WPS3622
Trade Policy, Income Risk, and Welfare
Tom Krebs
Brown University
Pravin Krishna
Johns Hopkins University
William Maloney
World Bank
Abstract
This paper studies empirically the relationship between trade policy and individual
income risk faced by workers, and uses the estimates of this empirical analysis to
evaluate the welfare effect of trade reform. The analysis proceeds in three steps. First,
longitudinal data on workers are used to estimate timevarying individual income risk
parameters in various manufacturing sectors. Second, the estimated income risk
parameters and data on trade barriers are used to analyze the relationship between trade
policy and income risk. Finally, a simple dynamic incompletemarket model is used to
assess the corresponding welfare costs. In the implementation of this methodology using
Mexican data, we find that trade policy changes have a significant short run effect on
income risk. Further, while the tariff level has an insignificant mean effect, it nevertheless
changes the degree to which macroeconomic shocks affect income risk.
World Bank Policy Research Working Paper 3622, June 2005
The Policy Research Working Paper Series disseminates the findings of work in progress to
encourage the exchange of ideas about development issues. An objective of the series is to get the
findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and
conclusions expressed in this paper are entirely those of the authors. They do not necessarily
represent the view of the World Bank, its Executive Directors, or the countries they represent.
Policy Research Working Papers are available online at http://econ.worldbank.org.
We would like to thank Alberto Alesina, Pol Antras, Robert Feenstra, Pierre Gourinchas, Kishore
Gawande, Boyan Jovanovic, Mark Melitz, Marcelo Olarreaga, Arvind Panagariya, J. David Richardson and
seminar participants at Brown, Columbia, Georgetown, Harvard, International Monetary Fund, New York
University, Princeton, University of Pennsylvania, Rutgers, Syracuse, World Bank Research Department
and the 2004 Summer Meetings of the Econometric Society for many helpful comments and suggestions,
and Jungjin Lee for outstanding research assistance. We also gratefully acknowledge support from the
Research Committee and the Office of the Chief Economist for Latin America and the Caribbean at the
World Bank.
Corresponding Author. School of Advanced International Studies and Department of Economics, Johns
Hopkins University. Email: Pravin Krishna@Jhu.edu.
I. Introduction
The recent years have seen an increased integration of countries into the world economy
through trade and capital market liberalization. This has led to a parallel surge of inter
est in the academic and policy literature on the implications of increased "openness" of
countries to crossborder trade in goods and factors.1 The economic benefits and costs of
openness are now being actively debated: While many economists have pointed to the gain
in allocational efficiency that results from free international exchange, others have pointed
out potential downsides, arguing that openness may lead to an increase in income inequality
and, separately, income risk (income volatility). Although there is by now a large empirical
literature analyzing the impact of trade openness on wage levels and the distribution of in
come,2 an empirical analysis of the effect of trade openness on individual income volatility
has so far been lacking. This paper conducts such an empirical investigation, and uses the
empirical results in conjunction with a simple dynamic general equilibrium model to assess
the corresponding welfare effects.
The theoretical literature has suggested various channels through which trade reform might
affect individual income risk. For example, lowering trade barriers leads to an increase in
foreign competition in the importcompeting sectors and is likely to induce a reallocation
of capital and labor across firms and sectors. In the short run, the resulting turbulence
may raise individual labor income risk.3 Rodrik (1997), going beyond the short term re
1For a general discussion of the debate, see for instance, Rodrik (1997) and Bhagwati (2001).
2Early papers in this area include Lawrence and Slaughter (1993) and Borjas, Freeman and Katz (1992).
See Feenstra and Hanson (2002) for a comprehensive survey treatment.
3See, for instance, the analysis of policy change by Fernandez and Rodrik (1991), in which exante identical
workers experience expost different outcomes since some workers retain their jobs while others are forced to
move to other firms. More recently, Melitz (2003) has developed a formal framework in which trade policy
changes affecting an entire sector lead to heterogeneous outcomes at the firm level.
1
allocational effects of trade reform on income risk, has additionally argued that increased
foreign competition following trade reform will increase the elasticity of the goods and the
derived labor demand functions. If a higher demand elasticity translates any given shock
into larger variations in wages and employment, lower trade barriers may lead to increased
individual income risk.4 On the other hand, it has also been suggested that the world
economy is likely to be less volatile than the economy of any single country, which leads
to goods prices that are more stable worldwide than in any single autarkic economy. This
opens up the possibility that greater openness may reduce the variance in individual incomes.
Thus, theoretically, the opennessvolatility relationship is ambiguous, that is, the theoretical
literature does not offer a strong prior on the sign or magnitude of this relationship.5
In this paper, we study empirically the effects of trade policy on individual income risk using
the following approach. For each industry (sector), we use longitudinal data on individual
earnings to estimate timevarying parameters of individual income risk using a methodology
that follows the approach taken by the extensive empirical literature on labor market risk.6
More specifically, we focus on the variance of (unpredictable) changes of individual income as
a measure of income risk, and carefully distinguish between transitory and persistent income
shocks. The distinction between transitory and persistent income shock is important since
workers can effectively "selfinsure" against transitory shocks through borrowing or own
savings, which implies that the effect of these types of shocks on workers' consumption and
welfare are quite small (Aiyagari (1994), Heaton and Lucas (1996), Levine and Zame (2002)).
4While Rodrik (1997) appears to have in mind mostly aggregate volatility, it is easy to see that his argu
ments equally apply to individual income volatility if there are idiosyncratic shocks to firmlevel productivity.
5Clearly, this signambiguity does not extend to the shortterm reallocational effect of trade policy
reforms which, as we have discussed above, are generally expected to raise income risk. However, we do not
have strong priors on the magnitude of this relationship either.
