28 A.I. Gershberg, T. Schuermann Economics of Education Review 20 2001 27–40
and for analysts is whether it is possible to control for unobservables and for the relevant behavioral incentives
in analysis of school policies.” He goes on to list instru- mental variable approaches as among the most promising
and calls for more research in this area. This study helps to answer that call see also Akerhielm, 1995.
We therefore model and estimate a welfare function that reveals the efficiency–equity trade-off resulting from
the allocation of primary and secondary school expendi- tures by the Federal Government in Mexico. In doing so,
we quantify the trade-off with respect to the educational outcomes observed in the 31 states, and we develop a
methodology that considers the simultaneous determi- nation of educational expenditures and outcomes. In
addition, we explicitly account for the correlation between expenditure and average student endowments in
the schooling production function.
In particular, we analyze the Federal Government’s allocations to states, and we explore two criteria often
considered relevant in the decision-making process: 1 the equity–efficiency trade-off and 2 different treatment
of states based on their socio-economic and political characteristics. The underlying structural welfare relation
cannot be estimated directly because welfare is not observed; however, our analysis derives expressions in
terms of behavioral input and output variables in order to unveil critical parameters of the welfare function.
2
This is important because official policy statements from the Government never reveal such parameters
3
and, while qualitative analysts such as Morales-Go´mez and
Torres 1990 have shown a keen acumen in discerning such parameters, such political analyses need sound
quantitative studies to support them in the policy arena. In short, while other Latin American countries e.g.
Chile have made advances in using formula grants to allocate educational resources transparently to sub-
national jurisdictions, Mexico has not. Our analysis shows that the Mexican allocation pattern does not obvi-
ously incorporate rational or effective allocation patterns.
We follow a model developed by Behrman and Craig 1987 and Craig 1987 in which a government with
central authority allocates fixed total resources in a sector among the various localities under its control. In order
to control for endogenously determined production of the public service, in their case crime prevention, Behrman
and Craig 1987 use an instrumental variable approach whereas Craig 1987 uses 3SLS to estimate the whole
public service expenditure–production system. In con- trast to Behrman and Craig 1987, our model involves
2
This concise description of our objectives is due to an anonymous referee.
3
See for instance Partido Revolucionario Institucional 1976 and Secretaria de Educacion Publica 1989 for official
policy statements relevant to the two time periods studied.
the simultaneous determination of two public service sectors, education and roads, which will allow for vari-
ous different solutions to the endogeneity of production problem. Specifically, while it is straightforward to
address the simultaneous determination of educational expenditures and outcomes, this is only possible if, in
the schooling production function, average student endowments are not correlated with educational expendi-
tures. Since we cannot reasonably make this assumption, we must use expenditures from another public service,
such as roads, to serve as an instrument for educational expenditure. This joint modeling is important and we
provide for a straightforward and easily replicable sol- ution. We thus hope to help fill the gap highlighted in
Behrman 1996 p. 348 by providing a useful “statisti- cal procedure to control for choices in the presence of
unobserved variables.”
We hypothesize that this central government allocates resources in the education sector as if to maximize a
social welfare function, considering public service out- comes as a function of inputs.
4
The model yields the distributional concerns vis-a`-vis localities under its
control of the central government implicit in the observed choice of outcome allocation.
We test the model on Mexican state-level data from 1980 and 1990.
5
We also provide an empirical explo- ration of several phenomena widely analyzed by political
scientists in a more qualitative manner, such as the influence of voting behavior and political opposition on
federal allocations.
6
2. A model of Mexican literacy and schooling
Education in Mexico has traditionally been a centrally financed public good. The Federal Government is
responsible for approximately 80 of total expenditure
4
In using this ‘as if’ statement we follow a long tradition in political economics, reviewed excellently in Inman 1987.
5
Mexico is a federation of 31 states and the Federal District DF. Our study deals strictly with the states, largely because
the DF has a different and complex institutional education struc- ture.
