190 M. Binder Economics of Education Review 18 1999 183–199
being measured.
21
This result suggests that students’ enrollment decisions depend on current and expected
future economic activity. Although very few families are likely to have anticipated the 1982–83 crash, sluggish
growth for the rest of the 1980s was probably quite pre- dictable.
6.3. Efficiency rates
22
Economic indicators are poor predictors of efficiency rates at the primary level. The high adjusted R
2
results from a positive and precise trend variable. In their study
of primary education in Latin America, Wolff et al. 1994, 20–22 present anecdotal evidence that repetition
rates—which bear directly on efficiency rates—depend more on arbitrary school policies than on student
achievement. If school policies are not responsive to economic conditions, then efficiency rates will bear no
relation to the economy. This explanation does not hold at the secondary levels, where efficiency rates are quite
responsive to income and price effects: at the upper-sec- ondary level, the income elasticity is a striking 1.2, a
five per cent increase in GDP growth rates reduces efficiency by nearly nine per cent, and the model
explains 75 per cent of the variation in efficiency rates over time. The large elasticities and explanatory power
here contrast with the weaker performance for continu- ation rates at the upper-secondary level. It appears that
continuation to upper-secondary school is not well pre- dicted by economic conditions. But for the relatively
elite group of students that do continue, staying on and finishing within the expected course of study does
depend, to a large extent, on the economy.
6.4. Enrollment rates Primary enrollment rates are poorly predicted by econ-
omic conditions, although the income and price effects have the expected signs.
23
Secondary enrollment rates, however, are very responsive to the economy, with
income elasticities of close to 0.9 and a coefficient of 0.7 for the growth rate at the school-year end. Note that
these enrollment rates combine both the lower and upper-secondary levels. As with the primary and junior
vocational retention rates, the price effect is larger at the end of the school year. This is probably because the
21
In other models not reported here, GDP growth rates in the year following the school end had tiny and insignificant
effects for retention and efficiency rates.
22
Although efficiency rates contain responses to conditions over several years, my analysis considers only current economic
conditions. The results should be interpreted as the marginal effect of economic conditions on students who are close to
graduation.
23
See footnote 1.
World Bank data from which the enrollment series are drawn correspond more faithfully to the calendar year
than do the SEP data. In any case, the schooling indicators by and large
show positive income and negative price effects. Indi- cators that more closely reflect marginal decisions—such
as the decision to continue on to the next schooling level—tend to respond more strongly to economic con-
ditions. Vocational and more advanced students appear to be more responsive to price and income changes than
those in academic and lower-level programs, respect- ively. Finally, while primary school enrollment rates
appear to be insensitive to economic conditions, second- ary enrollment rates are among the most responsive of
all the schooling indicators.
What do these estimates tell us about how Mexico’s economy has affected schooling over the past 15 years?
The estimates suggest that income effects slightly domi- nate price effects. For example, a ten per cent increase
in the income level will raise the continuation rate from primary to lower-secondary by five per cent, or 4.3 per-
centage points. Taking the increase in five per cent growth rates over two years would reduce the continu-
ation rate by slightly more than three per cent, or 2.9 percentage points. Applied to the recent experience in
Mexico, the model predicts that in the 1994–95 school year during which the economy contracted by more than
six per cent, lower-secondary continuation rates would have fallen by two percentage points and the secondary
enrollment rate for both secondary levels would have remained unchanged from the previous year. Taking as
a counter factual what would have happened if the econ- omy had remained the same in 1995 as it was in 1994
instead of declining by 6.2 per cent, then lower-second- ary continuation rates instead would have fallen by one
percentage point and enrollment rates would have risen by one percentage point. The difference is not very great.
However, a long period of economic decline will inten- sify the backsliding. If, for example, the 1980s economy
had grown at half its average growth rate of the ten years leading up to the 1982 crash, then lower-secondary con-
tinuation rates would have reached 97 per cent by 1994, eight percentage points higher than the actual figure. Sec-
ondary enrollment rates would have reached 68 per cent by 1991, instead of the recorded 56 per cent. Since nega-
tive income effects tend to outweigh the positive price effects of economic contraction, the cumulative effects
of a stagnating and crisis prone economy are indeed dire.
7. State series
In this section I consider the marked variation among states to study first, whether the aggregate patterns exist
at the state level and second, what determines the uneven performance in schooling indicators among states.
