PS 2 706
POLICY RESEARCH WORKING PAPER 2706
Household Income Is effective social protection
an investment with long-term
Dynamics in Rural China benefits? Does inequality
impede growth? Household
panel data on incomes in
Jyotsna Jalan
rural China offer some
Martin Ravallion
answers.
The World Bank
Development Research Group
Poverty Team
November 2001
POLic)' RESEARCH WORKING PAPER 2706
Summary findings
Theoretical work has shown that nonlinear dynamics in nonlinearity in the income and expenditure dynvmaics,
household incomes can yield poverty traps and there is no sign of a dynamic poverty trap.
distribution-dependent growth. If this is true, the The authors argue that existing private and sacial
potential implications for policy are dramatic: effective arrangements in this setting protect vulnerable
social protection from transient poverty would be an households from the risk of destitution. Howvem e r, their
investment with lasting benefits, and pro-poor findings imply that the speed of recovery from an income
redistribution would promote aggregate economic shock is appreciably slower for the poor than for others.
growth. They also find that current inequality reduces fLiture
Jalan and Ravallion test for nonlinearity in the growth in mean incomes, though the "growth (ost" of
dynamics of household incomes and expenditures using inequality appears to be small. The maximum
panel data for 6,000 households over six years in rural contribution of inequality is estimated to be 4-7 percent
southwest China. While they find evidence of of mean income and 2 percent of mean consumption.
This paper-a product of the Poverty Team, Development Research Group-is part of a larger effort in the grou p to better
understand the dynamic processes influencing household welfare in risk-prone environments. Copies of the paper are
available free from the World Bank, 1818 H StreetNW, Washington, DC 20433. Please contact Catalina Cunaran, room
MC3-542, telephone 202-473-2301, fax 202-522-1151, email address ccunananteworldbank.org. Policy Research
Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at
jialan(aworldbank.org or mravallion@worldbank.org. November 2001. (28 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas a )ut
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. khe
papers carry the names of the authors and should he cited accordingly. The findings, interpretations, and conclusions expressed in ihis
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executitve Directors, oi the
countries they represent.
Produced by the Policy Research Dissemination Center
Household Income Dynamics in Rural China
Jyotsna Jalan and Martin Ravallion'
Indian Statistical Institute and the World Bank
I The research reported here would not have been possible without the help of the Rural Household
Survey Team of China's National Bureau of Statistics and our colleague Shaohua Chen at the World
Bank. Our thanks also go to the World Institute for Development Economics Research (WIDER) and the
World Bank for their support of this research and to Stefan Dercon, Marcel Fafchamps and participants at
a WIDER conference for their comments.
1. Introduction
It is widely believed that a publicly provided safety net - based on transfer payments to
those deemed to be currently poor - can provide an important short-term palliative in the
presence of uninsured risk. However, a body of recent theoretical work has suggested that safety
net policies may well serve a deeper role in alleviating poverty in the longer term.
This new perspective stems from the realization that widespread credit and risk-market
failures can entail efficiency enhancing functions for a well-designed safety net. With limited
access to credit, or other forms of (formal or informal) insurance, a household will suffer from a
transient shock - an unexpected but short-lived drop in income. However, it is also possible in
theory that such a shock can cause a previously non-poor family to become poor indefinitely; or
cause a moderately poor family to fall into persistent destitution. If this theoretical possibility is
borne out by the evidence then there are important implications for knowledge about poverty and
anti-poverty policies. Lack of a well-functioning safety net might well be a structural cause of
persistent poverty. And there will be large long-term benefits from institutions and policies that
protect people from transient shocks.
The long-run effect of a transient shock depends on properties of household income
dynamics. And they are properties which we currently know very little about. Granted, if
household incomes follow the simplest type of linear auto-regression then a household that
experiences a transient shock will see its income bounce back in due course. The serial
dependence will mean that the family stays poor for a longer period than the duration of the
shock. Incomes will not adjust instantaneously. Nonetheless, the household will recover from
any draw from a distribution of serially independent income shocks. However, there is no
theoretical reason why incomes would behave this way. Linear dynamics is an ad hoc
2
assumption. Indeed, economic theory has pointed to the possibilities for poverty traps arising
from multiple equilibria in the dynamics such that destitution can arise from short-lived shocks.