6
For instance, Morales-Go´mez and Torres 1990 p. 51 assert: “Educational financing in general has been used to
counteract radical trends emerging from the political conflict permeating society. In this sense, educational policies and pro-
grams are used as powerful tools for the political cooptation of leaders, and to eliminate sources of dissatisfaction and conflict
in certain social sectors.” These same authors state p. 173 that: “although education is expected to produce human capital, in
practice it is designed to produce political capital for the [Mex- ican] State and the elites.” See also Dresser 1994.
29 A.I. Gershberg, T. Schuermann Economics of Education Review 20 2001 27–40
in the sector.
7
In 1978, the Ministry of Education Secretarı´a de Educacio´n Pu´blica; SEP instituted a
deconcentration program and established federal, state- level delegations in each state to handle the duties of
service provision as well as sub-state resource distri- bution and budgeting. SEP has continued to allocate
funds centrally, deciding the strategy with which to meet educational demand nationally. Hiring and distribution
of personnel also continued until 1992 as a function car- ried out in a highly centralized manner through both
SEP’s own decisions and those made through negotiation with the teacher’s union, which is in turn highly cen-
tralized.
In May of 1992 the Federal Government, together with all 31 states, signed a major accord supposedly decentral-
izing responsibility for educational services to the states. Called the Agreement for the Modernization of Basic
Education, this transfers all federal educational infra- structure as well as teachers and administrative personnel
to the states. Most of the financing, however, will con- tinue to have a federal source. Funds will be transferred
annually to the states in much the same manner they had previously been transferred to the federal delegations.
The states will then have considerable freedom to use those funds, and one imagines that the Federal Govern-
ment will not be able to hold them as accountable as it did its own delegations. This point immediately begs the
following question about educational service provision in the decade preceding the agreement: How has the Fed-
eral Government performed as a centralized provider of education? Have federal allocation patterns, for instance,
exhibited an attempt to fulfil the functional responsibility of Federal Government, outlined in Peterson 1995, to
redistribute educational outcomes from relatively well- performing states to relatively poor performing states?
What are the other determinants of federal educational expenditures? These questions provide the motivation of
our study.
Perhaps the most consequential point for this study is that while the Federal Government must respond to
7
We have used direct federal spending as our expenditure data in order to isolate the effect of that expenditure over which
the federal government clearly has direct control. In fact, doing so is not unreasonable, even given the model’s assumption that
allocation be centralized. State school systems where they existed during the period studied were entirely separate from
the federal system. Funds for the two were unmixed. We should note here that there is, thus, a potential effect on central allo-
cation from the state expenditures on their own separate sys- tems. As Steven Craig pointed out to us, it may be possible to
incorporate this effect by including it either in the production function or as a state characteristic. However, the data necessary
for doing so are not currently available, and the process could potentially cloud the results we wish to obtain. We have, there-
fore, used only direct federal expenditure.
budget requests from states as well as to basic salary needs for teachers and administrative personnel in each
state, SEP has considerable discretionary leeway in the way in which it allocates resources to states. In addition,
priorities are almost surely set in part at a level higher than SEP, by the Mexican president himself. These pri-
orities would address both development and political needs as perceived by the Institutional Revolutionary
Party PRI, the ruling party.
8
This study gives some indication of how the Federal Government has chosen to
pursue its policies. The central government maximizes a social welfare
function that considers the outputs in each state from the two public sectors: schooling and roads.
9
This welfare function is additively separable and linear in the two sec-
tors:
W5US;N1VR;M 1
and is maximized subject to the following budget con- straints
G
S
O
ns i51
E
S i
N
i
G
R
O
ns i51
E
R i
M
i
, 2
where S is the vector of per capita state outputs from schooling literacy; R is the vector of per capita state
outputs from roads miles of roads;
10
N is the vector of state school-age populations; M is the vector of state
total population; G
S
and G
R
are the total national expen- diture in education and roads, respectively, for the time
period; ns is the number of states in Mexico; E
S i
is the per school age capita educational expenditure and E
R i
the per capita road expenditure in each state; N
i
is the state school-age population, and M
i
is the state total
8
See Latapı´ 1982 p. 88 for a discussion of the lack of coherence in the Government’s rationales for educational
resource allocation.