191 M. Binder Economics of Education Review 18 1999 183–199
Tables 6 and 7 in Appendix A present summary statistics for schooling indicators and state-level characteristics,
respectively. States vary considerably in all schooling indicators, but the differences are particularly acute for
enrollment rates. For example, the upper-secondary enrollment rate varies from 15 per cent in the state of
Guanajuato to 56 per cent in Mexico City.
24
Other state characteristics are equally diverse. For example,
Mexico City had a per capita income nearly five times that of the poorest state of Oaxaca in 1988. In 1990, only
eight per cent of Nuevo Leon’s population was rural, compared to 61 per cent in Oaxaca; and per student
spending in Mexico City was more than three times the spending in Guanajuato.
In investigating income and price effects at the state level, I add measures of state economic performance to
the analysis to distinguish between national and local economic conditions. State-level GDP data are not avail-
able annually. I therefore use annual Gross State Rev- enues GSR as a proxy for state income Inegi, 1986.
25
GSR measures the total income accruing to a state government in a calendar year, including local taxes and
the receipt of federal funds. In a state cross-section, the correlation between GSR and state-level GDP in each of
the years for which both are available 1980, 1985 and 1988 was greater than 0.94. I begin with a fixed effects
model which measures the response of state-level schooling indicators to national and state-level price and
income effects:
logs
it
5 b 1
b
1
logGDP
t
1 b
2
DGDP
t BEGIN
1 b
3
DGDP
t END
1 b
3
TREND
t
1 g
1
logGSR
it
2 1
g
2
DGSR
it BEGIN
1 g
3
DGSR
it END
1 a
i
1 m
it
where the beta terms duplicate Eq. 1, GSR proxies the state-level income effect, the DGSR’s proxy the state-
level price effects at the beginning and end of the school year, respectively, and the g’s are coefficients. The
schooling indicator, s, is now subscripted by state i and
24
Enrollment rates were calculated by dividing total lower and upper-academic secondary matriculation by the number of
13—15 year-olds and 16–18 year-olds, respectively for each state in 1990. Because some matriculated students may be older
than expected based on normal progress through the schooling system, the rates are likely to be inflated. See footnote 1.
25
GSR figures were converted to constant 1980 pesos by using metropolitan price index data also available in the Anua-
rio Estadı´stico op. cit.. States were assigned the index pro- vided by the sample city within the state with an index. Seven
states had no city included in the sample: their indices were drawn from an average of their bordering states.
time t, and a
i
represents a time invariant state fixed effect.
Table 2 shows estimates of Eq. 2 for retention and continuation rates for the academic sequence.
26
The state schooling indicators display similar responses to the
aggregate data with respect to income and price effects measured by GDP and DGDP. The magnitudes are
similar to those reported in Table 1, except for dramatic changes in the continuation rates to upper-secondary
school. Compared to the national totals, the state analy- ses show a sign reversal for income, a drastic decline in
the negative price effect at the start of the school year, and an increase in the positive price effect at the school-
year end.
27
This instability in estimates reinforces the interpretation of the imprecise estimates in Table 1 that
continuation to the upper-secondary school is not con- sistently determined by current economic conditions.
The state time-series economic indicators are very small in magnitude and generally imprecisely measured:
the largest income elasticity is 0.03.
28
Moreover, in three of the five models reported in Table 2, the income and
price effects are exactly reversed. That is, for primary and upper-secondary retention and lower-secondary con-
tinuation rates, higher state income has a negative effect and higher state economic growth has a positive effect,
holding national economic conditions constant. Suppose in a given year both national and state-level income lev-
els rise. In states with higher income levels, the overall income effect will be less. Similarly, the negative price
effect will be attenuated by a positive response at the state level. Given the small magnitudes of the state-level
effects, the overall income and price effects will remain with the expected signs, but richer states appear to exhi-
bit less elastic schooling indicators with respect to econ- omic conditions. We should expect that better-off states
would be less responsive to current changes in economic conditions, since fewer families are likely to face binding
liquidity constraints Becker and Tomes, 1986. In any case, these results alert us to the possibility that the
response of schooling indicators to economic conditions may vary with the affluence of the state.
To explore this possibility, I interact the economic indicators with the proportion of low-income workers in
each state in 1980 Pick et al., 1989.
29
Table 3 provides the results of fixed effects models that include these
26
Efficiency rates are omitted from this analysis because of strong evidence of serial auto-correlation see Table 1.
