Comparisons of Intergenerational SchoolingMobility Estimates Based on Household Surveys
from Latin America and the Caribbean
by
Jere R. Behrman and Miguel Székely1
November 9, 2000
(Preliminary version. Please do not quote.)
1 Behrman is the William R. Kenan, Jr. Professor of Economics at the University of Pennsylvania([email protected]). Székely is Research Economist in the Research Department, Inter-American Development Bank ([email protected]). Behrman collaborated in this paper as a consultant tothe Carnegie Endowment for International Peace. We thank Alejandro Gaviria and Nancy Birdsall forsuggestions and help on this paper. Only Behrman and Székely, and not Carnegie nor IDB, are responsiblefor the content of this paper.
1
Introduction
There is a growing consensus that income inequality has increased in a large number of
countries in the world in recent years.2 The main concern is that, precisely because of the
high inequalities, absolute poverty rates are much greater and that economic growth has
not been immediately translated into poverty reduction.
It is important to know, however, the extent to which inequality is driven by individual
differences in ability, work ethic, or simply good luck, rather than by differences in
opportunities. Thus, if some individuals prefer to work more hours or to invest more
energy in their work than others, the income inequality that will occur as a result of these
differences would not necessarily be a policy issue. In fact, reducing this type of
inequality through policy interventions could well lead to reductions rather than increases
in welfare.
But this type of “efficient” inequality probably does not explain the extent of inequalities
in most countries in the world. Rather, inequality likely originates substantially from the
absence of opportunities for large segments of the population. The outright (or implicit)
exclusion of some groups on the basis of their gender, ethnic origin, place of residence or
social status can in turn explain inequality of opportunity. Two different societies with
the same “snapshots” of income distribution at a point of time may have different levels
of social welfare if in one of them these characteristics are a more important determinant
of individual’s fates in life.
Since income inequality measurements in cross-sectional data are “snapshots” each at a
point of time which can change due to many factors, they do not necessarily inform on
whether welfare in society is changing, for instance, due to reduced equality of
opportunity. Friedman (1962) argues that a given extent of income inequality in a rigid
system in which each family stays in the same position in each period may be more a
cause for concern than the same degree of income inequality due to great mobility and
dynamic change associated with equality of opportunity. Thus, if the objective is to
2
determine whether welfare levels are improving, it is essential to characterize the degree
of social mobility both across generations and within generations.
For such reasons there have been increasing recent efforts to measure actual or perceived
social mobility and changes in such mobility in the region. Several of these are
summarized in Birdsall and Graham (2000). But such efforts are limited by the limited
availability of longitudinal data with which to follow the same individuals over time.
Therefore some of the recent studies have based their estimates on cross-sectional data,
with focus on intergenerational mobility in schooling – in particular, Behrman, Birdsall
and Székely (2000) and Dahan and Gaviria (2000) both have used multiple household
surveys to assess the extent of intergenerational schooling mobility. Behrman, Birdsall
and Székely basically define intergenerational mobility to be the extent to which school
gaps of children who co-reside with their parents are not associated with parents’
characteristics, primarily schooling. Dahan and Gaviria characterize mobility to be
greater when the between family variance in child schooling success is small relative to
the total variance in schooling success using data on siblings who are co-residing with
their parents (where “success” is defined as not lagging more than a grade below the
median for each age level).
This paper compares and contrasts empirical estimates of intergenerational schooling
mobility based on cross-sections of household surveys from LAC. The paper focuses on
the Behrman, Birdsall and Székely and Dahan and Gaviria approaches, because to our
knowledge these are the most recent attempts to characterize inter-generational mobility
with cross sectional data consistently for a number of countries. To perform the analysis
we use the micro data from 123 household surveys. Of these, 87 belong to 18 Latin
American countries, for the period 1977-1999. These countries cover around 95% of the
total population of the region. We use 19 Current Population Surveys (for 1980-1998) for
the United States, and 17 Family Income and Expenditure Surveys for Taiwan, for 1980-
1996.
2 See for instance Székely and Hilgert (1999) for a recent comparison for the 1990s decade for 35 countries.
3
Our analysis illustrates that even when we restrict the measurement of mobility to only
few options, the way in which inter-generational mobility is measured has strong
implications for three important issues. The first is country rankings. Economic policies
and the performance of countries are commonly evaluated in terms of social indicators,
and countries where inter-generational mobility is relatively high are thought of as being
more successful. Our results show that if countries are ranked according to different
mobility measures, a very different idea is obtained about their performance relative to
others.
The second issue is the evolution of inter-generational mobility over time. We compare
the trends followed by three measures over 20 years for Latin America and the Caribbean
(LAC), the United States and Taiwan, and conclude that depending on the measure
chosen to estimate mobility, a different picture emerges. This has important implications
because depending on the measure chosen, the policy conclusion may shift from giving
priority to compensatory measures for sectors of the population that have been “losers”
during the past years, to giving priority to policies aimed at leveling the “play field”.
The third issue is the correlation between mobility and economic reform. One of the main
attractive features of reforms is that they are supposed to improve market functioning,
and this would be expected to act in the direction of leveling the “play field”. Our
preliminary results on this show that the correlation between reforms and mobility also
depends on the specific methodology selected to measure inter-generational mobility.
The paper has three sections. The first summarizes some conceptual issues regarding
measuring social mobility in the literature. The second presents empirical estimates for
some of these alternatives. The third concludes.
4
Section 1. How is Social Mobility Statistically Modeled and Measured?
How social mobility has been modeled and measured has varied, not surprisingly,
depending on aspects of social mobility that are discussed in Behrman (2000), as well as
the available data. We review some of the more prominent approaches to statistically
modeling social mobility in this section, focusing on integenerational schooling mobility
as an example. This is because schooling is normally thought to be an important factor in
income distribution and this is the type of mobility that perhaps can be most easily
characterized with cross-sectional household data because such data permit the
representation of schooling for two generations that are co-residing.