9
We thank Tony Smith for noting that, if it seems unreason- able or counter-intuitive to conceive of the government maxi-
mizing a social welfare function, the problem may be re-written as a government maximizing its own utility function. The
results would not change. Thus, the analysis yields information on the government’s preferences that is not otherwise observ-
able.
10
As we shall see in Section 3, the inclusion of roads as a second sector is motivated by the necessity of finding a good
instrument for the estimation of the schooling expenditure equ- ation. We may use another public service, such as the provision
of drinking water, instead of roads, without losing the flavor of the model. For the sake of clarity, we wish to emphasize that
our concern in this study is to explore the efficiency–equity trade-off and other determinants of expenditures inherent in the
federal education allocation to states. We are not concerned with the determinants of federal road allocations. We will
include roads formally in the model merely to extract a clear instrument.
30 A.I. Gershberg, T. Schuermann Economics of Education Review 20 2001 27–40
population.
11
The notion behind the different population variables is simply that roads are consumed by everyone,
whereas education generally only by those of appropri- ate age. While the Government implicitly wishes to max-
imize schooling and road output S and R, it has no direct control over them. The Government does, how-
ever, control spending, and it thus impacts outcomes indirectly through production. The schooling and road
production functions are assumed to have partial log-lin- ear form:
ln S
i
5d
S
ln E
S i
1hz
S i
1e
S
i
3 ln R
i
5d
R
ln E
R i
1gz
R i
1e
R
i
, where
d
j
is a production function elasticity for sector j, e
S
i
and e
R
i
are sector-specific error terms which may include unobservables, and h and g can be any functional
forms as long as it exhibits positive marginal pro- ductivities over the input vector z, albeit with dimin-
ishing returns.
12
A more detailed discussion of the pro- duction behavior can be found in Section 3 where we
assume the production functions to be log-linear. Following Craig 1987 and Behrman and Craig
1987, we specify a Kohm–Pollak welfare function for Eq. 1 and note that doing so “allows a test of whether
the [government] is concerned only with aggregate out- put, or whether there is some distributional concern over
absolute differences” in outcomes from the service being provided Craig, 1987, p. 300. In our analysis, we test
whether the Federal Government has distributional con- cerns for outcomes from schooling expressed in the way
it allocates educational funding to states.
13
Outputs are, after all, what planners should be interested in, and the
model specified shows how the distribution of outputs by the central authority could occur in the opposite direc-
tion from inputs because of the inherent characteristics of the states’ residents involved.
The Kohm–Pollak welfare function tests for two kinds of distributional concern: the first, inequality aversion,
reveals the extent to which the Federal Government
11
Note that this assumes that national amounts of educational and road expenditures are fixed in the time period, and that
the central government simply allocates these resources among states according to the social welfare function.
12
The CES production function, with suitable parameter restrictions, is one such example.
13
We do not wish to imply, here or elsewhere in the study, that the Federal Government is a single entity with clearly
definable goals. Of course, the process of allocating resources across states is a contentious fiscal and political process that
results from complex interplay between the President, the Fin- ance Ministry, the Ministry of Education and each state gov-
ernor. No matter what the intention of the Government, how- ever, this approach has the capacity to identify key policy
parameters.
attempts to trade efficiency for equity; the second, unequal concern, reveals the extent to which particular
state characteristics influence the Federal Government’s allocation of resources based upon the resulting out-
come it expects from those resources.
14
It takes the fol- lowing form:
W5 1
q
S
ln
F
O
n i51
a
i
N
i
N e
q
S
S
i
G
1 1
q
R
ln
F
O
m i51
a
i
M
i
M e
q
R
R
i
G
4 where
N5
O
ns i51
a
i
N
i
, M5
O
ns i51
a
i
M
i
. 5
The parameter q
j
is the measure of inequality aversion which grows stronger the smaller, or more negative, the
value for the parameter for sector j, and the a
i
are the parameters of unequal concern.