This is not a new idea. Nonlinear dynamic models with multiple equilibria have been widely
used in explaining why seemingly similar aggregate shocks can have dissimilar outcomes.2 A
central feature of these models is the existence of a nonconvexity in the dynamics of househo ld
incomes, giving rise to a low-level unstable equilibrium. The nonconvexity can stem from effrcts
of past consumption on current productivity, as in the Efficiency Wage Hypothesis (Mirrlees,
1975; Stiglitz, 1976). In such models, a vulnerable household may never recover from a
sufficiently large but short-lived shock.
Whether such nonconvexities in the dynamics are important in practice, and constitute a
new case for safety net interventions, is a moot point. If multiple equilibria existed then there
will be high social returns to arrangements that protect vulnerable households - arrangements
that might well be implementable by private means, such as through repeated interaction in risky
environments (Coate and Ravallion, 1993). It can be conjectured that institutions will develor
that assure - possibly imperfectly and at non-negligible cost - that most incomes exceed the
low-level unstable equilibrium, thus avoiding the dynamic poverty trap.
Even without poverty traps, it is known that credit market failures can generate nonlinear
dynamics whereby the rate of growth in an economy depends critically on the initial distribution
of income or wealth (Benabou, 1996; Aghion and Bolton, 1997; Aghion et al., 1999). By
implication, as long as redistributive policies do not unduly jeopardize other determinants of
growth, they can enhance long-term prospects of escaping poverty. The arguments that initial
2 In macroeconomics, examples can be found in models of the business cycle (Chang and Smyta,
1971; Varian, 1979) and certain growth models (Day, 1992; Azariades, 1996). Similar ideas have been
employed in modeling micro poverty traps (Dasgupta and Ray, 1986; Banerjee and Newman, 1994;
Dasgupta, 1997) and in understanding famines (Carraro, 1996; Ravallion, 1997).
3
distribution matters to future growth also rest on a type of nonlinearity in the dynamics, such that
individual income is a concave function of its own lagged value, i.e., a concave recursion
diagram. While there is some supportive evidence from cross-country regressions, this is
arguably a rather weak basis for testing, given the known problems encountered, such as the
potential for spurious correlations between growth and inequality arising from inconsistent
aggregation across the underlying microeconomic relationships (Ravallion, 1998)
This paper tests for nonlinearity in income and expenditure dynamics in rural China. The
setting for our empirical work is rural southwest China in the period 1985-90. With Deng's
reforms starting in the late 1 970s, the collective mode of agricultural production had been
disbanded in favor of a household-based responsibility system. These reforms brought rapid
growth in rural incomes - initially in agriculture, but in due course helping foster non-farm
rural development. But it is likely that greater self-reliance that came with the break up of the
collectives, and more heavy reliance on markets, also left many households facing greater risk.
We analyze a household-level panel data set spanning six years, 1985-90, in four
contiguous provinces, Guangdong, Guangxi, Guizhou and Yunnan. From past research
(reviewed later) we know that poor farm-households in this setting are exposed to uninsured
incomes and health risks. However, identifying the long-term effects of measured risks is clearly
difficult. Six years is not long enough to confidently distinguish a slow process of adjustment
after a shock - such that a unique long-run equilibrium is restored - from a more complex
dynamic process with multiple equilibria arising from a non-convexity at low incomes.
We adopt a different approach that is feasible with the data. Instead of attempting to
trace the long-run impacts of measured shocks, we directly study the process of income
dynamics to see if it is consistent with the type of nonlinearity postulated in the aforementioned
4
theoretical work. With repeated shocks we are presumably observing most households out (if
their steady-state equilibrium. The time series for each household can then reveal the dynamics
of adjustment out of equilibrium. At any given long-run equilbrium, some households will
simply be returning to that equilbrium. However, if there is also a low-level unstable equilibrium
and sufficiently large uninsured shocks, then we should find both rising and falling incomes
amongst the currently poor, with a tendency for incomes to fall amongst the poorest. To make
this test feasible with only six years of data, the adjustment process is assumed to be common
across households (though allowing for household-specific long-run equilibria). The
specification allows the possibility of a low-level unstable equilibrium. In the process, we also
see if the recursion diagram is concave, such that current distribution matters to future growth.