6See, for example, Carroll and Samwick (1997), Gottschalk and Moffitt (1994), Gourinchas and Parker,
(2002), Hubbard, Skinner, and Zeldes (1994), Meghir and Pistaferri (2004), and Storesletten, Telmer, and
Yaron (2004).
2
In contrast, highly persistent or permanent income shocks have a substantial effect on the
present value of future earnings, and therefore lead to significant changes in consumption
even if workers can borrow or have own savings (Constantinides and Duffie (1996) and Krebs
(2003a and 2004)). Thus, from a welfare point of view, persistent income shocks matter the
most, and we therefore focus on the relationship between trade policy and the persistent
component of income risk.7 More specifically, after obtaining the estimates of the persistent
component of income risk for each year and industry, we use these estimates in conjunction
with tariff data (as a proxy for trade policy) to study empirically the effect of trade policy
on income risk.
In addition to the empirical analysis of the relationship between trade policy and income
risk, this paper also provides a quantitative evaluation of the welfare consequences of any
changes in income risk that are brought about by changes in trade policy. If insurance
markets and other institutional arrangements for sharing individual income risk are miss
ing (incomplete markets), then changes in income risk will alter consumption volatility and
therefore workers' welfare. To find out how income risk is linked to consumption volatility
and welfare, we use a dynamic general equilibrium model with incomplete markets in which
the consumption/saving choice of workers in the presence of idiosyncratic income risk is ex
plicitly modeled. As is well known, general versions of such models are difficult to solve, and
most work in the literature has therefore been computationally intensive (Aiyagari (1994),
Huggett (1993), Krusell and Smith (1998), RiosRull (1996)). In contrast to this literature,
we rely upon an extended version of the incompletemarkets model recently developed and
analyzed by Constantinides and Duffie (1996) and Krebs (2004) that is highly tractable,
7To see the importance of this distinction more clearly, consider the example of a worker who loses his
job due to plant closure or any other "exogenous" event. If the worker quickly finds a new job that pays
him as well as the previous job, then the worker's consumption level is not likely to drop by too much either
during or after the period of unemployment. If, on the other hand, the worker is forced to accept a job that
pays him a permanently lower wage because, for example, firm or occupationspecific human capital has
been lost, then the worker's likely response is to reduce consumption.
3
but still rich enough to allow for a tight link between the econometric framework and the
theoretical model. The welfare expressions that we derive theoretically can then be used to
translate changes in individual income risk into welfare changes.
Our previous discussion highlights the need for longitudinal information on incomes at a
disaggregated level (individual or household)8 in countries that have undergone discernable
(and ideally substantial) changes in their external regime. Unfortunately, countries that
maintain detailed longitudinal records on individual incomes have rarely undertaken major
trade reforms and countries that have undertaken extensive trade policy reforms have rarely
collected data on individuals of requisite scope and quality. In this paper, however, we focus
on one country that satisfies both criteria, namely Mexico. As it is well known, the Mexican
economy experienced substantial changes in trade policy in the late 1980's and in the later
half of the 1990s.
Our empirical results for the Mexican case can be summarized as follows. First, we find that
trade policy changes have a significant short run effect on income risk for industries with
high levels of import penetration, with a tariff reduction of five percent raising the standard
deviation of the persistent shocks to income by about twenty five percent. In terms of welfare,
we find that this increase in income risk is equivalent to a decrease in lifetime consumption
by almost one percent (using a discount factor and degree of risk aversion that are standard
in the macroeconomic literature, Cooley (1995)) for workers in the high importpenetration
industries.9 Second, the effect of the tariff level on income risk is insignificant. Third,
8It should be clear that our need for longitudinal data follows from our desire to study how trade policy
impacts the magnitude and frequency of individual income shocks (changes). This is a quite distinct task
from that of measuring the impact of trade policy on the distribution of income levels.
9Even though these are only shortrun effects, the fact that we are dealing with permanent income shocks
to individual workers means that in this relatively short period some of the workers get scarred for life.
Thus, ex ante, workers are willing to give up a substantial amount of their expected lifetime consumption in
return for the elimination of the risk of losing with a trade reform.
4
while the tariff level has an insignificant mean effect, it nevertheless changes the degree to
which macroeconomic shocks affect income risk. For instance, we find that tariff reductions
increase the cost of recessions substantially. More specifically, at a tariff level of ten percent
a reduction in the growth rate of GDP of five percent is estimated to raise the standard
deviation of persistent income shocks by twelve percent, whereas at a five percent tariff rate
the same reduction in GDP growth increases income risk by twenty five percent. In terms of
welfare, this amounts to an increase in the cost of recessions that is equivalent to almost half
a percentage point of lifetime consumption. Notice, however, that our empirical estimates
also indicate that tariff reductions decrease individual income risk during economic booms,
so that the net welfare cost of tariff reforms due to this interaction effect is smaller than half
a percentage point of lifetime consumption.10
At this stage, it is worth pointing out some of the limitations of our analysis. First, we focus
exclusively on the link between trade policy and individual income risk, and therefore neglect
other channels through which trade policy may affect the economy. More specifically, one
would expect trade liberalization to have positive effects on the efficiency of resource allo
cation and economic growth (the mean of income changes), and these effects are important
factors that any comprehensive welfare analysis of trade liberalization ought to take into
account. Second, our welfare calculations do not allow for the possibility that an increase in
income risk might lead to a simultaneous rise in insurance opportunities (endogenous mar
ket incompleteness).11 Third, we follow a longstanding tradition in economics and measure
risk by the variance (second moment) of the relevant distribution, which is justified if (as
10Because of space limitations, in this paper we do not attempt to find a precise estimate of this welfare
cost taking into account both the increase in income risk during recessions and the decrease during economic
booms. Such an estimate could be found by adopting the methodological approach used in the literature on
the welfare cost of business cycles when markets are incomplete. See, for example, Krebs (2003b) and Lucas
(2003) for more details.