27
Decomposition analyses of these changes showed that they are due to a combination of the use of the state series and the
inclusion of the GSR variables.
28
These results also persisted in random effect specifications, not reported here, that controlled for population size.
29
This designation includes workers who earned less than 1081 pesos in 1980, or about US50. Results were similar using
interactions with the 1990 low-income figures.
192 M. Binder Economics of Education Review 18 1999 183–199
Table 2 Fixed effects analysis using state panel for school years 1976–77 to1990–91
1
Standard errors in parentheses Log retention rate
Log continuation rate Primary school
Lower-secondary Upper-secondary
To lower-secondary To upper-secondary
Log GDP 0.0391
0.0112 0.0448
0.0158 20.0629 0.0591
0.6362 0.0675
20.0509 0.2216 DGDP begin
20.0485 0.0134
20.0791 0.0188
20.3662 0.0704
20.4911 0.0804
20.0940 0.2640 DGDP end
20.0581 0.0119
20.0429 0.0167
20.1179
†
0.0629 20.4941
0.0713 0.5524
0.2342 Log gross state
20.0036 0.0017
0.0040
†
0.0024 20.0097 0.0091
20.0346 0.0104
0.0282 0.0342 revenue GSR
DGSR begin 0.0029
†
0.0017 20.0007 0.0024
0.0128
‡
0.0091 0.0266
0.0104 20.0610
†
0.0340 DGSR end
0.0015
†
0.0008 20.0005 0.0011
0.0039 0.0043 0.0110
0.0049 20.0106 0.0161
Trend 20.0016
0.0003 20.0009
0.0004 0.0004 0.0013
20.0129 0.0015
0.0010 0.0050 R
2
within 0.170
0.156 0.103
0.329 0.020
between 0.000
0.056 0.198
0.005 0.051
overall 0.016
0.095 0.003
0.018 0.037
Significant at the 1 level; Significant at the 5 level;
†
Significant at the 10 level;
††
Significant at the 15 level;
‡
Significant at the 20 level.
All specifications also include a constant term. Log GDP refers to the year in which the school year ends. For example, 1977 GDP is used for the 1976–77 school year. “Begin” and “End” refer to the calendar year in effect at the beginning and end of the
academic year.
1
The series is limited by the availability of GSR only though 1991.
Table 3 Fixed effects analysis using interactions of the proportion of low-income workers with economic indicators for school years 1976–
77 to 1990–91 Standard errors in parentheses Log retention rate
Log continuation rate Primary school
Lower-secondary Upper-secondary
To lower-secondary To upper-secondary
Log GDP 0.0607
0.0164 0.0620
0.0231 0.0410 0.0858
0.5961 0.0952
20.3339 0.3243 X low income
20.2769 0.1403
20.2091 0.1977 21.2148
†
0.7349 0.7951 0.8148
2.9568 2.7758 DGDP begin
20.0836 0.0316
20.0628
‡
0.0445 20.5151
0.1657 20.2668
††
0.1838 20.6535 0.6261
X low income 0.3814 0.3036
20.0875 0.4629 1.7249 1.5897
22.3131
‡
1.7635 5.3366 6.0076
DGDP end 20.0724
0.0304 20.0518 0.0431
0.3999 0.1599
20.0942 0.1765 20.1472 0.6014
X low income 0.1638 0.3005
0.1169 0.4251 22.9485
†
1.5765 24.3094
1.7456 7.3976 5.9465
Log gross state 20.0046 0.0046
20.0105
††
0.0065 20.0580
0.0243 20.0966
0.0270 0.1193
‡
0.0918 revenue GSR
X low income 0.0251 0.0508
0.1698 0.0714
0.5746 0.2659
0.5853 0.2950
20.9995 1.0051 DGSR begin
0.0085
†
0.0052 20.0062 0.0073
0.0444
†
0.0270 0.0304 0.0300
0.0278 0.1021 X low income
20.0564 0.0491 0.0460 0.0691
20.3451
‡
0.2569 20.0698 0.2850
20.8259 0.9708 DGSR end
0.0019 0.0029 0.0049 0.0041
0.0293
†
0.0152 0.0259
††
0.0169 20.0365 0.0575
X low income 20.0078 0.0305
20.0638
††
0.0430 20.2890
†
0.1598 20.1587 0.1773
0.2997 0.6040 Trend
20.0016 0.0003
20.0010 0.0004
0.0002 0.0013 20.0138
0.0015 0.0017 0.0050
R
2
Within 0.189
0.089 0.128
0.385 0.034
Between 0.455
0.066 0.000
0.172 0.085
Overall 0.342
0.066 0.003
0.123 0.063
Significant at the 1 level; Significant at the 5 level;
†
Significant at the 10 level;
††
Significant at the 15 level;
‡
Significant at the 20 level.