Our estimation method allows for measurement error in observed incomes and other sources of
correlation between lagged incomes and the error term.3
The following section describes the setting for our study. Section 3 puts the present paper
in the context of our other recent work on the same data set. Section 4 reviews the arguments as
to why we might expect to find nonlinear dynamics. We then turn to our econometric model
(section 5), and results (section 6). Conclusions can be found in section 7.
2. The setting and data
The household panel used in this study was constructed from China's Rural Household
Surveys (RHS) conducted by the National Bureau of Statistics (NBS) since 1984.4 The data set
3 In a linear ARI model, under (over) estimating the lagged income would lead to over (under)
estimation of the subsequent change in income - a source of bias in OLS estimates of dynamic models
commonly known as "Galton's fallacy". The problem is more complicated in a nonlinear dynamic model,
but the general concern with measurement error in lagged incomes remains.
4 Further details on this survey, and the way it has been processed for this study, can be found in
Chen and Ravallion (1996).
5
covers four contiguous southern provinces over the period, 1985-90. Three of the four provinces
(Guangxi, Yunnan and Guizhou) constitute one of China's poorest regions, while the fourth is
the prosperous coastal province of Guangdong (Chen and Ravallion, 1996). The original panel
consists of over 6,000 households observed over the period 1985-90 (after which the sample was
rotated).
The RHS is a good quality budget and income survey, notable in the care that goes into
reducing both sampling and non-sampling errors (Chen and Ravallion, 1996). Sampled
households maintain a daily record on all transactions, as well as log books on production. Local
interviewing assistants (resident in the sampled village, or another village nearby) visit each
sampled household at roughly two weekly intervals. Inconsistencies found at the local NBS
office are checked with the respondents. The sample frame of the RHS is all registered
agricultural households except those who have moved to cities.
Our measure of consumption expenditure based on the RHS includes spending (either in
cash or the imputed values of in-kind spending) on food, clothing, housing, fuel, culture and
recreation, books, newspapers and magazines, medicines and non-commodity expenditures like
transportation and communication, repairs etc. The income variable includes both cash and
imputed values for in-kind income from various sources (farm-household production, forestry,
animal husbandry, handicrafts, gifts) as well as labor earnings and income received as a gift.
Our income variable does not include borrowings from (or loans to) informal and/or formal
sources.
There was very little sample rotation in the RHS between 1985 and 1990. The panel was
formed from the sequence of cross-sectional surveys. From discussions with RHS staff we
decided that the identifiers in the data could not be trusted for forming the panel. Fortunately,
6
virtually ideal matching variables were available in the financial records, which gave both
beginning and end of year balances. Relatively stringent criteria were used in defining a panel
household, with extensive cross-checks to assure that the same household was being tracked over
time. The relatively few ties by these criteria could easily be broken using demographic data.
About one third of the original sample could not be matched by our criteria. Some of this is
attrition, but probably the main reason was that the household changed sufficiently for it not to
be classified as a panel household by our criteria.
In studying nonlinear income dynamics using panel data, there is a concern that attrition
may well be endogenous to shocks (Lokshin and Ravallion, 2001); for example, with a sufficient
negative shock, a household may become destitute and drop out of the panel. We cannot
distinguish such households from those that changed too much to keep in the panel or those who
were replaced by the surveyors for some other reason and so were dropped from the panel.
However, endogenous attrition may not be a concern in this setting. Sampled households in the
RHS are paid to participate, and no doubt this encourages continuing participation by the poor.
Furthermore, results from Lokshin and Ravallion (2001) indicate that estimates of the
nonlinearity in income dynamics for Russia and Hungary are robust to allowing for endogenous
attrition (through a non-zero correlation between the error terms in the attrition model and the
dynamic income regression).
3. Risk and poverty in southwest China
In past research, we have found considerable vulnerability to both idiosyncratic and
(village-level) covariate risks in this setting. In Jalan and Ravallion (1999) we tested for
systematic wealth effects on the extent of consumption insurance against income-risk. Motivated
by the theory of risk-sharing, our tests entailed estimating the effects of income changes on
7
consumption (with current income treated as endogenous), after controlling for aggregate shocks
through interacted village-time dummies. We also tested for insurance against covariate risk at
village level. To test for wealth effects, we stratified our sample on the basis of household wealth
per capita, and whether or not the household resides in a poor area. The full insurance model was
convincingly rejected. The lower a household's wealth, the stronger is the rejection, in that the
estimated excess sensitivity parameter on changes in current income (implied by the test
equation for consumption changes) is higher for less wealthy households.5 We interpret these
results as indicating that, while there are clearly arrangements for consumption insurance in these
villages, they work considerably less well for the poor.
