Trade Openness, Education and Growth Parantap Basu 1 Durham University Keshab Bhattarai 2 University of Hull December 2008 Preliminary, Commets Welcome 1 Department of Economics and Finance, Durham University, 23/26 Old Elvet, Durham DH1 3HY, UK. e-mail: [email protected]. 2 Business School, University of Hull, HU6 7RX, Hull, UK. email: [email protected]
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Trade Openness, Education and Growth
Parantap Basu1
Durham University
Keshab Bhattarai2
University of Hull
December 2008
Preliminary, Commets Welcome
1Department of Economics and Finance, Durham University, 23/26 Old Elvet,
Durham DH1 3HY, UK. e-mail: [email protected] School, University of Hull, HU6 7RX, Hull, UK. email:
Tables 6 and 7 report the comparative dynamics of the steady state vari-
ables with respect to changes in�AH and �h respectively. A higher
�AH
can be interpreted as an improvement in the quality of the human capital
or cognitive skill as in Hanoushek and Woessman (2008). The model pre-
dicts that a higher�AH induces agents to investment more time in education
and less time in goods production because education has a higher marginal
return vis-a-vis goods production. As agents transfer resources away from
goods to education, the physical to human capital ratio falls (last column of
the Table 6), and growth rate rises. As long as the relative price of capital
(pk > 1) such a scarcity of physical capital raises the marginal product of
physical capital (due to diminishing returns to factor proportion) as seen in
15
Table 7: Comparative Dynamics with Respect to dh
Scenarios �h lGt lHt xt=yt mt=yt g kt=ht
1 0.015 0.488 0.512 0.3243 0.3244 0.030 1.435
2 0.016 0.488 0.513 0.3243 0.3236 0.030 1.437
3 0.016 0.487 0.513 0.3243 0.3228 0.029 1.439
4 0.017 0.487 0.513 0.3242 0.3220 0.029 1.441
5 0.017 0.487 0.513 0.3242 0.3211 0.028 1.443
6 0.018 0.487 0.513 0.3242 0.3203 0.028 1.445
7 0.018 0.486 0.514 0.3242 0.3195 0.027 1.447
8 0.019 0.486 0.514 0.3241 0.3186 0.027 1.449
9 0.019 0.486 0.514 0.3241 0.3178 0.026 1.451
10 0.020 0.486 0.514 0.3241 0.3170 0.026 1.453
(26). Since the home country has the option to augment physical capital by
�nancing it through current account, it will take advantage of it by raising
its export and import share. Thus the country becomes more open on the
trade front. The bottomline is that as a consequence of higher�AH , the home
country invests more in education, its growth rises via the human capital
equation (1) and its trade share also increases. The e¤ect of a lower rate of
depreciation in �h is analogous to a higher�AHas can be read from Table 7
although its e¤ect is small compared to�AH .
16
4 Short Run Dynamics
Until now we only analyzed the steady states of the model. Such a steady
state analysis can be motivated by cross country comparison of various long
run averages such as average growth, trade share, education share. The
underlying assumption here is that each country is in di¤erent long run steady
states and the research question is what drives this cross country dispersion.
We identify TFP in each sector as a major fundamental for the cross country
dispersion of growth, education share and trade share. However, such a
long run analysis cannot re�ect how a country can respond to shocks to its
fundamentals. Analysis of this kind of within-country response to shocks
necessitates a short run analysis.
The short run system is given by equations (29) to (36) as following(The
appendix shows the derivation of these equations).
kt+1ht+1
=pk (1� �k) ktht + AGt(
ktht)�l1��Gt � ct
ht� (1 + r�) kt
ht
(pk � 1) f1� �h + AHt(1� lGt)g(29)
1 = mt+1:�AGt+1
�kt+1ht+1
���1l1��Gt+1 + (1� �k)pk � 1� r�
pk � 1 (30)
AGtAht
:l��Gt :(ktht)� =
mt+1
�AGt+1Aht+1
:l��Gt+1:(kt+1ht+1
)� f1� �h + AHt+1(1� lGt+1)g+ AGt+1�kt+1ht+1
��l1��Gt+1
�(31)
where mt+1 is the discount factor given by
17
mt+1 =�(ct=ht)
(ct+1=ht+1)
1
(AHt+1(1� lGt+1) + 1� �h)(32)
Export and import share equations are given by:
xtyt
= [1 + r� � pk(1� �k)](kt=yt) (33)
+(pk � 1)(kt+1=yt+1)(AGt+1=AGt)�kt+1=ht+1kt=ht
��f1� �h + AHtlhtg:
�lGt+1lGt
�1��
mt
yt= pk
"kt+1yt+1
:AGt+1AGt
:
�kt+1=ht+1kt=ht
���lGt+1lGt
�1��f1� �h + AHtlhtg � (1� �k):
ktyt
#(34)
The ratio of current account to GDP is de�ned as:
catyt=xtyt� mt
yt(35)
The physical capital:output ratio is given by the production function (2)
as:
ktyt= A�1Gt (kt=ht)
1��l��1Gt (36)
The education share equation is given by:
Educt =(1� �)lHt
lGt(37)
Finally the gorwth rate of output is given by:
18
yt+1yt
=AGt+1AGt
:
�AGt+1AGt
� �kt+1=ht+1kt=ht
��fAHtlHt + 1� �hg:
�lGt+1lGt
�1��(38)
4.1 Impulse Responses
There are eight endoegenous variables namely, ct=ht , lGt; xt=yt, mt=yt,
Educt; CAt=yt; kt=ht; yt+1=yt and two exogenous variables, AGt and AHt:
Among these endogenous variables, only kt=ht is predetermined. The im-
pulse response analysis is based on loglinearlized deviations of these variables
from the steady state. Since this is a model of endgenous growth, the loglin-
earization is done around the balanced growth path described earlier. Figures