All specifications also include a constant term. Log GDP refers to the year in which the school year ends. For example, 1977 GDP is used for the 1976–77 school year. “Begin” and “End” refer to the calendar year in effect at the beginning and end of the academic
year. “Low-Income” refers to proportion of workers in each state with very low 1980 earnings. See note 29. The X terms are interactions with the previous variable.
193 M. Binder Economics of Education Review 18 1999 183–199
interactions. The interactions with log GDP are uni- formly negative for retention rates and significant for the
primary and upper-secondary levels. This means that states with more low-income workers respond less elasti-
cally to changes in income than states with fewer low- income workers. Note that, for the range of possible low-
income proportion values see Table 7, the national income effect is always positive, but it is nonetheless
quite small: in Mexico City, with only 3.2 of workers earning very low wages, the estimated income elasticity
for primary school retention is 0.052; in Yucatan, with a low-income proportion of 21.1, the elasticity is only
0.002. Still, the expected Becker-Tomes effect is work- ing opposite to what had been expected. One possible
explanation for this puzzle is that in richer states, school- ing is more accessible. This would mean that poorer chil-
dren are more likely to be involved in schooling, but since they are more likely to drop out,
30
retention rates will be worse.
Even if this is the case, the effect is very small. For retention at the primary level, no other interactions are
statistically significant. For lower-secondary retention, there is a significant and positive interaction for the log
of GSR-the income for state income. This means that poorer states respond more strongly to changes in state
income. Although this appears to contradict the idea that poorer states have fewer economically marginal students,
the effect is again extremely small: for the state average of 9.35 low income workers, the effect of gross state
revenue is close to zero. For Yucatan the effect is posi- tive, but still tiny, with an elasticity of 0.025. Overall,
both the primary and lower-secondary retention rates do not vary greatly among states of different income levels.
For upper-secondary retention the interactions appear to be much more important. Poorer states still have lower
national GDP elasticities the interaction coefficient is negative, but all four of the other significant interaction
terms suggest greater elasticity for states with more low- income workers: the state income interaction coefficient
is positive and all significant price interaction coef- ficients are negative. Thus in poorer states, the upper-
secondary retention rates are more responsive to econ- omic conditions. It is certainly true, as mentioned earlier,
that the direct and opportunity costs are much more pro- nounced for this schooling level than for earlier levels.
As such, even the middle-class students that comprise a much greater share of upper-secondary schooling are
more likely to be affected by economic fluctuations at this schooling level, and more so in states with lower
wages.
30
Positive effects of income or wealth on various schooling indicators in developing countries are reported in Glewwe and
Jacoby 1994, Jamison and Lockheed 1987 and Birdsall 1985.
The continuation rates to lower-secondary also appear to be more responsive to economic conditions in poorer
states. The interaction terms for the national price effects are large and negative and the interaction for the state
income effect is large and positive. In contrast, the con- tinuation rate to upper-secondary does not appear at all
sensitive to economic conditions when interaction terms are present. This finding mirrors the unstable estimates
for upper-secondary continuation rates in earlier dis- cussions of Tables 1 and 2. In any case, the interaction
analysis has shown that upper-secondary retention and lower-secondary continuation rates are more responsive
to economic conditions in poorer states. In these states, deteriorating economic conditions will have harsher
consequences for schooling outcomes.
States vary not only in their sensitivity to economic conditions but also in their economic structure and edu-
cational spending patterns. These differences may also influence schooling outcomes. For example, the supply
of accessible schooling may be greater in states with more heavily concentrated populations, states that spend
more per student may provide higher quality education, and more industrialized states may provide more income
security but also higher opportunity costs.
31
The follow- ing analyses incorporate state characteristics in an effort
to identify the variation among states in schooling out- comes. Unfortunately, annual time series data are not
available for urbanization, sectoral structure and school spending measures.