Section 1.1 Intergenerational Correlations or Markov Statistical Models of Social
Mobility for Continuous Socioeconomic Indicators
A common statistical characterization of mobility dating back at least to Galton’s (1889)
model of regression towards the mean is the first-order Markov model in which the
relevant socioeconomic indicator -- say schooling -- for entity i in period t (Sit) depends
on the value of that indicator in the previous period (Sit-1) and a stochastic term (wit) that
is independent of the previous period indicator and that is independently distributed
across individuals and across periods:3
(1) Sit = bSit-1 + wit.
This approach is basically what Behrman, Birdsall and Székely (2000) use. In that
context, each period can be a generation and i refers to the family dynasty. Thus the
previous period indicator carries all relevant past information about family i, including
the past experience regarding transitory (in the sense of being for only one generation)
shocks (which means that the variance of S increases with t). The parameter b is positive
3 With data on three (or more) periods the first-order Markov assumption can be tested by its implicationthat the correlation in Y between periods t and t + 2 equals the product of the correlations between t and t +1 and between t + 1 and t + 2.
5
and is greater than one if there is real growth in S. If Sit is defined relative to the mean of
its distribution, then the parameter b affects the relative position in the distribution and b
< 1 implies regression towards the mean (that is more rapid the smaller is b). The
parameter b is a measure of immobility. Another frequently utilized measure of mobility
is r, the inter-period correlation in S. As t goes to the limit, b and r coincide, but along
the path b consistently exceeds r (Atkinson, Bourguignon and Morrisson 1992, p. 9).
Estimates of relation (1) or of extensions of this relation (e.g., with population groups
with different mobility) may be used to characterize intergenerational (or
intragenerational) social mobility with continuous socioeconomic indicators such as
schooling (or income or earnings) measured in either absolute or relative terms.
Section 1.2 Inter- Versus Intra-Familial Variations
In this approach, which is basically what Dahan and Gaviria (2000) use (and which dates
back at least to Conlisk 1974), the variance in schooling success is decomposed between
within and between family components, and mobility is characterized as being greater the
greater is the intrafamily share of the variance. That is, if Sjic is the schooling success of
the jth child in the ith family, the total variance in schooling success across children
(perhaps conditioned on some age range) can be composed into the within family
variance Sj2 and the between family variance Si
2:
(2) Sij2 = Sj
2 + Si2, which implies:
(2A)1 = Sj2/ Sij
2 + Si2/ Sij
2.
The larger is the share of the interfamily variance in the total variance, the greater is
immobility.
6
Section 1.3 Markov Transition Matrix-Based Measures of Intergenerational
Mobility
Schooling can be represented by categorical variables. A convenient and standard way to
characterize intergenerational mobility with categorical variables is to use transition
probability matrices for movements among segments of the distribution (e.g., relevant
categories, terciles, deciles) between generations. These generally are used in first-order
Markov processes with the assumption, as in relation (1) above, that the previous period
indicator carries all relevant past information about the family dynasty. In certain
respects transition matrices allow greater flexibility in characterizing mobility than do the
approaches based on continuous variables that are discussed in the previous sections (at
least as they usually are used) because they allow asymmetries and other non-linearities.
For example, transition matrices easily may capture a situation in which the probabilities
of moving in a large jump from the bottom of the schooling distribution to the top may be
larger than the probability of moving from the top to the bottom, with the difference
balanced out by differences in the probability of moving to the middle.
A transition probability matrix (P) is an n x n matrix, where n refers to the number of
categories. The element in the jth row and kth column of a transition probability matrix
(pjk) gives the probability that an entity moves from the jth category to the kth category
between generations (periods). The sum across elements in each row must be one
because every family that initially is in the jth category must end up in one of the
categories ( kpjk = 1 for each j), assuming that all family lines continue to the next
generation.
In general the sum of elements in each column need not be one. If the categories have
equal numbers in them and there is relative or exchange mobility (see Behrman 2000) so
that distribution does not change between generations, the sum of the elements in each
column is one.4 Following are examples of such matrices for population terciles (so there
4 As noted above, the latter term is frequently used by sociologists concerned with social mobility incontrast to “structural” mobility if the distribution is changed. If the sum of the elements in each of therows and of the elements in each of the columns is one, the matrix is said to be “bi-stochastic.”
7
are three segments) for two special cases of interest: no intergenerational mobility (PN)
and “complete” intergenerational mobility (PC):
1.00 0.00 0.00 0.33 0.33 0.33
(3) PN = 0.00 1.00 0.00 ; PC = 0.33 0.33 0.33
0.00 0.00 1.00 0.33 0.33 0.33
For PN, there is no relative intergenerational mobility, so there are no nonzero off-
diagonal elements. Children end up in exactly the same part of the distribution as their
parents – the completely rigid social system noted in the introduction to which Friedman
(1962) refers. For PC, there is “complete” intergenerational mobility in the sense that the
probabilities are equal of ending up in any of the three terciles after the transition,
independent of the initial starting point.
One important strain in the literature is concerned with how to infer the extent of
intergenerational (or other types of social) mobility from transition probability matrices
of the types indicated above. In essence, the problem is how to reduce such a probability
matrix to a scalar that characterizes the extent of mobility (immobility). A number of
possibilities have been proposed in the literature and are summarized by Dardanoni
(1993), to which the interested reader is referred for further discussion and references:
1. Trace [trace (P) - 1)/(n - 1)]: The intuition behind this measure is that the
greater the concentration on the diagonal the less the mobility. The obvious
limitation is that the trace only distinguishes between being on and off the
diagonal, not whether the latter are close or far from the diagonal.