15
Specifically, qP2 `,0 such that as q approaches zero, the government has
no inequality concern and is purely concerned with efficiency the utilitarian outcome; thus the government
simply sums productivity over weighted individual out- comes. Likewise, as q approaches negative infinity, the
government is purely concerned with equity the Rawl- sian outcome.
16
The government maximizes Eq. 4 subject to Eqs. 2 and 3 by choice of E
S i
and E
R i
. Without loss of gener- ality, we will exhibit the constrained optimization prob-
lem for the schooling sector only. We start with the first- order condition:
∂ W
∂ S
i
∂ S
i
∂ E
S i
2lN
i
0, 6
where l is the Lagrange multiplier associated with the
sectoral budget constraint. In the case of the Kohm–Pol- lak welfare function and the partially log-linear pro-
duction function, the first-order conditions take on the following form:
14
Geometrically, inequality aversion is reflected by the degree of curvature concavity of the welfare surface: the more
sharply curved, the higher the degree of inequality aversion. Unequal concern is reflected by the degree of asymmetry of the
welfare surface about the 45 °
ray from the origin.
15
Note that the a
i
are the same up to a factor of pro- portionality for the two sectors; a set of state characteristics
should affect each sector the same.
16
For a proof of this proposition, please see Appendix A. Behrman and Craig 1987 found the Kohm–Pollak welfare
function to dominate empirically a generalized CES form, while Behrman and Birdsall 1988 found CES to weakly dominate
Kohm–Pollak. Considering that the Kohm–Pollak welfare func- tion, through the parameter q, already allows for a broad range
of functional shapes see Appendix A and footnote 14, we choose instead to focus our modeling efforts on proper instru-
mentation.
31 A.I. Gershberg, T. Schuermann Economics of Education Review 20 2001 27–40
[K
S
a
i
N
i
e
q
S
S
i
]
F
d
S
S
i
E
S i
G
5lN
i
. 7
where K
S
5
F
O
j
a
j
N
j
e
q
S
S
j
G
− 1
. 8
Canceling N
i
and M
i
on both sides and taking logs we get:
ln [K
S
a
i
e
q
S
S
i
]1ln
F
d
S
S
i
E
S i
G
5ln l. 9
Rearranging terms yields an equation that can be read- ily estimated:
ln
S
E
S i
S
i
D
5ln K
S
2ln l1ln d
S
1ln a
i
1q
S
S
i
. 10
The first three terms make up the intercept in the regression equation and are therefore not individually
identifiable. Collecting all unobservables in Eq. 10 into a con-
stant, we can rewrite the expenditure equation as ln
S
E
S i
S
i
D
5b 1ln a
i
1q
S
S
i
, 11
where the unequal concern parameter a
i
depends in log- arithmic form on the state characteristics and some unob-
servables:
17
ln a
i
5
O
p l51
b
l
ln x
li
1v
i
. 12
Those state characteristics should affect each sector the same up to a factor of proportionality. In fact, we shall
make use of this assumption later when trying to find an instrument for expenditure in the schooling production
function.
The expenditure equation is now stochastic:
18
17
Note that the unobservables are assumed to be independent of instruments used for S in Eq. 11.
18
Note that this is not the completed solution to the maximiz- ation problem. Rather, we assume the government acts in the
manner described as if to maximize the described social wel- fare function and test for the factors that influence its action
within the given framework. We can do so because both S and E are observable, as are the variables of unequal concern. In
this sense, the equation should not be construed as a cost func- tion. In fact it can be rewritten as
ln E
S i
5b 1
O
p l51
b
1
ln x
li
1q
S
S
i
1ln S
i
1v
i
which is unambiguously an expenditure equation.
ln
S
E
S i
S
i
D
5b 1
O
p l51
b
l
ln x
li
1q
S
S
i
1v
i
. 13
This is the form of the equation we finally wish to esti- mate to obtain values for q and
a
i
.
3. Stochastic structure and estimation problems