11See, for example, Attanasio and RiosRull (2000) and Krueger and Perri (2002), for a formal analysis of
this phenomenon in economies with limited commitment.
5
assumed in this paper) the economic variables of interest are (log)normally distributed. Fi
nally, the Mexican household survey we use to implement our general approach is a rotating
panel that follows individual workers for five quarters over time, which means that the panel
dimension of our income data is somewhat limited. Thus, our data do not allow us to assess
with certainty the persistence of income shocks beyond five quarters. However, a comparison
of our estimates of the income risk parameters with existing results that use data sets with
a much longer panel dimension suggests that a large fraction of the income shocks we label
"persistent" in this paper last indeed for many years (see Section II.5 for more details). In
short, the welfare results presented here do not necessarily show that trade liberalization is
costly, but they do provide strong evidence that any comprehensive welfare analysis of trade
liberalization ought to take into account the cost of increased labor market risk.
In summary, in this paper we articulate a general framework that allows us to study empiri
cally the impact of trade reform on individual income risk and to evaluate the corresponding
welfare effects. We use this framework to study the Mexican economy, which, as we have
argued above, seems wellsuited for such an analysis. In our empirical implementation of this
methodology using longitudinal data on Mexican workers, we find economically significant
effects of trade policy on income risk.
We conclude this introduction with a brief comment on some of the earlier empirical lit
erature on the relationship between trade policy and factors related to labor market risk.
The impact of trade liberalization on shortrun worker displacement has been investigated in
the wellknown papers of Currie and Harrison (1997), Gaston and Trefler (1994), Levinsohn
(1999) and Revenga (1997), among others. More recently, in an innovative paper, Trefler
(2004) has analyzed the shortrun adjustment costs borne by displaced workers simultane
ously with the long run benefits (of higher firm productivity and resource allocation) that
accrued in the context of the trade agreement between United States and Canada. While
6
these papers have provided us with very valuable analyses of the labor market impact of
trade policy reforms, they do not focus directly on income risk, which is the primary topic
of interest to the current paper. Specifically, none of the existing studies estimates an in
dividual income process that allows one to gauge the severity and persistence of shocks
to individual income (resulting, for instance, from job displacement following trade policy
reform), which, as we have argued above, is crucial when thinking about the welfare con
sequences of trade reform. In a similar vein, while several scholars have commented upon
the potential importance of the link between openness and aggregate volatility in the pres
ence of market incompleteness,12 empirical studies of the relationship between openness and
aggregate volatility (Rodrik (1998)) have the drawback that the welfare effects of aggregate
fluctuations are often found to be quite small (Lucas (2003)). In short, none of the previous
studies has analyzed the link between openness and income risk in the manner and detail
that we do here.
II. Income Risk
The first stage of our analysis concerns the estimation of individual income risk. Our esti
mation strategy follows earlier approaches in the literature estimating US labor income risk
(Carroll and Samwick (1997), Hubbard et al (1994), Gourinchas and Parker (2002), Meghir
and Pistaferri (2004), and Storesletten et al. (2004)) with some important differences which
we discuss in detail below. As in these papers, we define income risk as the variance of
(unpredictable) changes in individual income, and carefully distinguish between transitory
and persistent income shocks. From a welfare point of view, this separation is essential for
12Early theoretical analyses of trade patterns and optimal trade policy with aggregate risk and incomplete
markets include Eaton and Grossman (1985) and Helpman and Razin (1980), among others. An interesting
and somewhat related theoretical literature on international production and trade patterns with incomplete
contracting has been developed recently (see Antras (2004) and Helpman and Grossman (2002)), but it has
not (yet) considered explicitly either aggregate or idiosyncratic risk in the economic environment.
7
two reasons. First, consumption smoothing through borrowing or own saving works well for
transitory income shocks (Aiyagari (1994), Heaton and Lucas (1996), and Levine and Zame
(2002)), but not when income shocks are highly persistent or permanent (Constantinides
and Duffie (1996) and Krebs (2003a and 2004)). Thus, highly persistent income shocks have
a large effect on consumption volatility and welfare, whereas the effect of transitory shocks is
relatively small. Second, the transitory term in our econometric specification of the income
process will absorb the measurement error in individual income, and therefore allows us to
arrive at a better estimate of the true amount of individual income volatility. For these
reasons, we eventually focus on persistent shocks and their relation to trade policy.
II.1. Data
In Mexico, the National Urban Employment Survey (ENEU) conducts extensive quarterly
household interviews in the 16 major metropolitan areas and is available from 1987 (we use
data from 19871998 in our study). The ENEU is structured so as to track a fifth of each
sample across a five quarter period. The sample is selected to be geographically and socio
economically representative. The treatment of sample design, collection and data cleaning
is careful. The survey questionnaire is extensive in scope and covers all standard elements
such as participation in the labor market, earnings etc.13
We use information on labor market participants between the ages of 16 and 65. Individual
panels were constructed by matching workers by their position in an identified household,
level of education (years of schooling), age and sex. Questions referring to labor income refer
to income earned in the previous quarter. Workers earnings include their overall earnings
from fixed salary payments, hourly or daily wages, piecemeal work, commissions, tips and
any entrepreneurial earnings (earned by the selfemployed). Taken together, we have 44
13The actual surveys and documentation of methodology are available on request.
8
complete panels of 5 periods (i.e., quarters) each, spanning a total of 12 years (48 quarters).
Table I presents a summary description of the workers surveyed by the ENEU. Other aspects
of our ENEU data  the evolution of the mean and variance of earnings and returns to
education over time (not presented here but available on request)  matched the facts
about earnings in the Mexican labor market reported by previous authors.14
Data on sectoral trade barriers and other sectoral and macroeconomic variables were obtained
from the World Bank.