2. Determinant [|P|1/(n-1)]: The determinant incorporates information about off-
diagonal elements as well as the diagonal elements. But the determinant is zero
(implying complete mobility) if any two rows or any two columns are identical no
matter what is the distribution of elements elsewhere in the matrix, which is a
definite limitation as a mobility indicator.
8
3. Mean First Passage Time: If two individuals are drawn from the population at
random and there is a steady-state Markov chain of transitions, the mean first
passage time is the expected number of periods which must pass before the first
individual achieves the state of the second individual (Conlisk 1990).
4. Bartholomew’s (1982) Measure [ j k jk|k-j|]:5 The expected number of
category boundaries crossed from one generation to the next when the chain is in
steady state.
5. Second Largest Eigenvalue: This index has been proposed to represent the
speed of escape from the initial conditions and of regression to the mean.
Unfortunately, as Dardanoni (1993) emphasizes, these mobility indicators do not
consistently rank different transition matrices. He illustrates with the following three
transition matrices:
0.60 0.35 0.05 0.60 0.30 0.10 0.60 0.40 0.00
(5)P1 = 0.35 0.40 0.25 ;P2 = 0.30 0.50 0.20 ; P3 = 0.30 0.40 0.30
0.05 0.25 0.70 0.10 0.20 0.70 0.10 0.20 0.70
He shows that any of these three matrices may be considered to represent the greatest
mobility, depending on which mobility index is used:
Dardanoni therefore derives a partial Social Welfare Function (SWF) ordering with an
additive SWF placing greater weights on individuals who start in lower positions in
society. Conditional on this SWF, he derives a condition for the partial ordering of
alternative transition matrices.6 He also shows that most of the mobility indices
5 is the equilibrium probability vector, which exists and is the unique solution to ’ = ’P if P is regular (i.e.,for some large enough integer m, Pm is strictly positive).
6 He shows that welfare is greater for transition matrix P than for Q (if both are monotone regular transitionmatrices for SWF weights and instantaneous utilities that are nondecreasing in income) if T’ [P( )-Q( )]T 0
9
mentioned above (with the exception of Bartholomew’s measure and a modified
eigenvalue measure) do not necessarily imply greater mobility for transition matrices that
give families starting with lower initial schooling better schooling lotteries.
Such considerations point to the facts that currently there is no one “correct” way to
measure relative mobility with transition matrices, different approaches may yield
different rankings for the same transition matrices, and to make much progress in such
cases may require explicit assumptions about the SWF – but even with such assumptions
complete orderings of transition matrices may not be possible.
Partly for this reason, Fields and Ok (1996) contribute an axiomatic approach to
characterizing mobility from longitudinal data. Based on seven axioms,7 they derive a
measure of total mobility that is additively decomposable into mobility from (i) the
transfer of resources among individuals with total resources held constant (relative or
exchange social mobility) and (ii) a change in the total resources available.
In particular, they define the relative mobility due to resource transfers (MR) in a growing
economy to be twice the amount lost by losers (twice because every unit lost by a loser is
gained by a winner):
(4A) MR = 2 ( (yjt - yit+1)), where j is summed over all losers.
where T is a n x n summation matrix with zeros below the main diagonal and ones elsewhere and 0 < 1 isthe discount factor.
7 The axioms are (i) linear homogeneity (i.e, an equiproportional change in all income levels both in theinitial and the final distributions results in exactly the same percentage change in the mobility measure), (ii)translation invariance (i.e., if the same amount is added to everybody’s income in the initial and the finaldistributions, the new situation has the same mobility as the initial one), (iii) normalization (i.e., a onedollar income gain and a one dollar income loss both produce one unit of mobility for that individual), (iv)strong decomposibility (i.e., the level of total income mobility experienced by a population is a function ofthe levels of mobility experienced by two disjoint and exhaustive subpopulations) (they also consider weakdecomposibility), (v) population consistency (i.e., in the contexts of populations of different sizes, if equalsare added to equals the results are equal), (vi) growth sensitivity (i.e., if unequals are added to equals theresults are unequal), and (vi) individualistic contribution (i.e., the contribution of one individual’s incomechange to total mobility depends only on the amount of his/her income change).
10
Relative mobility due to transfers in a shrinking economy is defined to be twice the
amount gained by winners:
(4B) MR = 2 ( (yjt+1 - yit)), where j is summed over all winners.
Mobility due to resource growth (MY) in a growing economy is defined to be:
(4C) MY = yjt+1 - yit, where j is summed over all members of the population.
Mobility due to resource contraction in a shrinking economy is defined to be:
(4D) MY = yjt - yit+1, where j is summed over all members of the population.
Total mobility (M) is defined to be:
(4F) M = |yjt+1 - yit|, where j is summed over all members of the population.
They show that with these definitions of mobility:
(4G) M = MR + MY.
This approach has several advantages over the previous literature. Total mobility is
decomposed into relative (exchange) mobility and resource change mobility as in relation
(4G) -- which is the first exact decomposition of resource mobility in the literature. This
approach can be applied in per capita terms to allow for comparisons across periods (or
surveys) with different numbers of people, which also permits comparisons with base
resources so that statements can be made such as “average mobility is 10% of initial
resources.” This approach does not depend on Markovian assumptions that have been
rejected by empirical studies of Britain, France and the United States (Atkinson,
Bourguignon and Morrisson 1992, Atoda and Tachibanaki 1991, Shorrocks 1976). It
also does not depend on normative assumptions regarding social welfare functions.
11
While their formulation is stated in terms of income, the resources of relevance could be
total schooling or any other resources.