It is not then surprising that we also find considerable transient poverty in this setting.
Year-to-year fluctuations in consumption account for one third of the mean poverty gap (Jalan
and Ravallion, 1998). About 40% of the transient poverty is found amongst those who are not
poor on average, but almost all of this is for households whose average consumption over time is
no more than 50% above the poverty line. A comparison with similar tests for three villages in
semi-arid areas of rural India (Chaudhuri and Ravallion, 1994) suggests that there is far more
transient poverty in this region of rural China.
These findings tell us nothing about the long-term consequences of uninsured risk. We
have also studied portfolio and other behavioral responses to idiosyncratic risk using the same
China panel (Jalan and Ravallion, 2001). In keeping with past empirical work on precautionary
wealth, we extracted a measure of income risk from a first-stage income regression estimated on
household panel data and then used this measure of risk as a regressor in attempting to explain
5 This conclusion was found to be robust to changes in the set of instruments, and to changes in the
wealth measure. It holds for both total consumption and food consumption, although the latter is better
protected. There is little sign, however, that living in a poor area enhances exposure to risk at a given
level of individual wealth.
8
liquid wealth holdings.6 Our results suggest that wealth is held in unproductive liquid forms to
protect against idiosyncratic income risk. However, we find that the effect is small; even if all
income risk were eliminated, the mean share of wealth held in liquid forms would fall only
slightly, from 26.5% to 25.8%. We also find that there is an inverted U relationship between ihe
precautionary wealth effect and permanent income, such that neither the poorest quintile nor the
richest appear to hold liquid wealth because of income risk; it is the middle income groups that
do so. We suspect that the rich do not need to hold precautionary liquid wealth, and the poor
cannot afford to do so. We have found some evidence that liquid wealth is also held as a
precaution against risk to foodgrain yields (independently of income risk). We found no clear
signs of a precautionary response to health risk, though our measure (based on medical spending)
is far from ideal (Jalan and Ravallion, 2001). Schooling and (hence) future incomes appear to be
protected from both income and health risk. However, greater uncertainty about incomes at home
does appear to constrain the temporary out migration of family labor.
In the following analysis we turn to yet another possible longer-term implication of risk,
such that vulnerable households can never escape from the adverse impact of a short-lived
(serially independent) but sufficiently large uninsured shock. We next discuss how this might
come about in theory.
4. Theoretical models with nonlinear dynamics
Probably the simplest model that can generate a dynamic poverty trap assumes that a
family cannot borrow or save and derives income solely from labor earnings, but with a
nonconvexity at low earnings arising from a dependency of the worker's productivity and
6 We extended past methods by allowing for serial dependence in income shocks and by using
quantile regression methods that are more robust to the evident non-normality in the data on liquid wealth
holdings (Jalan and Ravallion, 2001).
9
(hence) wage rate on consumption. (We discuss alternative interpretations of this nonconvexity
below.) Nonlinear dynamics can be introduced by simply assuming that the wage rate in any
period is contracted at the beginning of the period. Finally we assume that this dynamic process
of income determination has at least one stable equilibrium.
Combining these assumptions, the process generating the current income of household i
(y, 2 0 ) with exogenous characteristics xi, can be written as the nonlinear difference equation:
Yi, = f (Yi,- ], xid (1 )
where f is continuous and vanishing for all y0) and the function is increasing and concave
in Yit-I for all y>yo. (The control variables xit are of a sufficient dimension that the functionf is the
same across all i.) An equilibrium of this model is a steady-state solution that varies with xit such
that y = f(y, xi,) . It is evident that if there is more than one such solution then there will be an
unstable equilibrium. The recursion diagram in Figure I illustrates a case of multiple equilibria.
There are two attractors, at 0 and yT (>yo), and y* is an unstable equilibrium. Consider a
household at y . With any shock exceeding y - y ** , the household will be driven beyond the
unstable equilibrium, and will then see its income decline steadily towards zero. Destitution will
be the inevitable result.
