Educational planning models: problems of initial values

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UNITED NATIONS

AFRICAN INSTITUTE FOR ECONOMIO DEVE10PMENT AND PLANNING

IDEP/ET/LXXV!!I/2083

D A KA R.

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EDUCATIONAL PLANNING MODELS: PROBLEMS OF INITIAL VALUES.

by

Mr. B.K. LODH.

JUNE 1968 .• •

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IDEP/ET/LXXVIII/2083 Page 1.

Educational Planning Modela: Problems of initial value

In the discussions of the Tinbergen-Bos type of modela 1/we assumed the following important aspects of the relationship of education to economiv growth: (a) the l~bour force with seoondary and higher levels of education are related to income where labour force is used in the stock sense and

includes the new-corners a13 additions. to the· stock; · (b) the· number

·o:r

student>: in the 2nd and the higher education levels are related to the number of

tea.chers.in terms of flows· whereas the teachers are included in the stock of the higher level education, and ( c) time period o:f.. the educational level

···f-or· completTon in each leval, 2nd and higher is treated to be equal to 6

. years wi th the a.ssumption of primary e.ducational level stoak· of manpowor

--to·b;-~o bottleneck in the system. The :tormU.i,ation then proceeds to gi~re -~~-.

numerical .values ta the coefficients of the -system and···to··-fitm-·oüt the time -^-·--···

- ---·-·paths of the variables, given specifie rates of gro:wth

e>(

i~come. èonse-

quently i t was found that llD:~~r __ ·èff~:r.ent .. rates of grawth--the initial vah ws

.. ·-.. ^{-·· .}

have _ _ _ _

^to.be different which suggest that a~country witl:).

a

given set of initial va.lu.es can orÙy

acbiev_~ _-:_:a;_:::a.lle.c.if.ic

-rate

of , ·gr~-t~appr-è)jfri ate

to

-·.-. ---^---~ -. . ---

--

---~---~

____

^{...,__ ' . ;..' ' .}

that given set of initial values and ca~mot choose to have _.

è.

_! different growth ·ra"!i~ .... !l!lless it can change the initial values themselves. This note will elabora te on this p;rg]:>J.__em_. ... - __ ~ . ---

. -·······-- ··-··---··-- --· .. ~

We give the

fol~owing

table reproduced from the original article

~

showing the bala.nc.ed growth pa'ths of the educational ~;ystem for two growth rates.

1 üee Econometrie Models of Education- Sorne applications, OECD Paris 1965,

g}

Ibid, P• 1}.

;.·

.. , .. , .: ·i 1

. t .· . . . \

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ID :FtP /ET/I,,JCXVIII/ 208 3 Page 2.

Balanced growth of the _educational syetem for two:.growth ra tes: (A)

3 01b

and (B')

- 4 : 0 % ·p'~r - 6 yea ;s ·- -wh. er~ ..: 6

^..

;;~;s ----~~an

^one time unit.

,.

(P.roduction in ,biliions of $) ··-

·., . ___ .r!"

(Population in mill.ions ) · ^{- r ,; , __ , , : •. • . :..;_} -^{· ..}

Variables.

y

rr,2

-T_~· _--·

3

Case , -A: 30%

B: 4 0% _---

1 1 :ⁱ 2 ^' 3 ⁱ

i

' ^! ....

,

^..

Time :per;iods, t

' ' .. 0

i

^{2 1 3}

^lo

i

!

Voluine

of

:production

! '

i 1 t

1)0 . 169 :219 j100 : 140 ! 196 \27~ _

__!

! ! ^{t .}

100

Manpower '·Wi th secon-' dary education

\ 1 i

20.0 j 2,6.0 :33·7 43·7 20.0 28.0! 39. 2 :,54:_~_)

! ! ^{1 -} !

i

ⁱ

Manpower wi th _ tl:l.:i.r;d., ,,

.l • ' •• _ f,. ~-' .. '···

'level educatio!f .. '\

1 1 . 1

2.111::; 3_.19 4.14 !5.35 2.~⁷ 3.6015.02 7.03 1

~ t ~ : ~

Students in, secon-.

dary' sch~ol~ . ..