Section 2. Alternative Estimates of Intergenerational Schooling Mobility in Latin
America and the Caribbean Based on Cross-Sectional Household Surveys
Section 2.1 Data
For our exploration of alternative intergenerational schooling mobility estimates for LAC
we use a compilation of household surveys for Latin America, as well as a series of the
Current Population Survey for the United States, and a series of household surveys for
Taiwan. We believe that the comparison between this particular region and countries is
illustrative about the differences across levels of development. Since we have access to
the micro data in these surveys, we are able to construct comparable indicators on the
critical information for this paper, which are the measures of schooling attainment for
multiple co-resident family members – parents and children for the Markovian methods
in Sections 1.1 and 1.3, and siblings for the variance decomposition in Section 1.2. Some
details of the data can be found in Appendix Table A1.
From each survey we use only a restricted sample of children ages 13 to 21. This age-
group is selected so that individuals are still co-resident with their parents, however, their
schooling attainment is censored in many cases because they still are in schooling at the
time of the survey. For these reasons, studies such as Behrman, Birdsall and Székely
(2000) and Dahan and Gaviria (2000) focus on children who are young enough so that
they are still co-resident with their parents but old enough so that many of these children
will have completed their schooling – typically their late teens. In addition, these studies
use measures for the children’s schooling that indicate to what extent children have
relatively low schooling conditional on their age, even if some may subsequently
continue in school after the surveys. In particular, Behrman, Birdsall and Székely use the
schooling gap, defined as the difference between the number of schooling grades that
would have been completed if a child entered school at the earliest legal age (e.g., six)
12
and progressed satisfactorily one grade each subsequent year minus the number of actual
completed grades. This indicator indicates various possible degrees to which children of
a given age lag behind what would be possible in their schooling attainment due to late
entry, grade repetition or dropping out. Dahan and Gaviria use an dichotomous index for
lagging behind in schooling that distinguishes between children of a given age who have
completed the median number of schooling grades for that age versus those who have at
most one grade less than the median number of completed grades for that age. This
indicator indicates whether or not children are below some cutoff in their schooling
attainment to date. The latter index is analogous to the headcount poverty index with the
poverty line at the median schooling, with the former index is analogous to a poverty
index that indicates how far one is below the poverty line with the poverty line at the
schooling level that would have been attained with entry on time and successful
promotion each year. Both of these indices, or variants of them (including one analogous
to the distribution-weighted poverty index) can be constructed and used with any of the
measures of intergenerational schooling mobility that are discussed in Section 1.
Although the data used to compute these mobility measures is of high quality, relative for
instance to income data from household surveys, which varies considerably in terms of
coverage, definitions, and quality, it is not without its problems. For instance, household
surveys not always inform on whether a child residing at a household is effectively a
child of the head. In the cases where this can be verified, the proportions are surprisingly,
not that high. For instance, Table 1 shows the proportion of children that are children of
the head. In countries such as Venezuela, the proportion is only around 78 percent, and
only 76 percent of all children ages 13-19 reside in a household where the head is the
parent, and where the parent has a spouse who is also a parent of the same child. Due to
the age restriction, sample sizes for computing the mobility measures examined here are
relatively small, so imposing an additional constraint of kinship between head and
children stretches the data in many cases.
13
Section 2.2 Alternative Estimates of Intergenerational Schooling Mobility
Behrman, Birdsall and Székely (BBS henceforth) consider schooling gaps separately for
four age groups: 10-12, 13-15, 16-18, and 19-21 years old because family background
may have differential effects depending on how close a child is to marginal schooling
decisions. Additionally, they consider separately five parental schooling quintiles. These
quintiles are defined by parental schooling because parental schooling represents not only
important components of permanent household income, but also possibly important non
income characteristics such as genetic endowments and preferences regarding schooling
as well as parental price-of-time considerations. For each subgroup of the population, two
indexes are computed. The first (which we label BBS1) consists on regressing schooling
gaps of children on parental schooling, household income and other household
characteristics. From the estimated coefficients of the three family background variables
two basic intergenerational schooling mobility indices are constructed: (1) the
Aproportional intergenerational schooling mobility index@ defined as the proportion of the
variance in the schooling gap that is associated with the weighted average of parental
schooling and household income, where the weights are the regression coefficient
estimates for these three variables (labeled BBS1). (2) the Agap-adjusted intergenerational
schooling mobility index@ defined as the proportion of the variance in the schooling gap
that is associated with the weighted average of parental schooling and household income
multiplied by the average gap relative to the expected schooling for that subsample)
(labeled BBS2).
The measure by Dahan and Gaviria (DG henceforth), is defined in two steps. The
first uses the following correlation:
∑∑
∑ ∑∑
= =
= ==
−
−−=
F
f
S
ssf
F
f
S
kfkf
S
ssf
gf
ff
gg
Sgggg
1 1
2
1 1
2
1
2
)(
/)()(
ρ ,
where F is the number of families in the sample, Sf is the number of teenage
siblings in family f, gsf is the binary indicator of socioeconomic failure of individual s in
14
family f, and g is the average indicator in the entire sample. Since ρg could yield positive
values even if family background is inconsequential -as will be the case, for example,
when children are assigned to families randomly, the authors define an alternative index
as follows:
FS
Sga −
−−−=
1)1(1 ρρ , (2)
where S is the number of children in the sample. The new index (ρa), which corresponds
now to the adjusted R2 obtained by regressing earnings on family dummies, will yield
positive values only if the previous index (ρg) is greater than would be expected purely
by chance. Positive values of ρa can thus be unambiguously interpreted as evidence that
family background does play a role in the determination of schooling outcomes.
The BBS1, BBS2, and DG indexes just described, refer to immobility, rather than
mobility indexes. For ease of interpretation, in what follows we slightly transform these
indexes by defining: Index=1-original index.
Figures 1a, 1b and 1c plot the transformed BBS1, BBS2, and DG mobility indexes,
respectively, and correlates them with the Gini coefficient for the distribution of
household per capita incomes. In all three cases the correlation is quite strong (.44, .55
and .56, respectively), but the figures clearly illustrate that inequality and
intergenerational mobility are not the same. Countries with high mobility in general tend
to have lower inequality, but this is not always the case.