II.2. Specification
Our survey data provide us with earnings (wage rate times number of hours worked) of
individuals. As in previous empirical work, we assume that the log of this labor income of
individual i employed in industry j in period t, log yijt, is given by:
log yijt = jt + t · xijt + uijt . (1)
In (1) jt and t denote timevarying coefficients, xijt is a vector of observable characteristics
(such as age and education), and uit is the stochastic component of earnings. The stochastic
component uijt represents individual income changes that are not due to changes in the
return to observable worker characteristics. For example, income changes that are caused
by an increase in the skill (education) premium are not contained in uijt. In this sense,
uijt measures the unpredictable part of changes in individual income. Notice that we allow
the fixed effects jt to vary across sectors, but that the coefficient t is restricted to be
equal across sectors. The latter assumption is made in order to ensure that the number of
observations is large compared to the number of parameters to be estimated.
14See Hanson (2003) for a broad analysis of wage patterns in Mexico in the 1990s based on population
census data.
9
We assume that the stochastic term is the sum of two (unobserved) components, a permanent
component ijt and a transitory component ijt:
uijt = ijt + ijt . (2)
Permanent shocks to income are fully persistent in the sense that the permanent component
follows a random walk:
ij,t+1 = ijt + ij,t+1, (3)
where the innovation terms, { ijt}, are independently distributed over time and identically
distributed across households. Notice that we allow the parameters to depend on time t and
industry j, but not on individual i. We further assume that ij,t+1 N(0,2j,t ). Transitory
+1
shocks have no persistence, that is, the random variables {ijt} are independently distributed
over time and identically distributed across households. Clearly, ijt captures both temporary
income shocks and measurement error. We assume that they are normally distributed with
zero mean and a variance that is independent of i, but may depend on time or industry:
ijt N(0, jt).
2
Our specification for the labor income process is in accordance with the empirical work on
US labor income risk. For example, Carroll and Samwick (1997) and Gourinchas and Parker
(2002) use exactly our specification. Hubbard, Skinner and Zeldes (1994) and Storesletten,
Telmer and Yaron (2004) assume that the permanent component is an AR(1) process, but
estimate an autocorrelation coefficient close to one (the random walk case). Finally, some
papers have allowed for a third, MA(1), component. See, for example, Meghir and Pistaferri
(2004). Notice also that with the exception of Meghir and Pistaferri (2004) and Storesletten
et al. (2004), the previous literature has confined attention to the special case of time
independent variances (homoscedastic case). As we discuss in II.3, the introduction of time
variation in the parameters 2jt and jt makes the estimation of these parameters more
2
challenging.
10
II.3. Estimation
Consider the change in the residual of income of individual i between period t and t + n:
nuijt = uij,t +n  uijt (4)
= ij,t+1+ ... + ij,t+n+ ij,t+n  ijt .
We have the following expression for the variance of these income changes:
var[nuijt] = 2j,t . (5)
+1 + ...2j,t 2 2
+n + jt + j,t +n
We use the moment restrictions (5) to estimate the parameters 2jt and jt using GMM,15 2
where the sample analogs to the moment conditions are formed by using the estimates of
uijt obtained as residuals from regressions of labor income on observable characteristics as
specified in (1)  an approach also used by Meghir and Pistaferri (2004), Storesletten et
al. (2004) and Gourinchas and Parker (2002).16 Specifically, the estimator is obtained by
minimizing:
2
var[nuijt]  2j,t (6)
+1 + ...2j,t 2 2
+n+ jt + j,t +n
t,n
The firstorder conditions corresponding to the parameters 2j,t and j,t are given by:
2
t : = 0 (7)
2j,t
t : = 0
j,t 2
15More specifically, we follow the bulk of the literature and use the equally weighted minimum distance
(EWMD) estimator. Altonji and Segal (1996) suggests that the EWMD estimator (identity weighting matrix)
is superior to the twostage GMM estimator (optimal weighting matrix) once smallsample bias is taken into
account.
16Notice that Meghir and Pistaferri (2004) and Storesletten et al. (2004) exploit additional moment
restrictions that follow from the autocovariance function of income changes.
11
Notice that in general there are many more moment conditions (5) than there are parameters
to be estimated. More precisely, for each time period t and each industry j, there are two
parameters (2jt and jt), but n moment conditions (5). For example, in our data set on
2
Mexico, for each industry j we have t = 48 quarters and n = 4 quarters (individuals drop
out of the sample after 5 quarters), and the number of parameters is therefore 2 (48),
whereas the number of moment conditions is approximately 4 (48).17 The system is thus
overidentified.
Notice also that the objective function (6) is quadratic, which implies that the firstorder
conditions associated with the corresponding minimumdistance problem are linear in 2jt
and jt a feature that facilitates the estimation substantially. Specifically, the firstorder
2
conditions can be organized into a linear equation system
A · = b (8)
where = (2, ....2,t...2,T, , ..2,t..,T) is a 2(T1)dimensional vector of income param
2 2
2 2
eters (T being the total number of time periods). Estimates of these income parameters can
then easily be obtained through matrix inversion: = A b. 1
Some intuition for the way in which our approach separates transitory from permanent
income shocks can be obtained from the following simple example. Suppose that risk is
timeinvariant, 2jt = 2j and jt = j, an assumption that has been made by most of
2 2
the previous empirical literature on income risk. In this case, the moment restrictions (5)
become the following:
var[nuijt] = 2j + n 2j
2 (9)
Thus, the variance of observed nperiod income changes is a linear function of n, where
17We say "approximate" because towards the very the end of the sample period, clearly fewer than n = 4
income changes are observed. In the penultimate quarter, for instance, only one income change is observed.