One can propose more complicated models. For example, one can allow for some
positive lower bound to incomes. Assuming that this lower bound is below y in Figure I there
will be a stable equilibrium at the lower bound. Again, with a large negative shock, a household
at its high (stable) income will see its income decline until it reaches the lower bound.
There are several possible interpretations of the nonconvexity. One is the Efficiency
Wage Hypothesis (Mirrlees, 1975; Stiglitz, 1976; Dasgupta and Ray, 1986; Dasgupta, 1993).
10
This assumes that labor productivity and earnings are zero at a low but positive level of
consumption; only if consumption rises above some critical level, yo>0, will the worker be
productive. In the efficiency wage literature, yo is usually interpreted as the nutritional
requirements for a basal metabolism, which account for about two-thirds of normal nutritional
requirements (Dasgupta, 1993).
There are other interpretations. One can assume that a minimum expenditure level is
necessary to participate in society, including getting a job. The expenditure is required for
housing and adequate clothing. Thus one can say that consuming below this point creates "social
exclusion." Higher consumption permits social inclusion, but there are presumably diminishing
income returns to this effect. For example, earnings rise but at a declining rate until after some
point the productivity effect of consumption vanishes.
Alternatively, we can think of a liquidity-constrained household that faces the choice of
investing in (physical or human) capital accumulation or consuming all income in a given period.
Suppose that the household is only willing to forgo current consumption in order to invest if its
income exceeds a critical level yo. The investment yields an income at time t off (yt-) where this
function has the same properties as above.
Nonlinearity in the dynamics also has implications for the growth rate of mean household
income. Mean current income is:
n
y' = If (yi,- ],xi,)/n (2)
i=1
If the functionf is nonlinear in yi, l then initial distribution will matter to future income at given
current income. Iff is strictly concave in yit-l then the mean current income will be a strictly
quasi-concave function of the levels of income in the previous period. By the properties of
concave functions, higher initial inequality will entail lower future mean income for any given
11
initial mean, holding x,t constant for all i. Recent theoretical papers have shown how concavity
of the recursion diagram for income or wealth can arise from credit market failures, given
decreasing returns to own capital (Benabou, 1996; Aghion and Bolton, 1997; Aghion et al.,
1999; Banerjeee and Duflo, 2000).
This type of model has a powerful policy implication. A transfer payment not less than
y will eliminate the low-income unstable equilibrium. The family will be fully protected from
the possibility of a transient shock having an adverse long-term effect. Not only will the transfer
help protect current living standards, but it will also generate a stream of future income gains. An
effective safety net will then be a long-term investment, and with a potentially high return.
5. Econometric model
We now look for evidence in our data of the type of nonlinear dynamics discussed above.
We introduce the nonlinearity in the form of a cubic function of the lagged dependent variable in
a panel data model. (Lokshin and Ravallion, 2001, further discuss this specification choice.)
Another point to note is that we allow for only first-order autoregression in our model. This is
done primarily to estimate a parsimonious model given that we have a very short time-series for
each household. We also allow for an independent time trend. Thus our general econometric
specification for i at date t is of the form:
Yit = a + St + ±iYi,-I + A2Yit_l + A3Yi3-I + Pi + 6it (i = 1,2..N; t = 1,2,..T) (3)
where ,ui is an unobserved individual effect, and ci, is an identically and independently distributed
innovation error term. We estimate this model for both income and consumption. We eliminate
the unobserved fixed effect gui which is potentially correlated with lagged income (and its
squared and cubed values) by taking the first differences of equation (3) giving:
12
Ayv, = y + f,Ayi,1 + i2ty2 + Ayj,1 + Ac, (4)
This model is estimated with and without the trend in income or expenditure, to see how this
affects the estimated dynamics.