Sensitivity of Country Rankings
Figures 2a, 2b and 2c plot the correlation between the three indexes. As expected, BBS1
and BBS2 in panle 2c, have a stronger correlation (of .87). The correlation between
BBS1 and DG is of .35, while the correlation between BBS2 and DG is of .49. But even
though the correlation is significant in statistical terms, the use of different indexes may
lead to different conclusions about the extent of social mobility in one country compared
to others. Table 3 illustrates this. In the first column, countries are ranked according to
BBS1. The country with the highest mobility appears to be the United States, and the one
15
with the lowest is Paraguay. The second column shows the ranking according to BBS2.
There are several reversals. Peru, Uruguay and Argentina now appear to have higher
mobility, while Guatemala has lower mobility. The number of re-rankings is much larger
when the comparison is made between BBS2 and DG. Mexico changes from being a
country with moderate mobility to being one of the countries with lower mobility. Similar
changes are observed for Argentina and Honduras. Paraguay and Peru, on the other hand,
appear to have much more mobility in terms of DG than in terms of BBS2. The United
States and Taiwan are the two countries that consistently appear as having high mobility,
independently of the measure chosen.
Sensitivity of Time Trends
Figures 3a, 3b and 3c show the evolution of intergenerational mobility for the BBS1,
BBS2 and DG indexes, for the average LAC country, the United States and Taiwan. The
United States seems to be the only case where the trend is very similar, independently of
the measure chosen to measure mobility. However, BBS1 and BBS2 show a continuous
increase in mobility for LAC, while DG shows a decline after around 1990. For Taiwan,
the choice of index also makes an important difference. According to BBS2 it has been
increasing since the mid 1980s. According to BBS1 it declined sharply towards 1985 and
has been erratic thereafter, while there has been a considerable increase since 1980
according to the DG measure.
Figures 4a and 4b plot the three measures for Costa Rica and Peru. Of the sample of 20
countries we consider, these are the two cases where the conclusion about the evolution
intergenerational mobility is most sensitive to the choice of measure. In Costa Rica,
BBS2 shows an increase, while DG declines sharply. In Pery BBS2 declines, and DG
raises in the 1990s.
Sensitivity of Correlation with Economic Reform
Finally, it is also of interest to determine whether the choice of measure leads to different
conclusions about the correlation between mobility and economic reform. To explore
this, we regress mobility indexes for LAC on several indexes of economic reform. The
16
analysis is restricted to the LAC data because reform indexes are only available for this
region.
To characterize the pace and depth of different types of reforms, we use reform indices
developed by Lora (1997) and modified and extended by Morley, et al. (1999). These
indices summarize information on trade reform, financial liberalization, tax reform,
liberalization of external capital transactions, and privatization for the period 1970-1995.
Unlike proxies commonly used in the literature, these reform indices have the advantage
that they are based on direct indicators of governmental policies, so that they reflect
policy “effort”. The trade reform index is the average of the average level of tariffs and
the average dispersion of tariffs. The index of domestic financial reform is the average of
an index that controls for borrowing rates at banks, an index of lending rates at banks,
and an index of the reserves to deposit ratio. The index for international financial
liberalization averages four components: sectoral controls of foreign investment, limits
on profits and interest repatriation, controls on external credits by national borrowers and
capital outflows. The tax reform index averages four components: the maximum marginal
tax rate on corporate incomes, the maximum marginal tax rate on personal incomes, the
value added tax rate, and the efficiency of the value-added tax. The tax reform index is
higher, the lower is the average of the marginal tax rates. The privatization index is
calculated as one minus the ratio of value-added in state owned enterprises to non-
agricultural GDP. Finally, the labor market reform index considers firing costs after 1
and 10 years of work, mandatory costs for over-time work, restrictions on temporary
contracts, and the value of contributions to social security. All the indices are normalized
between 0 and 1, where in each case, 0 refers to the minimum value of the index across
all Latin American countries in the relevant time period (including those that do not
appear in our data on wage differentials), and 1 is the maximum registered in the whole
sample. Thus, the indices are comparable across countries in the region.
Table 4a presents the results from regressing BBS1 on an average of the five reform
indexes. The regression corresponds to a fixed effects estimation performed by linking
the average mobility index across age groups and parental education quintile for each
17
country and year, with the reform index for the same country and year. Even though we
control for all country fixed characteristics, we interpret this only as a correlation since
we do not control for time-varying unobserved variables that are correlated with reforms,
and that might affect BBS1. The correlation is positive and statistically significant,
indicating that intergenerational mobility, as characterized by BBS1 is strongly correlated
with economic reform in Latin America. Table 4b presents similar results for BBS2, and
leads to the same conclusions.
In Table 4c we performed a similar fixed effects regression, but the BBS indexes are
substituted by the DG measure. Interestingly, the correlation between reforms and
mobility is still positive, but it is not statistically significant.
Tables 5a, 5b and 5c, BBS1, BBS2 and DG are regressed on each of the reform indexes
included independently. The conclusion about the correlation between different measures
and each reform varies depending on the mobility index chosen. Tax reform and financial
market reform are positively correlated with BBS1, while capital account liberalization is
negatively and significantly correlated with this same measure. There is no statistically
significant association between trade reform and privatization and BBS1. The main
difference with BBS2 is that for this index we do not find a significant correlation with
capital market liberalization, and that the correlation with privatization is negative, rather
than positive as with BBS1. A totally different picture emerges when DG is used as
dependent variable. Trade and Capital market reforms now appear to have a positive
correlation, while tax reform has a negative significant correlation with this mobility
index.