However, this does not pose a problem for the estimation of any but the parameters of the very last quarter.
12
the slope coefficient is equal to 2j. The insight that the random walk component in income
implies a linearly increasing income dispersion over time is the basis of the estimation method
used by several authors. For example, Carroll and Samwick (1997) estimate 2 by performing
OLS regressions of the lefthandside of (9) on n. While the preceding example, with time
invariant parameters, serves to illustrate the intuition underlying the estimation procedure,
it should be clear that our exercise is more general in the sense that it allows for arbitrary
timevariation in the income risk parameters.
II.4. Estimation using ENEU Data
The preceding section provided a detailed description of a general econometric methodology
that may be used to estimate timevariant income risk parameters given longitudinal data
on individual incomes. We note here some additional issues that arise in applying this
methodology to our data, with particular emphasis on the type of income risk accounted for
by our estimation procedure.
In forming the sample analogs to the moment conditions (5), we use information on all indi
viduals who are present in a given manufacturing industry in both time periods t and t + n
(with n 5) regardless of their employment status in any intermediate period. In doing
so, we pick up shocks to workers who retain their jobs but experience income changes due
to changes in their wage rates or the number of hours worked. Moreover, we also account
for changes in income experienced by workers who have lost their job in period t, but are
reemployed in the same industry in some subsequent period t + n (with n 5), and this
is true even if these workers are unemployed in any intermediate period. In particular, we
do account for the longterm earnings losses of a large fraction of displaced workers, namely
all those displaced workers who are reemployed in the same industry but have lost firm
13
or occupationspecific human capital.18 In contrast, displaced workers who are reallocated
to a different manufacturing industry are not taken into account.19 However, in our data
set, the exclusion of such workers is not expected to cause too much of an underestimation
of the income risk parameters since the fraction of displaced manufacturing workers who
make the transition from one manufacturing sector to another is very small. Indeed, exam
ining reemployment rates for workers who start in manufacturing and go through a period
of unemployment suggests that only approximately ten percent of these displaced workers
undergo a transition from one manufacturing sector to another. Note that this finding is
consistent with observations from the United States that most job creation and destruction
takes place within industries (see, for instance, Davis, Haltiwanger and Schuh (1996)).
Finally, our construction of the sample analogs to the moment conditions (5) could lead
to an underestimation of the persistent component of income risk due to the noninclusion
of workers undergoing prolonged spells of unemployment (specifically those workers who
experience unemployment spells exceeding four quarters). However, this is not a severe
problem here. One consequence of the lack of any governmentprovided unemployment
insurance in Mexico and the very active informal labor market is that there are few labor
force participants in our survey with extended unemployment durations. Specifically, of those
workers looking for work, the proportion who had experienced unemployment durations of
four quarters or more was extremely small (less than 0.05 percent of workers).
Finally, we should mention that the variability in income experienced by workers in our data
set derives from both changes in the number of hours worked and changes in the real wage.
18For the U.S., these longterm earnings losses have been estimated to be very large (on average 25% for
hightenure workers according to Jacobson, LaLonde, and Sullivan (1993)).
19This allows us to circumvent the extremely difficult problem of assigning industries (and thus trade
policy) to individuals who transit to different industries. Including individuals who make transitions to the
service (nontradables) sector by using the procedure of counting them as belonging to the manufacturing
sector in which they are first observed does not result in any qualitative difference in our reported results.
14
Real wage changes, in turn, can be positive or negative, and in our Mexican data substantial
declines in the real wage are quite common. More specifically, Mexico experienced very high
inflation rates during our sample period with annual declines in the aggregate real wage as
high as 25 percent during this time (see, for instance, Hanson (2003)), implying that the
wage rates of some individual workers declined by an even larger amount. Thus, despite the
often cited downward rigidity of wages, our sample includes large numbers of workers whose
real wages declined dramatically.
II.5. Results
As described before, we have individual income data for the time period 19871998 covering
21 different manufacturing sectors in Mexico. Using the methodology outlined above, we
estimate the risk parameters 2 and for each quarter and each manufacturing sector. In
2
Tables II and III we provide the average estimate of 2 and for each year (averaged across
2
industries) and for each industry (averaged over time) respectively.20 The mean value (across
industries and over time) of the quarterly variance of the persistent shock, 2, is estimated
to be 0.008, or 0.032 annualized (i.e., , is estimated to have a mean quarterly value of 0.09
and a mean annualized value of 0.18).21 As expected, given the extent of measurement error
in the income data (see our discussion in Section II), the estimated variances of transitory
shocks are much larger in magnitude. More precisely, the mean value of the annualized
variance of transitory shocks is 0.2 (an annual standard deviation of 45 percent), which is
20The averages presented in Tables II and III are merely summary descriptions and do not allow for any
direct inferences regarding the relationship between trade policy and income risk.
21Given that in Section III we seek to uncover the relationship between trade policy and income risk using
our estimates of the income risk parameters , it is also interesting to investigate to what extent these
estimates differ across industries and over time after making some adjustment for the fact that there is
estimation error. To quantify this variation, we use the methodology of Krueger and Summers (1988). More
specifically, we compute a measure of the "adjusted standard deviation" of the point estimates of the income
risk parameters. In turns out that this number (0.018) is over twice the mean value of in our sample 
indicating that the variation in across industries and over time is indeed significant in our exercise.
15
clearly too large to be a true measure of income volatility.