32
I therefore use two alternative approaches for exploring the role of these state character-
istics. In the first approach, I use only one value of these measures from an early or middle point in the series. In
the second approach, I limit the analysis to 1980 and 1990, years for which the structural measures are avail-
able. Although the second approach severely restricts the number of observations, it has the advantage of exploring
the effects of changes in urbanization, sectoral structure and school spending on schooling outcomes. In addition,
I am able to expand the studied schooling outcomes to include state-level enrollment rates, since the decennial
censuses provide state population counts by age for these years.
For both approaches I estimate random effects models which facilitate the analysis of between-state variation,
while still controlling for correlated error terms for same-
31
Another potentially important variable is state-to-state migration, which may influence schooling indicators on the
demand side. Net in-migration, though, was so closely and positively correlated with state income, sectoral structure and
urbanization that identifying separate effects was impossible. The variables that were included may therefore proxy migration
inflows: their estimated effects should be interpreted cautiously.
32
Urbanization measures are available decennially, as is the labor force distribution by sector. School spending by state is
available annually after 1985.
194 M. Binder Economics of Education Review 18 1999 183–199
Table 4 Fixed state characteristics and log schooling indicators using random effects models for school years 1976–77 to 1990–91 Standard
errors in parentheses Log retention rates
Log continuation rates Primary school
Lower-secondary Upper-secondary
To lower-secondary To Upper-Secondary
Log GDP 0.0350
0.0110 0.0459
0.0151 20.1076
0.0547 0.6190
0.0653 20.0184 0.2078
DGDP begin 20.0463
0.0134 20.0798
0.0186 20.3416
0.0695 20.4822
0.0800 20.1131 0.2602
DGDP end 20.0564
0.0119 20.0435
0.0166 0.1377
0.0621 20.4878
0.0710 0.5394
0.2311 Log gross state
20.0023
††
0.0016 0.0037
†
0.0020 0.0040 0.0059
20.0294 0.0089
0.0181 0.0249 revenue GSR
DGSR begin 0.0026
††
0.0017 20.0006 0.0024
0.0096 0.0089 0.0256
0.0103 20.0581
†
0.0335 DGSR end
0.0011
‡
0.0008 20.0004 0.0011
20.0003 0.0036 0.0096
0.0046 20.0079 0.0141
Trend 20.0016
0.0002 20.0009
0.0003 0.0011 0.0013
20.0127 0.0015
0.0005 0.0048 Log per capita
20.0050 0.0109 20.0021 0.0105
0.0304
‡
0.0224 0.1024
0.0478 0.0818 0.1049
income in 1980 Log per student
20.0100 0.0210 20.0001 0.0203
20.0759
†
0.0429 0.1233
‡
0.0919 0.1298 0.2010
spending in 1985 Rural in 1980
0.0514 0.0256
0.0293 0.0243 0.0287 0.0499
20.4590 0.1106
20.6487 0.2368
Labor force in manufacturing in
0.1419
†
0.0837 0.1459
†
0.0794 0.0677 0.1628
20.7789 0.3612
21.3345
†
0.7721 1980
R
2
Within 0.169
0.156 0.097
0.328 0.020
Between 0.228
0.188 0.235
0.657 0.444
Overall 0.216
0.176 0.148
0.592 0.264
Significant at the 1 level; Significant at the 5 level;
†
Significant at the 10 level;
††
Significant at the 15 level;
‡
Significant at the 20 level.
All models include a constant term. Log GDP refers to the year in which the school year ends. For example, 1977 GDP is used for the 1976-277 school year. “Begin” and “End” refer to the calendar year in effect at the beginning and end of the academic year.
state observations. In these models, the time-invariant state error term in Eq. 2, a
i
, is divided into explained and random components as follows:
a
i
5 d
1
C
i
1 h
i
3 where C is a vector of state characteristics, including
state economic, demographic and education financing characteristics, d
1
is a parameter, and h
i
is a random error term. Combining Eqs. 2 and 3 gives:
logs
it
5 b 1
b
1
logGDP
t
1 b
2
DGDP
t BEGIN
1 b
3
DGDP
t END
1 b
4
TREND
t
1 g
1
logGSR
it
4 1
g
2
DGSR
it BEGIN
1 g
3
DGSR
it END
1 d
1
C
i
1 h
i
1 m
it
The random effects model assumes that the state-spe- cific error term, h
i
, is uncorrelated with the other explanatory variables. A Hausman specification test sup-
ports this assumption. Table 4 shows estimates of the random effects model
in Eq. 4 using all available years and the following fixed measures for the C
i
vector: the log of state per capita income in 1980 this is a direct measure that does
not use the GSR proxy, the log of per student spending in 1985, the proportion of the population living in rural
communities in 1980 and the proportion of the labor force employed in manufacturing in 1980. Since the
national and state-level price and income coefficients are similar to those reported in Table 2, they are not repeated
in Table 4.