3. Conclusions
18
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23
Table 1Table 1. Most Mobile Matrix Conditional on Mobility Index Used
Trace Determinant Mean First
Passage Time
Bartholomew’s
Measure
Eigenvalue
P1, P3 P1 P3 P1, P2, P3 P2
Table 2
Table 3
Share of Teenagers (age 13-19)Children
Children Related Other Own household of Headof Head to Head non-relative head or spouse (Two Parents)
Arg* 88.71 7.59 1.22 2.47 83.72Bol 84.84 9.40 2.12 3.65 83.06Chl 84.11 13.52 0.99 1.39 83.26Bra 83.70 10.29 1.42 4.59 81.60Ven 78.63 17.56 1.58 2.22 76.61
*GBA onlySource: Duryea, Edwards and Ureta 2000. "Adolescents and Youth in Latin America"
Correlation CoefficientsGini Index BBS1 BBS2 DG
Gini Index 1BBS1 -0.4482 1BBS2 -0.551 0.8701 1DG 0.5658 -0.3505 -0.4959 1
24
Table 4country bbsr country bbsag country dg
Paraguay 0.929258 Brazil 0.7329 El Salvador 0.387343Brazil 0.935106 Paraguay 0.745058 Mexico 0.416248Peru 0.94028 Guatemala 0.749411 Nicaragua 0.427939Bolivia 0.940713 Nicaragua 0.790979 Guatemala 0.44914El Salvador 0.94611 El Salvador 0.814268 Brazil 0.449868Uruguay 0.946572 Bolivia 0.848708 Ecuador 0.453114Guatemala 0.947686 Peru 0.850669 Argentina 0.467544Nicaragua 0.949789 Mexico 0.865842 Bolivia 0.474531Mexico 0.953171 Ecuador 0.868582 Costa Rica 0.492356Costa Rica 0.956957 Uruguay 0.868625 Colombia 0.493189Ecuador 0.958991 Costa Rica 0.875188 Honduras 0.500401Panama 0.961621 Dominican Republic 0.897136 Dominican Republic 0.522026Dominican Republic 0.962695 Colombia 0.900487 Venezuela 0.524479Argentina 0.96671 Venezuela 0.905804 Chile 0.550535Venezuela 0.967292 Panama 0.909905 Peru 0.562818Colombia 0.970244 Honduras 0.92553 Uruguay 0.587608Taiwan 0.972216 Argentina 0.932881 Panama 0.588539Chile 0.975943 Chile 0.946481 Paraguay 0.629256Honduras 0.979925 Taiwan 0.970515 Taiwan 0.828759United States 0.98686 United States 0.97967 United States
25
Table 4a. xtreg bbsr totidx, i(id) fe
Fixed-effects (within) regression Number of obs = 48Group variable (i) : id Number of groups = 15
R-sq: within = 0.1859 Obs per group: min = 1 between = 0.0105 avg = 3.2 overall = 0.0474 max = 7
F(1,32) = 7.31corr(u_i, Xb) = -0.0034 Prob > F = 0.0109
------------------------------------------------------------------------------ bbsr | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+------------------------------------------------------------------- totidx | .0275703 .0102001 2.703 0.011 .0067934 .0483472 _cons | .9363158 .0072426 129.279 0.000 .9215631 .9510685------------------------------------------------------------------------------ sigma_u | .01818868 sigma_e | .00700375 rho | .87087372 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(14,32) = 17.62 Prob > F = 0.0000
Table 4b
. xtreg bbsag totidx, i(id) fe
Fixed-effects (within) regression Number of obs = 48Group variable (i) : id Number of groups = 15
R-sq: within = 0.3012 Obs per group: min = 1 between = 0.0221 avg = 3.2 overall = 0.1165 max = 7
F(1,32) = 13.79corr(u_i, Xb) = 0.0709 Prob > F = 0.0008
------------------------------------------------------------------------------ bbsag | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+------------------------------------------------------------------- totidx | .2000376 .0538637 3.714 0.001 .0903208 .3097544 _cons | .6995948 .0382461 18.292 0.000 .62169 .7774996------------------------------------------------------------------------------ sigma_u | .08742295 sigma_e | .03698483 rho | .8481932 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(14,32) = 19.67 Prob > F = 0.0000
26
Table 4c. xtreg dg totidx, i(id) fe
Fixed-effects (within) regression Number of obs = 47Group variable (i) : id Number of groups = 15
R-sq: within = 0.0179 Obs per group: min = 1 between = 0.0021 avg = 3.1 overall = 0.0487 max = 7
F(1,31) = 0.57corr(u_i, Xb) = 0.1565 Prob > F = 0.4579
------------------------------------------------------------------------------ dg | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+------------------------------------------------------------------- totidx | .0597081 .079426 0.752 0.458 -.1022823 .2216985 _cons | .4797011 .0568667 8.436 0.000 .3637206 .5956816------------------------------------------------------------------------------ sigma_u | .08126226 sigma_e | .05352345 rho | .69743716 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(14,31) = 7.64 Prob > F = 0.0000
27
Table 5a. xtreg bbsr kapidx tradeidx finidx prividx taxidx, i(id) fe
Fixed-effects (within) regression Number of obs = 49Group variable (i) : id Number of groups = 16
R-sq: within = 0.4455 Obs per group: min = 1 between = 0.0014 avg = 3.1 overall = 0.0037 max = 7
F(5,28) = 4.50corr(u_i, Xb) = -0.6181 Prob > F = 0.0039
------------------------------------------------------------------------------ bbsr | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+------------------------------------------------------------------- kapidx | -.0314912 .015394 -2.046 0.050 -.0630244 .0000421tradeidx | -.0098675 .0125867 -0.784 0.440 -.0356502 .0159151 finidx | .0148581 .0076401 1.945 0.062 -.0007919 .0305082 prividx | .0101721 .0128029 0.795 0.434 -.0160535 .0363977 taxidx | .0420371 .0168488 2.495 0.019 .007524 .0765502 _cons | .9484621 .0102614 92.431 0.000 .9274427 .9694815------------------------------------------------------------------------------ sigma_u | .02102453 sigma_e | .00617939 rho | .92048387 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(15,28) = 12.78 Prob > F = 0.0000