It seems informative to compare our estimates of the permanent component of income risk,
2, with the estimates obtained by the extensive empirical literature on U.S. labor market risk
using annual income data drawn from the PSID. Most of these studies find an average value of
around .0225 for the annual variance 2 (Carroll and Samwick (1997), Gourinchas and Parker
(2002), Hubbard, Skinner and Zeldes (1994), and Storesletten, Telmer and Yaron (2004)),
with a value of 2 = .0324 being the upper bound (Meghir and Pistaferri, 2004). Assuming
that these income shocks are i.i.d. over time (the maintained random walk assumption),
this means that these studies have found a quarterly variance of 2 = .0056, with one study
estimating 2 = .008. Thus, the average value of our estimates of permanent income risk
is in line with the estimates that have been obtained by the previous literature on U.S.
labor market risk, although our estimates lie somewhat on the high end. Notice that our
estimates are obtained using a fivequarter rotating panel, whereas Carroll and Samwick
(1997), Gourinchas and Parker (2002), Hubbard, Skinner and Zeldes (1994), Meghir and
Pistaferri (2004), and Storesletten, Telmer and Yaron (2004) use the PSID data with a
panel dimension of many years. Thus, as long as Mexican workers face similar amounts
of permanent labor income risk as U.S. workers (or more), this result suggests that most
income shocks we label "permanent" in this paper indeed persist for a very long time.
III. Trade Policy and Income Risk
The procedure outlined in the previous section provides us with estimates of individual
income risk, 2jt, for each industry (i.e., manufacturing sector) j and time period, i.e.,
quarter, t. We now use these timevarying, industryspecific estimates in conjunction with
observations on trade policy, jt, to estimate the relationship between income risk, 2jt, and
openness, jt, using a linear regression model. As mentioned before, in this paper we focus
16
on permanent component of income risk, 2, instead of the transitory component, , for 2
two reasons: i) transitory income shocks are unlikely to generate substantial consumption
volatility and ii) is likely to contain a large amount of measurement error. Despite these
2
theoretical arguments, it might still be of interest to study the relationship between trade
policy and income risk using as a measure of income risk. We therefore also conducted a
2
similar regression analysis (not reported here) for transitory incomeshock parameters, , 2
but we did not find any statistically significant relationship between transitory shocks to
income and trade policy.
III.1. Specification
We first consider a linear specification that allows for industry fixed effects and aggregate
time effects:
2jt = 0 + 1 + 2 + jt + jt + jtDjt + jt .
j t 1 2 (10)
In (10) we have included on the right hand side the following variables:  the ad valorem
sectoral tariff rate,  the change in the tariff over the preceding year, D  the tariff
change over the preceding year interacted with an indicator variable that takes the value one
if the import penetration ratio is greater than its sample median and zero otherwise,22 j
 an industry fixed effect, and t  a time dummy that captures general macroeconomic
trends in the economy.
The inclusion of industry dummies in the specification (10) allows us to control for any fixed
industryspecific factors that may affect the level of riskiness of income in that industry.
Moreover, the inclusion of time dummies controls for any changes in macroeconomic condi
22Clearly, measures the effect of a trade policy change in sectors that had lower than median import
1
penetration both before and after this change and + correspondingly measures the effect of trade
1 2
policy changes in sectors that had higher than median importpenetration both before and after the change.
This is also true with specification (10') below.
17
tions that affect the level of income risk. While this ensures that our estimation results are
not driven by changes in macroeconomic conditions (business cycle effects and/or longrun
structural changes) unrelated to trade policy, it also means that identification of the rela
tionship between 2jt and jt will have to be based on the differential rate of change in trade
barriers across sectors over time (or the vector of observations on tariffs in the panel cor
responding to (10) will be perfectly collinear with the timedummy vector). This, however,
does not pose problems for our estimation since trade barriers in Mexico and their changes
over time do in fact do exhibit substantial crosssectional variation.23
Specification (10) provides the starting point for our econometric analysis. An alternate
specification is the following:
2jt = 0+j+ jt+ jt+ jtDjt+eet+ggt+e(1+jt)et+g(1+jt)gt+jt .
1 2
(10 )
Specification (10') exploits the within industry variation in tariffs over time to a greater
extent by dropping the time dummies and including instead the following two macroeconomic
variables: e, the depreciation of the real exchange rate over the preceding year, and g, the
GDP growth rate. Also included are the interaction terms (1 + )e and (1 + )g, which
measure the extent to which the relationship between income risk and these macroeconomic
factors varies with trade policy.24
Several econometric issues arise in the estimation of equations (10) and (10') above, most
of which we discuss in more detail below (sections III.3 and III.4). At this stage, we only
23For instance, in Mexico, tariffs varied between 80 and 20 percent prior to the trade reforms of 1987 and
ranged between 20 and 10 percent by 1994  implying a variation in tariff changes across sectors that is quite
substantial.
24Note that the only variable that is interacted with the dummy variable D (representing greaterthan
median import penetration) is the change in tariffs, jt. The remaining variables such as exchange rate
depreciation, et, and growth rate of GDP, gt, are already interacted with the tariff level (which itself has a
quite strong within industry correlation with import penetration). Estimating (10') separately for industries
with D = 0 and D = 1 gave results very similar to those reported here.
18
note the following. First, one concern is that the lefthandside variable, income risk, is
estimated and not observed. This is not a substantial problem by itself as it is well known
that while "measurement error" in the dependent variable does reduce precision, it does
not bias our estimates. Second, a concern arises from the fact that the estimates of 2jt
have different standard errors across industries, that is, the specification we have described
above suffers from a heteroscedasticity problem. Third, since the industries all belong to
the same macroeconomic environment, there is a possibility of contemporaneous correlation
in their 's even after controlling for observable macroeconomic factors as in (10'), i.e.,
Cov(jtj ) = 0. Finally, serial correlation in income volatility within an industry is a
t
possibility, i.e., Cov(jtjt ) = 0. Given the possible presence of heteroscedasticity, spatial
correlation and serial dependence, consistent estimates of the standard errors associated with
the coefficient estimates in (10) and (10') above are obtained by using robust estimation
techniques.