Least squares estimation of equation (4) would still yield biased and inconsistent
coefficient estimates due to correlation between lagged income changes and the differenced
innovation error term. Assuming that the /i,'s are serially uncorrelated, the GMM estimator is the
most efficient one within the class of instrumental variable (IV) estimators. In estimating (4), we
follow standard practice in using Yit-2 or higher lagged values (wherever feasible) as instrumental
variables (Arellano and Bond, 1991). (The Appendix gives further details, including on
diagnostic testing.) Similar moment conditions are used for Ay i,1 and Ay,_I. We do not
necessarily use all the moment conditions available to us. We choose the most parsimonious set
of moment conditions based on the minimum value of the estimated objective function. In
checking the validity of our instruments, the null hypotheses of the tests for over-identification
and second-order serial correlation were accepted within standard levels of significance
(Appendix). Notice that our GMM estimation method allows for any serially independent
measurement error.
6. Results
For purely descriptive purposes, Table 1 gives household recovery times following a drop
in measured expenditure. We chose all households who had a decline in their real expenditure
between the first two years of the surveys and categorized these households according to the time
it took them to get back to at least 98% of their expenditure in the first year of the survey.
13
We find that slightly more than half of the households that had a negative expenditure
change recovered the loss within one year. However, 20% had not recovered within five years.
The time it takes to recover depends of course on the size of the initial expenditure contraction.
Among households that experienced a decline in expenditure of less than 5% between the first
and the second year of the survey, 63% recovered within one year. Among those that lost more
than 10% between the first two years of the survey, two-thirds had not recovered after five years.
These calculations might be interpreted as indicating that two types of dynamics exist.
For the first type, an initial income shock leads to only a temporary drop in household income.
For the second type the shock appears to have been more devastating, putting them on a
declining income path possibly leading to chronic poverty.
That interpretation is questionable, however, since there are other ways one might explain
Table 1. Possibly the households that had not recovered, experienced other shocks in the
intervening period. Or possibly they were returning more slowly to their steady state equilibrium.
Or possibly the first shock was not transient, and lasted for many years. Or the shock may have
been transient, but the recursion process is linear with a slow speed of adjustment due to sizable
lagged effects of past incomes on current incomes.
For these reasons, one cannot conclude from Table 1 that short-lived shocks have long-
lived impacts. We need to use our model of the dynamics to see if the structural process
generating consumption and income is consistent with the type of non-linearity whereby
sufficiently large shocks can create long-term poverty.
Turning to the model of income dynamics, Table 2 gives our estimates of equation (4)
without the trend (suppressing the constant term in 4).7 Table 3 gives the results including the
7 The sample mean annual income is Yuan 446 per capita at 1985 prices (with a standard deviation
of 264), while the corresponding mean for expenditure is Yuan 345 (standard deviation of 166).
14
trend. The trend coefficient (i.e., the constant term) is not significantly different from zero for
income, but it is for expenditure. The preferred model for income is that without the trend w.ile
that for expenditure is with a trend.
Figures 2 to 5 give the recursion diagrams in all four cases. To retrieve the recursion
diagram from the estimated parameters of (4) we treat the distribution of time mean incomes and
expenditures as the distribution of long-run (steady) state values. Thus the recursion diagram for
the p'th percentile with income yP is:
yp .P p J1 (Y pt_l _ p ) + f2 (yp,_] _ y p)2 + A3 (Yp- _ y )p (5)
Figures 2 to 5 indicate that there is nonlinearity in the range of the data, with concavity suggested
in all cases except the expenditure model without trend. However, there is no sign of a
nonconvexity, even at low levels of long-run income or expenditure.
The concavity in the recursion diagram implies that higher initial income inequality (in
the sense of mean-preserving spreads) will reduce future mean income at a given current mean.
We can construct a natural measure of the contribution of inequality to growth as:
I, = f[M(yi,)] - M[f(y;,)] (6)
where M[.] denotes the mean of the term in brackets (the mean being taken over all i at date t'l.
This must be positive wheneverf is concave. Using the models without trend, our estimates of
(6) represent 4. 1% of mean income and 1.7% of mean expenditure; in the models with trend, the
corresponding numbers are 6.5% and 2.1%.
A further implication of concavity in the recursion diagram is that the speed of
adjustment will be lower for households with lower steady-state incomes. The speed of recovery
from an income loss is 1- ay,, / &y,,, . At one extreme, a (serially-independent) transient shock to
a household at date t-l has no impact on the household's period t's income and thus the speed of
15
adjustment is unity. At the other extreme, if income at data t is still lower than it would have
been otherwise by the full amount of the shock at t-l then the speed of recovery is zero. Given
thatf is strictly concave, the speed of recovery must be a strictly increasing function of yi,I .