Per capita income has a small positive effect on upper- secondary retention and a more pronounced but still
modest positive effect on continuation to the lower-sec- ondary level. Per student spending in 1985 the earliest
year for which this measure is available has small nega- tive effects on high school retention and positive but
imprecise effects on continuation rates into both second- ary levels of schooling. Note, though, that the spending
measure is very broad: it divides the total of all federal, state and private expenditures for education by the num-
ber of students enrolled in academic programs at the pri- mary and secondary levels. The true per student figure
is much lower, since vocational, pre-school and post-sec- ondary students are excluded. In addition, the measure
is an average over all schooling levels: it does not dis- tinguish between a state that spends lavishly on univer-
sities and one that spends proportionately more on pri-
195 M. Binder Economics of Education Review 18 1999 183–199
mary schools. The imprecision of this measure may result in its small influence on schooling indicators.
33
The coefficient on the portion of the population that is rural is positive for the retention rates and significantly
negative for the continuation rates, suggesting that rural states do a better job of retaining students, but are worse
at inducing students to continue from one level to the next. Schools may be relatively less accessible in states
where larger proportions of the population are rural, so that the relatively better-off attend school and with econ-
omic conditions constant, are less likely to leave school. In the 1988–89 school cycle, for example, 20 per cent
of primary schools nationally offered less than a six-year program, compared with 44 per cent in the rural state of
Chiapas Salinas de Gortari, 1989.
At the same time, continuation rates are likely to be lower in rural states because secondary schools tend to
be concentrated in larger towns. A state with a rural pro- portion at half the national median of 41 per cent would
have a lower-secondary continuation rate nine percent- age points higher than a state with the median proportion
and the upper-secondary continuation rate would be 13 percentage points higher.
The per cent of the labor force employed in manufac- turing has a modest positive effect on retention rates and
a large negative effect on continuation rates. Inasmuch as manufacturing jobs offer higher wages and more stab-
ility than jobs in other sectors, the results suggest that manufacturing jobs enhance the ability of students to
complete the academic year of schooling, once they have begun it. However, higher opportunity costs appear to
reduce continuation rates considerably: every percentage point increase in the manufacturing share of labor
reduces the lower-secondary continuation rate by 0.8 per cent and the upper-secondary continuation rate by 1.3
per cent.
Differences in per capita income, urbanization, school spending and manufacturing prominence are quite suc-
cessful in explaining between-state variation, especially for lower- and upper-secondary continuation rates, where
the models account for 66 and 44 per cent of the observed variation, respectively.
Table 5 shows parameter estimates of the second approach, which uses data for 1980 and 1990. The trend
variable picks up changes in national economic con- ditions and any other changes that are uniform among
states.
34
The patterns for retention rates and continuation
33
1985 was also a recession year, so that the cross-section may not accurately reflect school quality among states. This
problem is at least partly corrected in the 19801990 analysis that follows, in which 1990 school spending is also included.
34
Because only two years are available for each state, only one time-varying variable that is identical for all states can be
identified by the model.
rates controlling for changes in state characteristics are similar to the point-in-time state characteristics used in
Table 4. For example, larger rural population and manu- facturing labor proportions lead to better retention rates
and worse continuation rates, although the within-state effect measured by the R
2
appears to be very small for continuation rates. Per student spending appears to have
larger effects in the 19801990 model, with positive elas- ticities of around 0.2 for the continuation rates. The
response of enrollment rates to state characteristics is similar in direction to the response of continuation rates,
although the magnitude of the response is attenuated: the log of per student school spending has a positive effect
on enrollment, while the proportion of the population that is rural and the proportion of the labor force
employed in manufacturing have negative effects. For enrollments, the effect of within-state changes of these
characteristics appears to be quite large: the model accounts for more than two-thirds of the within-state
variation.
8. Conclusions