III.2. Results
In (10), the effect of the tariff level on income risk is given by the coefficient and the effect
of tariff changes on income risk is given by the coefficient . The first column in Table IV
presents the estimation results. We note first that the estimate of is insignificant and we
are therefore unable to reject that the mean effect of the tariff level on income risk is zero.
However, trade policy changes, in sectors with abovemedian level of import penetration
(D = 1), have statistically and economically significant short run effect on income risk
(^ +
1 ^ = 0.125, with an estimated standard error of 0.05). This estimate indicates that
2
lowering the tariff rate by five percent would, for a year, raise 2 by .00625 from, for example,
.008 (its mean value) to .01425 . In terms of the standard deviation , this amounts to an
increase from .089 to .1193, that is, an increase by more than thirty percent  a substantial
increase in income risk indeed.
19
Estimates from (10') are presented in the second column of Table IV. Note that tariff changes
in high importpenetration sectors continue to have economically and statistically significant
effects of magnitude quite similar to those obtained from estimation of (10) (^ + =  1 ^ 2
0.092, with an estimated standard error of 0.045). More specifically, a five reduction in tariffs
increases 2 from a mean level of .008 to .0126, which in terms of the standard deviation
amounts to an increase from .089 to .1122 (a twenty five percent increase). Interestingly, the
coefficient is now significant. However, the effect of the tariff level on income risk is now
given by ( + ee + gg). After substituting in the mean values of e and g from the
sample, this estimated sum revealed to be insignificantly different from zero (^ +^eÆe+^ggÆ
= 0.02, with an estimated standard error of 0.02). Thus, we are again unable to reject that
the mean effect of the tariff level on income risk is zero.25
Consider now our estimates of how the tariff level alters the effect of macroeconomic variables
on income risk. The coefficient on real exchange rate depreciation, e, is estimated negative
and significant as is the coefficient on GDP growth, g, while the coefficients e and g
relating to the interaction terms, (1 + )e and (1 + )g, are both positive and significant.
The extent to which the tariff level alters the effects of exchange rate changes on income risk
is given by e. As reported in Table IV, this parameter is estimated to have a mean value
of 0.54 and an estimated standard error of 0.18. Consider a real exchange rate appreciation
of ten percent under two scenarios  when the tariff rate is ten percent and when the tariff
rate is five percent. If the tariff rate is ten percent, our estimates indicate that an exchange
rate appreciation of ten percent (in the preceding year) raises 2 from 0.008 to 0.0108 (an
25Our estimates of the timing and magnitude of the effect of trade policy changes on measured income
shocks (i.e., large changes in the year following policy changes and zero mean effects) also indicate that our
results are not being driven by other "unobserved" factors such as skill and sector biased technical changes
that are possibly correlated with trade policy changes. More specifically, we would expect any such changes in
technology to impact income in a gradual manner taking several years for its full impact to be realized. Note
also that our own estimates of the returns to education suggest a striking similarity across manufacturing
sectors in Mexico, which provides indirect evidence against the view that technological progress in Mexico
during the relevant sample period was both skill and sector biased.
20
increase of just about thirty five percent). In contrast, if the tariff rate is five percent instead,
the same appreciation implies an increase in income risk from 0.008 to 0.013 (an increase of
over sixty percent). Similarly, if the growth rate of GDP, g, is lowered by five percent, 2
is raised from 0.008 to 0.01 (an increase of over twenty five percent) when the tariff rate is
ten percent, but the same change in g results in a short run increase in income risk from
0.008 to 0.013 (an increase of over sixty percent) when the tariff rate is at five percent. Of
course, as noted earlier, our empirical estimates also indicate that tariff reductions lead to
a corresponding reduction in individual income risk during economic booms. Overall, our
estimates suggest that the magnitude of the (short run) effects of macroeconomic shocks on
income risk is significantly altered by the tariff level.
The dependence of the income risk parameter 2 on cyclical conditions is not only observed
in Mexico, but has also been well documented for the United States (Meghir and Pistaferri
(2004), Storesletten, Telmer and Yaron (2004)). However, this literature has not studied
how trade policy affects this dependence of idiosyncratic risk on cyclical conditions. Thus,
the estimation results reported in Table IV provide the first empirical evidence that trade
liberalization increases the sensitivity of idiosyncratic risk to business cycle conditions. The
oretically, one might speculate that a mechanism similar to the one modeled by Newberry
and Stiglitz (1984) is behind our empirical finding. More specifically, Newberry and Stiglitz
(1984) argue that a negative productivity shock would have a smaller equilibrium effect on
output and employment in a closed economy than an open one  as prices rise with a neg
ative supply shock in the former but are constrained by world prices in the latter. With
heterogeneous effects on firms and individuals, the link between macroeconomic downturns
and idiosyncratic income risk may therefore also be amplified in more open economies. A
more rigorous modeling of this idea within the context of a dynamic general equilibrium
model with incomplete markets is an interesting topic for future research.
21
III.3. Endogeneity and Selection Bias
One concern that arises in our estimation of equations (10) and (10') is that tariff rates
are not fully exogenous. Indeed, the theoretical literature on the political economy of trade
policy has proposed several hypotheses concerning the endogenous determination of tariffs.