2 and 3 represent the impulse responses of various endogenous variables with
respect to shocks to goods TFP, AGt and education TFP, AHt respectively
given the baseline parameters as in Table 5.6 In response to goods TFP
shock, more time is devoted to goods production and this makes educational
investment fall. Growth rate of output rises monentarily as more goods are
produced but then it quickly turns negative due to paucity of investment in
human capital. On the current account front, the home country responds
to this shock by importing a lot more physical capital than exporting. This
makes the current account (cay) decline in the short run.7
In response to an educational TFP shock the impulse response behaves
di¤erently. Agents devote more time to schooling less time to production of6 A variant of the algorithm of Blanchard and Kahn (1980) is used to plot the impulse
responses. All the calculations are done using DYNARE developed by Julliard (1996).7In the impulse response chart, ck = ct=kt , kh = kt=ht; xy = xt=yt; my = mt=yt,
cay = cat=yt:
19
�nal goods. Growth rate of output rises due to transfer of resources from
goods to education sector and then it picks up as more schooling increases the
human capital base. Both export and import shares fall although the latter
falls more than the former making the current account rise. At a later stage,
the nation starts allocating more resources to the goods sector which makes
import and export share rise. The current account shows greater volatility
in response to this shock.
Note the contrast between long run and short run e¤ects of AG: First, In
the long run scenario, a change in AG has neutral e¤ects on growth, education
and trade shares while this is not the case in the short run. A shock to goods
sector productivity has important e¤ects on time allocation to schooling and
hence growth and openness.
Second, the short run response of shocks to cognitive skill is remarkably
di¤erent from what we see in the long run. While in the long run, a higher
AH results in a higher trade share, a temporary positive shock to AH makes
the home country cut back in exports and imports to allow for growth in the
education sector. 8
8The short run correlation between trade share and education is negative while cross
country data suggets that it is positive. Note that the cross country correlations referes to
the long run comparision of countries which di¤er in terms of long run average TFP. This
basically means between-country variation in trade shares and education shares. The
short run analysis can be interpreted as within-country response of a transitory shock to
productivity.
20
5 10 15
0123
x 103 ck
10 20 30 400
0.01
0.02kh
10 20 30 402
0
2x 103 lg
10 20 30 402
0
2x 10
3 lh
10 20 30 401
0
1x 10
3 g
10 20 30 405
0
5x 10
3 educ
10 20 30 405
0
5x 103 xy
10 20 30 400.02
0
0.02my
10 20 30 400.02
0
0.02cay
Impulse Response to AG Shock
10 20 30
0.01
0
0.010.02
ck
10 20 30 400.2
0.1
0kh
10 20 30 400.1
0.05
0lg
10 20 30 400
0.05
0.1lh
10 20 30 400
0.01
0.02g
10 20 30 400
0.1
0.2educ
10 20 30 400.05
0
0.05xy
10 20 30 400.2
0
0.2my
10 20 30 400.2
0
0.2cay
Figure 3: Impulse Response to AH Shock
Since there are only two shocks, a natural query arises which one of these
account for the brunt of variation in the endogenous variables. The vari-
ance decompositions of variables are reported below to answer this. The
21
TFP shocks to education explains almost 100% of the variation. This high-
lights the importance of the education sector productivity as a fundamental
determinant of the covariation between openness, growth and education.
Table 8: Variance Decomposition (in percent)
Variable TFP shock to goods, �Gt TFP shock in human capital, �Ht
ck 0.59 99.41
kh 0.76 99.24
lh 0.01 99.99
g 0.28 99.72
lg 0.01 99.99
Educ 0.01 99.99
xy 0.92 99.08
my 0.88 99.12
cay 0.87 99.13
5 Conclusion
While a wave of literature exists analyzing the relationship between trade
openness and growth as well as growth and education, hardly any e¤orts
have been made to understand these variables in an integrated growth model.
The motivation for this study comes from cross-country evidence that trade
openness and educational spending positively covary. We construct an open
economy endogenous growth model in the tradition of Lucas (1988). The time
22
allocation between goods production and schooling is an essential ingredient
of human capital growth. Our model identi�es the productivity of human
capital as a crucial fundamental causing this comovement between education
and trade openness. This fundamental can be interpreted as cognitive skill
along the lines of a recent literature which pinpoints cognitive skill as a critical
determinant of growth. While cognitive skill is an exogenous technology
variable in our model, future research can delve deeper into the underlying
reasons for the cross country di¤erences in cognitive skills.
References
[1] Barro R. J.(1991) Economic Growth in Cross Section of Countries, Quar-
terly Journal of Economics, May, 407-433.
[2] Basu P and A Guariglia (2008) Does low education delay structural