Figure 6 gives the speed of recovery as a function of y,,1 for income (using the preferred
model without trend). For a household at zero income, the speed of recovery is 0.45. For a
household with annual income of around 240 Yuan per capita (around the mean poverty line
across the four provinces, as estimated by Chen and Ravallion, 1996) the speed of recovery is
0.52. For household with an income of 900 Yuan per capita (roughly the 95th percentile) the
speed of recovery from a shock rises to about 0.76, while it reaches unity at around 1400 Yuan
(the 99th percentile is at 1441 Yuan), at which point the shock has no effect beyond the current
year.
Figure 7 gives the corresponding figure for expenditures (based on the preferred model,
with trend). At given y,,1 , the speeds of recovery are considerably higher for expenditures,
reflecting consumption smoothing. The value of oy,, / 8yj,, becomes negative at high
expenditures (Figure 3), implying speeds of recovery over unity, which would seem unlikely and
may well reflect a problem with the model specification for consumption dynamics. However,
the bulk of the data (about 90%) is in the region with speeds of recovery below unity.
7. Conclusions
We have tried to assess whether existing (private and social) arrangements within a poor
rural economy are able to avoid what is possibly the worst potential manifestation of uninsured
risk, namely that a sufficiently large transient shock might drive a household into permanent
destitution. This requires a specific kind of nonlinearity in the dynamics of household incomnes.
16
Economic theory offers little support for the common assumption of linear dynamics, whereby
households inevitably bounce back in time from a transient shock. Theoretical work has pointed
to the possibility of a low-level nonconvexity in the recursion diagram, such that a short-lived
uninsured shock can have permanent consequences. It is an empirical question whether the
dynamics found in reality exhibit such properties.
Our test entails estimating a dynamic panel data model in which income (or expenditure)
is allowed to be a nonlinear function of its own lagged values. As is invariably the case, we have
had to impose a structure on the data. The most restrictive assumption we have had to make is
that, while long run-equilibria differ across households, the out-of-equilbrium adjustment process
is common to all households. Our household panel is not short by developing-country standards,
but in order to relax this restriction, more time series observations would be needed to relax this
restriction.
On calibrating the model to household panel data for rural areas southern China, we do
find some evidence of nonlinearity in the dynamics. However, we find no evidence of low-level
nonconvexities. The data are not consistent with the existence of an unstable equilibrium for the
poor. This suggests that households in this setting tend to bounce back in due course from
transient shocks. Our results are broadly consistent with those of Lokshin and Ravallion (2001)
using panel data for Russia and Hungary. While we do not find evidence of a poverty trap
arising from nonlinear dynamics, in other work we have found strong signs of geographic
poverty traps in these data, whereby location matters crucially to prospects of escaping povertv
at given (latent and observed) household characteristics (Jalan and Ravallion, 2002).
We find evidence of concavity in the recursion diagram. One implication of this findino
is that the speed of recovery from a transient shock is lower for those with lower initial income.
17
The differences in recovery speeds between the "poor" and "rich" appear to be sizable,
particularly for incomes. So, while our results suggest that the poor eventually bounce back
from short-lived shocks, the adjustment process is slower than for the non-poor.
The type of nonlinearity that we find also suggests that the growth rate of household
incomes in this setting will depend on higher moments of the initial distribution than its mean.
Depending on the model specification, we find that inequality contributes 4-7% to mean income
and about 2% to mean expenditure. These figures are appreciably lower than those obtained by
Lokshin and Ravallion for Russia and Hungary, where inequality appears to be more costly to
growth.
18
Appendix: GMM estimation of the nonlinear dynamic model
The GMM estimator for the parameter vector v = (y, 1, f8i2 , 83 ) is defined as:
v = (q'wa11w'q)' (q'wa,,w'Ay)
where q = [e, Ay_1, Ay21, Ay31 ]N is the set of regressors with eNa vector of ones, w is the
matrix of instrumental variables, a, is the weighting matrix, and Ay is the (NTxl) vector of the
first differences of the dependent variable. The optimal choice of a, (in the sense of giving the
most efficient estimator asymptotically) is proportional to the inverse of the asymptotic
covariance matrix (Hansen, 1982). Heteroscedastic consistent standard errors are computed
using the residuals from a first-stage regression to correct for any kind of general
heteroscedasticity.
