449259 153.64 0.000 6.814363
6.990862 --------------------------------
----------------------------------------------
23
Controlling for saving and population growth

• . xtreg lny lnY60 lns lnngd if group11
• Random-effects GLS regression
  Number of obs 540
• Group variable (i) kraj
  Number of groups 91
• R-sq within 0.0562
  Obs per group min 5
• between 0.6457
  avg 5.9
• overall 0.6097
  max 6
• Random effects u_i Gaussian
  Wald chi2(3) 206.77
• corr(u_i, X) 0 (assumed)
  Prob gt chi2 0.0000
• --------------------------------------------
  ----------------------------------
• lny Coef. Std. Err.
  z Pgtz 95 Conf. Interval
• -------------------------------------------
  ----------------------------------
• lnY60 .0002534 .0000278
  9.10 0.000 .0001988 .0003079
• lns .2594275 .0403126
  6.44 0.000 .1804161 .3384388
• lnngd -.7506613 .1733739
  -4.33 0.000 -1.090468 -.4108547
• _cons 5.574069 .4559533
  12.23 0.000 4.680417 6.467721

24
Hausman test

• . xthausman
• Hausman specification test
• ---- Coefficients ----
• Fixed Random
• lny Effects Effects
  Difference
• -------------------------------------------
  -----------
• lns .1734279 .2594275
  -.0859996
• lnngd -.6418418 -.7506613
  .1088195
• Test Ho difference in coefficients
  not systematic
• chi2( 2)
  (b-B)'S(-1)(b-B), S (S_fe - S_re)
• 31.07
• Probgtchi2 0.0000

25
Controlling for saving and population growth

• . xtreg lny lnY60 lns lnngd if group11, fe
• Fixed-effects (within) regression
  Number of obs 540
• Group variable (i) kraj
  Number of groups 91
• R-sq within 0.0571
  Obs per group min 5
• between 0.6378
  avg 5.9
• overall 0.5657
  max 6
• 
  F(2,447) 13.54
• corr(u_i, Xb) 0.6823
  Prob gt F 0.0000
• --------------------------------------------
  ----------------------------------
• lny Coef. Std. Err.
  t Pgtt 95 Conf. Interval
• -------------------------------------------
  ----------------------------------
• lnY60 (dropped)
• lns .1734279 .0432074
  4.01 0.000 .088513 .2583427
• lnngd -.6418418 .1774066
  -3.62 0.000 -.9904963 -.2931873
• _cons 6.26194 .471011
  13.29 0.000 5.336269 7.18761

26
Controlling for saving and population growth

• . reg lny lnY60 lns lnngd if group11
• Source SS df MS
  Number of obs 540
• -------------------------------------------
  F( 3, 536) 342.36
• Model 387.410632 3
  129.136877 Prob gt F 0.0000
• Residual 202.178054 536
  .377197862 R-squared 0.6571
• -------------------------------------------
  Adj R-squared 0.6552
• Total 589.588686 539
  1.09385656 Root MSE .61416
• --------------------------------------------
  ----------------------------------
• lny Coef. Std. Err.
  t Pgtt 95 Conf. Interval
• -------------------------------------------
  ----------------------------------
• lnY60 .0001856 .0000155
  11.95 0.000 .0001551 .0002161
• lns .6007277 .0406437
  14.78 0.000 .5208872 .6805683
• lnngd -1.204025 .2259398
  -5.33 0.000 -1.647861 -.7601891
• _cons 5.195703 .5954142
  8.73 0.000 4.026072 6.365335
• --------------------------------------------
  ----------------------------------

27
Controlling for human capital

• . reg lny lnY60 lns lnngd lnSCHOOL if group11
• Source SS df MS
  Number of obs 471
• -------------------------------------------
  F( 4, 466) 373.07
• Model 376.353388 4
  94.088347 Prob gt F 0.0000
• Residual 117.526225 466
  .252202199 R-squared 0.7620
• -------------------------------------------
  Adj R-squared 0.7600
• Total 493.879613 470
  1.05080769 Root MSE .5022
• --------------------------------------------
  ----------------------------------
• lny Coef. Std. Err.
  t Pgtt 95 Conf. Interval
• -------------------------------------------
  ----------------------------------
• lnY60 .0001264 .0000134
  9.46 0.000 .0001002 .0001527
• lns .3148332 .0456057
  6.90 0.000 .2252149 .4044514
• lnngd -1.093758 .2040205
  -5.36 0.000 -1.494672 -.6928435
• lnSCHOOL .3618771 .0245546
  14.74 0.000 .3136256 .4101285
• _cons 4.347212 .5360951
  8.11 0.000 3.293749 5.400675
• --------------------------------------------
  ----------------------------------

28
Restricted regression

• . reg lny lnY60 rhs1 rhs2 if group11
• Source SS df MS
  Number of obs 471
• -------------------------------------------
  F( 3, 467) 493.21
• Model 375.396246 3
  125.132082 Prob gt F 0.0000
• Residual 118.483367 467
  .253711707 R-squared 0.7601
• -------------------------------------------
  Adj R-squared 0.7586
• Total 493.879613 470
  1.05080769 Root MSE .5037
• --------------------------------------------
  ----------------------------------
• lny Coef. Std. Err.
  t Pgtt 95 Conf. Interval
• -------------------------------------------
  ----------------------------------
• lnY60 .0001386 .0000118
  11.72 0.000 .0001154 .0001619
• rhs1 -.7030645 .0375851
  -18.71 0.000 -.7769213 -.6292077
• rhs2 .36919 .0243385
  15.17 0.000 .3213636 .4170165
• _cons 5.374257 .0975428
  55.10 0.000 5.18258 5.565934
• --------------------------------------------
  ----------------------------------

29
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.

30
Cook book procedure for a research project

• Begin as soon as possible data sets are like a
  box of chocolates you never know what youre
  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.

31

• So so it is just like Solow said it should
  be
• GOOD LUCK!!!!!!