Table 5b. xtreg bbsag kapidx tradeidx finidx prividx taxidx, i(id) fe
Fixed-effects (within) regression Number of obs = 49Group variable (i) : id Number of groups = 16
R-sq: within = 0.5373 Obs per group: min = 1 between = 0.0469 avg = 3.1 overall = 0.0711 max = 7
F(5,28) = 6.50corr(u_i, Xb) = -0.2121 Prob > F = 0.0004
------------------------------------------------------------------------------ bbsag | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+------------------------------------------------------------------- kapidx | -.0364358 .0801527 -0.455 0.653 -.2006212 .1277496tradeidx | -.0714882 .0655356 -1.091 0.285 -.2057318 .0627555 finidx | .0667371 .0397801 1.678 0.105 -.0147487 .1482229 prividx | -.0587651 .0666614 -0.882 0.386 -.1953149 .0777847 taxidx | .2537579 .087727 2.893 0.007 .0740573 .4334584 _cons | .7880331 .0534281 14.749 0.000 .6785905 .8974756------------------------------------------------------------------------------ sigma_u | .08623046 sigma_e | .03217445 rho | .87779378 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(15,28) = 17.39 Prob > F = 0.0000
28
Table 5c. xtreg dg kapidx tradeidx finidx prividx taxidx, i(id) fe
Fixed-effects (within) regression Number of obs = 48Group variable (i) : id Number of groups = 16
R-sq: within = 0.2703 Obs per group: min = 1 between = 0.0000 avg = 3.0 overall = 0.0516 max = 7
F(5,27) = 2.00corr(u_i, Xb) = -0.4730 Prob > F = 0.1107
------------------------------------------------------------------------------ dg | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+------------------------------------------------------------------- kapidx | .1396252 .1255803 1.112 0.276 -.1180442 .3972947tradeidx | .2514425 .1011321 2.486 0.019 .0439365 .4589485 finidx | -.052167 .0611277 -0.853 0.401 -.1775908 .0732567 prividx | -.0662397 .1051264 -0.630 0.534 -.2819413 .1494619 taxidx | -.2457972 .1369205 -1.795 0.084 -.5267349 .0351406 _cons | .4161292 .0847136 4.912 0.000 .2423113 .589947------------------------------------------------------------------------------ sigma_u | .10075596 sigma_e | .04943549 rho | .80597497 (fraction of variance due to u_i)------------------------------------------------------------------------------F test that all u_i=0: F(15,27) = 7.27 Prob > F = 0.0000
29
Figure 1a
Figure 1b
Figure 1c
(mean) sdgini
bbsr Fitted values
.365103 .661942
.909011
.991575
(mean) sdgini
bbsag Fitted values
.365103 .661942
.586349
.987788
(mean) sdgini
dg Fitted values
.365103 .661942
.357098
.828759
30
Figure 2ª
Figure 2b
Figure 2c
bbsr
dg Fitted values
.909011 .991575
.357098
.828759
bbsag
dg Fitted values
.586349 .987788
.357098
.828759
bbsag
bbsr Fitted values
.586349 .987788
.909011
.991575
31
Figure 3a
Figure 3b
Figure 3c
year
bbsrlac bbsrusa bbsrtai
1980 1999
.928184
.991575
year
bbsaglac bbsagusa bbsagtai
1980 1999
.790935
.987788
year
bbsdglac bbsdgtai
1980 1999
.456006
.828759
32
Figure 4ª: Costa Rica
Figure 4b: Peru
year
bbsr bbsag dg
1987 1998
.398019
.965046
year
bbsr bbsag dg
1985 1997
.492406
.960831
33
Table A2 (Incomplete)
Household Surveys Used in Growth Regressions
Country Year Name of the survey Reference
Month for Incomes Households Individuals Labor Property Rent Capital Rent Transfers Non-Monetary Imputed Rent
1 Bolivia 96 Encuesta Nacional de Empleo June 8,311 35,648 X X X X n.a. n.a.
2 97 Encuesta Nacional de Empleo November 8,461 36,752 X X X X n.a. n.a.
3 Brazil 81 Pesquisa Nacional por Amostra de Domicilios September 103,193 481,480 X X X X n.a. n.a.
4 83 Pesquisa Nacional por Amostra de Domicilios September 113,599 511,147 X X X X n.a. n.a.
5 86 Pesquisa Nacional por Amostra de Domicilios September 65,277 289,533 X X X X n.a. n.a.
6 88 Pesquisa Nacional por Amostra de Domicilios September 68,833 298,031 X X X X n.a. n.a.
7 92 Pesquisa Nacional por Amostra de Domicilios September 78,188 317,145 X X X X n.a. n.a.
8 93 Pesquisa Nacional por Amostra de Domicilios September 80,054 322,011 X X X X n.a. n.a.
9 95 Pesquisa Nacional por Amostra de Domicilios September 85,167 334,106 X X X X n.a. n.a.
10 96 Pesquisa Nacional por Amostra de Domicilios September 84,862 331,142 X X X X n.a. n.a.
11 Chile 87 Encuesta de Caracterización Socioeconómica Nacional November 22,719 97,044 X X X X X X
12 90 Encuesta de Caracterización Socioeconómica Nacional October 25,793 105,189 X X X X X X
13 92 Encuesta de Caracterización Socioeconómica Nacional October 27,666 110,555 X X X X X X
14 94 Encuesta de Caracterización Socioeconómica Nacional October 45,379 178,057 X X X X X X
15 96 Encuesta de Caracterización Socioeconómica Nacional October 33,636 134,262 X X X X X X
16 Colombia 95 Encuesta Nacional de Hogares - Fuerza de Trabajo September 18,255 79,012 X Xb Xb Xb n.a. n.a.
17 97 Encuesta Nacional de Hogares - Fuerza de Trabajo September 32,442 143,398 X Xb Xb Xb n.a. n.a.