Inferences on the estimated parameter vector v are appropriate provided the moment
conditions are valid. Sargan's (1958) and Hansen's (1982) chi-square test of the over-identifying
restrictions was implemented to check whether the exclusion restrictions are consistent with the
data. The degrees of freedom for this test are calculated as the difference between the number of
columns in the instrument matrix and the number of parameters to be estimated in the model. A
second-order serial correlation test was also constructed, given that the consistency of the GMM:
estimators using twice (or higher) lagged dependent variables as instruments for the first
differenced model depends on the assumption that E(Ae,, A-ie2 ) = 0 (the test-statistic is
8 In the just-identified case (i.e. in the case where the number of moment conditions are exactly
equal to the number of parameters to be estimated), the parameter estimates do not depend on the
weighting matrix and hence the choice of an, is redundant.
19
normally distributed).9 Both tests passed at the 5% level.
9 There may be some first-order serial correlation, i.e., E(Ae1 t ) may not be equal to zero
since A-,1 are the first differences of serially uncorrelated errors.
20
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23
Figure 1: Recursion diagram exhibiting nonlinear dynamics
Yt Yt=Yt-I
I f(y I )
0 YO y* * tI
24
Figure 2: Expenditure model without trend
5th percentile Median
i---- 75th percentile 45 degrees line
1500 H
1000
0 500 1000 1500
Expenditure per capita
Figure 3: Expenditure model with trend
5th percentile - : Median
- --=/75th percentile 45 degrees line
1 500
1000
500 -
t ~~- a---atl-e H - H-9-F-=--a i --
0]
0 500 1000 1500
Expenditure per capita
25
Figure 4: Income model without trend
5th percentile - Median
e 75th percentile 45 degrees line
1500
1000
LI ~~~~~~~~A--tt -
L3
X, A
500-
0- -,-_ _ _ _ _ _ _ _ _ _ _ _ _ _ _-
0 500 1000 1500
Income per capita
Figure 5: Income model with trend
5th percentile - Median
-s---- 75th percentile -- 45 degrees line
1500
1000 -,
5~~~~ 0 l- C A A__Aff_A7 -- 5- - - --
I e-422~~~N ---
0
0 500 io00 1500
Income per capita
26
Figure 6: Speed of recovery from a transient income shock
1.1-
0.9-
E 0.8-/
0.7-
0.6 /
0
, 0.5- /
0.4
0 200 400 600 800 1000 1200 1400
Lagged income per capita
Figure 7: Speed of recovery from a transient expenditure shock
1.6
. 1.4-
0
E 1.2
0
> 1.0-
0
* 0.8
0.
0.6-
0 200 400 600 800 1000 1200 1400
Lagged expenditure per capita
27
Tablel: Recovery from an initial expenditure contraction
Recovery time Any shock Small shock Medium shock Large shock
after shock (Percentages)
I year 54.53 63.23 31.35 14.39
2 years 15.14 15.58 14.05 9.35
3 years 6.24 5.57 8.84 5.76
4 years 4.38 3.44 7.88 4.32
Never recovered 19.71 12.18 37.14 66.19
within the period
Note: Small shock: 5% or lower fall in household expenditure; Medium shock: 5%-] 0% fall in
household expenditure; Large shock: 10% or higher fall in household expenditure.
Table 2: Nonlinear dynamic model without trend
Expenditure Income
0.2468 0.5441
(11.989) (14.240)
Ay2 0.0113xI1-2 -0.0116x10-2
(4.067) (-5.228)
Ay 3 -0.0146x10-6 -0.0376x10-6
it-I ~~~~(-1.121 1) (-5.439)
Note: t-statistics in parentheses; higher lags used as instruments.
Table 3: Nonlinear dynamic model with trend
Expenditure Income
Trend 3.3894 -0.0316
(4.936) (-0.027)
Ayit-l 0.1613 0.5251
(6.428) (13.339)
2 -0.0893x10-3 -0.0101X0-2
(-2.420) (-4.539)
ty3 -0.01 15xl0-5 -0.0481x10-6
(-9.003) (-7.246)
Note: t-statistics in parentheses; higher lags used as instruments.
28
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