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Students in.third level' edu6ation ·

' . hl

Manpower >ii th secon- dary; education and ' · under 6 years employ- ment

Man:power with third level education

& .

0 6 under 6 years' employ- ~

ment

l ^{i :} 1

l

¹

1.27_l 1.65l 2.1:

~ 1.8~

2.54: 3·5! 1

1 l

^{!: \ .}

^{1 \ !}

8. 0

1 1

^{0. 5 ;1 3. 6}

ⁱ

^{7. 2 11 0. 1[ 14. 1[ 1}

9.

8 i

i ' l ⁱ 1

^{1 ___1}

1 . i 1 : \ 1

0.98!,1.27

~.66 ~

1.2911.80

2.54\

1 l ! '

Source: Econometrie models of Education, op.cit, p.13.

We shall observe from the above table that the initial values of the vari- ables at t=O are different for two growth rates A and B . .. This is because given the values of the coefficients one will solve 1

2 for t=O first by having the value of the coefficient::::x·

2 ⁼⁼ O. 2 which shows tha t 1

2 remains the same for both growth pa th A and B in the initial period. This value th en --~ ·· ' be taken;M

2 0 will be oalcul~ted and so on for other values by iterative procedure.

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Here the values of M2 • 0 will be different for A and B and so

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IDEP/ET/~XXVIII/2083 Page

3.

will ethers too. In the table we have underlined the initial values in the t1·ro cases to show that they are not equal. The policy implic_. ation o_. f this fact is -that a country which is on path A by the initial values cannat sT.Ti tch on to path 13 unless sorne time is allowed to pass as well as sorne

·coeffi'cients are allo"W"ed to be cbanged in time. The coefficients which can be chosen for such a purpose are teacher-student ratios in

th~ -~-~c- ~~d-l eve l

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and t he.third level education. Similarly with foreign aid but without changing the coeffici ents a transi ti on from pa th A to part B could b.e 0~fected. The method of analysis cons ists of wri ting down- the system of equations for a series of consecutive time periods and of finding out hoH many unknowns are available and how many are needed in order to make the

s~rs t em determinate.

On~-may come across anotber sort of prq~lems while dealing with the initial values. The initial values according to any growth :rate .. m9-y::oot be the same as the actual values of the country a.t the initial .period. This

• is because the initial values themselves are equilibrium values which

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^suggest a balanced_ growth ra te for the future ,for all the variables and

..

..

~hese values are the results of the estimation procedures for the cooffi- cL:mts,' To give an example~ let the following suggest two values at the ini t ial period.

Period t=O

Variables Equilitrium Actual values Difference of!

values (2) & (3) ¹

( 1 ) (2) (3) (41

y 100 100

-

i

L2 20.0 20.0

-

^!

L3 2.45 2.30

o.

15 ^j 1

e2 9·4 9.0 0.4

i

e3

o.

^{98 0.88 0. 10} 1

1

lVI 2 6.2 5·5 0.7

l

^{N 3 1 0.76 1 0.65 0. 11}

^l

1

.... 1 ..

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IDEP/ETjLxXviii/2083 Page 4•

Here the equilibr;.um values are the s.arne as the initial values of Table I _{,. '} of Case A with 30% growth rate of y over one time period i.e •

.6

years. The actual values are however different and are rnostly less than those of the equilibrium values. The lesson of this deficit is that the country in such a situation cannat be expected to grow at the rate of 30% , over 6 years i.e. path A,and will grow at a lower rate. Obviously to over come this deficit in column

(4),

One may have then taken by foreign aid and maintain the growth rate of

30%

from the start. Alternatively one can choose to change the coefficients and see wbether the path A can be accessible in period 2 or period 3 by taking the giv~n values of the variables in either of tbese two time periode for granted as given in Table 1 and choose the coefficients to vary. A sirnil~r procedure to eliminate surplus manpower can be adopted in which case the necessary changes should be in future enrolments i.e. e

2 and e

3 •

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For further elaborations on this methodology

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see Econometriê modela of Education, op. oit., Part 1

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