18 Costa Rica 81 Encuesta Nacional de Hogares - Empleo y Desempleo July 6,604 22,170 X n.a. n.a. n.a. n.a. n.a.
19 83 Encuesta Nacional de Hogares - Empleo y Desempleo July 7,132 23,449 X n.a. n.a. n.a. n.a. n.a.
20 85 Encuesta Nacional de Hogares - Empleo y Desempleo July 7,351 23,960 X n.a. n.a. n.a. n.a. n.a.
21 87 Encuesta de Hogares de Propósitos Múltiples July 7,510 34,591 X Xb Xb Xb n.a. n.a.
22 89 Encuesta de Hogares de Propósitos Múltiples July 7,637 34,368 X Xb Xb Xb n.a. n.a.
23 91 Encuesta de Hogares de Propósitos Múltiples July 8,002 35,565 X Xb Xb Xb n.a. n.a.
24 93 Encuesta de Hogares de Propósitos Múltiples July 8,696 37,703 X Xb Xb Xb n.a. n.a.
25 95 Encuesta de Hogares de Propósitos Múltiples July 9,631 40,613 X Xb Xb Xb n.a. n.a.
26 97 Encuesta de Hogares de Propósitos Múltiples July 9,923 41,277 X Xb Xb Xb n.a. n.a.
27 Dominican Republic 96 Encuesta Nacional de Fuerza de Trabajo February 5,548 24,041 X X X X n.a. n.a.
28 Ecuador 95 Encuesta de Condiciones de Vida July-Sept. 5,810 26,941 X X X X X X
29 El Salvador 95 Encuesta de Hogares de Propósitos Múltiples 1995 8,482 40,004 X Xb Xb Xb n.a. X
30 Honduras 89 Encuesta Permanente de Hogares de Propósitos Múltiples August 8,727 46,672 X n.a. n.a. n.a. n.a. n.a.
31 92 Encuesta Permanente de Hogares de Propósitos Múltiples August 4,757 24,704 X n.a. n.a. n.a. n.a. n.a.
32 96 Encuesta Permanente de Hogares de Propósitos Múltiples August 6,428 33,172 X n.a. n.a. n.a. n.a. n.a.
33 98 Encuesta Permanente de Hogares de Propósitos Múltiples February 6,493 32,696 X Xb Xb Xb n.a. n.a.
34 Mexico 84 Encuesta Nacional de Ingreso Gasto de los Hogares Third quarter 4,735 23,985 X X X X X X
35 89 Encuesta Nacional de Ingreso Gasto de los Hogares Third quarter 11,531 57,289 X X X X X X
36 92 Encuesta Nacional de Ingreso Gasto de los Hogares Third quarter 10,530 50,862 X X X X X X
37 94 Encuesta Nacional de Ingreso Gasto de los Hogares Third quarter 12,815 60,365 X X X X X X
38 96 Encuesta Nacional de Ingreso Gasto de los Hogares Third quarter 14,042 64,916 X X X X X X
39 Nicaragua 93 Encuesta Nacional de Hogares Sobre Medicion de Niveles de Vida February to June 4,455 24,542 X X X X X X
40 Panama 79 Encuesta Continua de Hogares - Mano de Obra July 8,593 24,284 X n.a. n.a. n.a. n.a. n.a.
41 91 Encuesta Continua de Hogares - Mano de Obra July 8,867 38,000 X Xa Xa X n.a. n.a.
42 95 Encuesta Continua de Hogares July 9,875 40,320 X Xa Xa X n.a. n.a.
43 97 Encuesta de Hogares July 9,897 39,706 X Xa Xa X n.a. n.a.
44 Paraguay 95 Encuesta de Hogares - Mano de Obra August to November 4,667 21,910 X X X X n.a. n.a.
45 Peru 85-86 Encuesta Nacional de Hogares sobre Medición de Niveles de Vida July 1985 to July 1986 5,108 26,323 X X X X X X
46 91 Encuesta Nacional de Hogares sobre Medición de Niveles de Vida August-October 2,308 11,507 X Xa Xa X X X
47 94 Encuesta Nacional de Hogares sobre Medición de Niveles de Vida April-June 3,623 18,662 X Xa Xa X X X
48 96 Encuesta Nacional de Hogares sobre Niveles de Vida y Pobreza April-June 16,744 88,863 X Xa Xa X X X
49 97 Encuesta Nacional de Hogares sobre Niveles de Vida y Pobreza August-October 3,843 19,575 X Xa Xa X X X
50 Venezuela 81 Encuesta de Hogares por Muestra Second semester 45,421 239,649 X n.a. n.a. n.a. n.a. n.a.
51 86 Encuesta de Hogares por Muestra Second semester 129,713 682,636 X n.a. n.a. n.a. n.a. n.a.
52 89 Encuesta de Hogares por Muestra Second semester 61,385 315,650 X n.a. n.a. n.a. n.a. n.a.
53 93 Encuesta de Hogares por Muestra Second semester 61,477 306,629 X n.a. n.a. n.a. n.a. n.a.
54 95 Encuesta de Hogares por Muestra Second semester 18,702 92,450 X Xb Xb Xb n.a. n.a.
55 97 Encuesta de Hogares por Muestra Second semester 15,948 76,965 X Xb Xb Xb n.a. n.a.
a. Can not separate between property and capital rent.
b. Can not separate between property rent, capital rent, and transfers.
Sample size Income