Furthermore, a number of empirical studies have explained (partially) the cross industry
variation in tariffs using a number of economic and political variables that vary across in
dustries such as the lobbying strength and employment size of particular sectors.26 While the
literature has not studied (or indeed even suggested) income risk as a determinant of cross
sectional variation in trade policy, the possibility that it might be a relevant determinant of
policy makes is potentially problematic. Consider, for instance, an economy in which raising
the tariff rate in a sector would in fact lower income risk in that sector. Consider further
that the government there is "equity" minded and chooses higher protection levels for those
industries with intrinsically high levels of income risk  thereby eliminating crosssectional
variation in income risk. If such an economy were studied purely in the crosssection, it may
appear that there is no relation between trade policy and income risk even though such a
relationship does exist. This type of purely crosssectional endogeneity, however, is not a
problem for our empirical analysis since we follow industries over time. More precisely, the
within estimator we use is formed by considering changes within industries in income risk
and tariffs over time, and any endogeneity bias deriving from purely crosssectionally varying
politicaleconomy determinants of trade policy is therefore eliminated.
Along the time dimension, estimation bias could arise if the government attempts to protect
vulnerable industries by raising tariff rates for those industries that have experienced an
increase in income risk. While such endogeneity bias is in principle a matter of concern,
there are at least two facts that speak against this view. First, the trade policy changes that
26See, for instance, Trefler (1993). Gawande and Krishna (2003) provide a survey discussion.
22
we study here are changes that were undertaken during major policy reform episodes (both
in the late 1980s and under NAFTA), and many observers have argued that the lowering
of trade barriers was mainly used by the Mexican government to signal its commitment to
overall policy reform (Tornell and Esquivel, 1995). Second, and somewhat related to the
first point, in our data virtually no industry experienced a rollback of the liberalization
effort once tariff rates had been reduced. Finally, we note that such pattern of endogeneity
would only cause a bias against our reported findings. That is, if such bias exists, the true
shortrun effect of trade policy changes on income risk is even larger than what we report in
this paper. However, it also means that our finding that trade liberalization has no longrun
"level effect" could be the result of two opposing effects canceling each other out.27
Estimation bias could, of course, also arise if systematic changes in nontariff barriers re
versed the effects of tariff reductions, but these changes in nontariff barriers were not taken
into account by us. To ensure that this is not the case, we studied the patterns in the use
of nontariff barriers (NTBs) in Mexico in the years included in our sample. NTB use in
Mexico primarily took the form of antidumping duties in these years and the antidumping
duties were concentrated entirely in the `Basic Metal Products', `Chemicals' and `Textiles'
industries.28 Studying the link between trade policy and income risk using data from the re
maining industries did not alter qualitatively or quantitatively any of the reported estimates
(see Table VIII).
Our estimation results could also be biased if there is unobserved heterogeneity among work
27Notice also that despite the work by Alesina and Drazen (1994) and others, major trade policy reforms
are in general rather difficult to understand theoretically once policy is treated as being endogenous. The
dominant theory of endogenous trade policy determination  the interest group theory  simply does not
predict such dramatic changes in policy. Since the competing strengths of various interest groups are not
expected to (and do not) change dramatically over the medium term, the theory predicts stickiness in trade
policy over these horizons (consistent with what is observed most of the time). Lacking theoretical guidance,
the choice of suitable "exogenous variables" to help with identification is even more difficult than usual.
28See the recent UNCTAD study, "Mexico's Experience with the use of Antidumping Measures," 2002.
23
ers and industries, and heterogenous workers select into different industries. Suppose, for
example, that industries with high levels of protection (high tariff levels) are also industries
with low job destruction rates.29 Suppose further that there are two types of workers, good
and bad, and that good workers quickly find a new job in the event of job displacement, but
bad workers do not. Other things being equal, we would expect bad workers to move to high
protection industries. In this world, high tariff rates lower income risk because they reduce
job destruction rates, but they also attract highrisk (bad) workers leading to a downward
bias of our empirical estimates of the relationship between income risk and tariff levels (the
coefficient in equation (10)). Thus, it is possible that our empirical finding that tariff
levels have no effect on income risk is simply due to this type of selection bias.30
In general, it is difficult to deal with the type of selection bias we have just described.
However, there is some evidence that in our case any effect due to selection bias is relatively
moderate. More specifically, we would expect workers with low job finding rates be mainly
lowability workers. If we use yearsofschooling as a observable proxy for (unobserved)
ability, then one implication of the type of selection bias described above is that yearsof
schooling (human capital) and income risk should be negatively correlated across industries.
However, in our data set, the correlation between average education levels and income risk
across industries is very small (0.06) and insignificant.
Clearly, there could be unobserved ability differences among workers that are uncorrelated
with yearsofschooling, in which case selection bias might still be problematic even if the
29We thank a perceptive referee for suggesting this example. Note also that the selection bias we discuss
here bears some resemblance with the type of lemons' problem discussed by Gibbons and Katz (1991).
30If trade liberalization mainly targets highprotection industries and highrisk workers leave industries
that experience large tariff cuts, then this selfselection effect also causes a downward bias of our estimates
of the relationship between tariff changes and income risk (the coefficients and in equation (10)) .
1 2
Thus, the true shortrun effect of trade liberalization might be even larger than the (already substantial)
effect reported in Table IV.
24
crossindustry correlation between yearsofschooling and income risk is nil. However, even
in this case we would expect any selection bias to manifest itself in unexplained wage differ
entials across sectors, at least as long as highability workers are paid higher wages. A casual
examination of the data, however, suggests that such cross industry wage differentials are
small (at least in relation to the differences in magnitudes of income risk across industries and
our estimates of changes in these magnitudes following trade policy changes). More precisely,
across the manufacturing sectors we study, the mean industry wages are highly correlated
with mean educational attainment. That is, the R2 of a simple cross sectional regression of
average earnings on average worker characteristics is about 0.8 (see the data prtesented in
Table V). Thus unobserved worker characteristics have very little influence on average earn
ings in an industry, suggesting little selectivity of workers of differing (unobserved) abilities
into different manufacturing sectors in our data.
III.4. Robustness
We conducted a series of additional estimation exercises to study the robustness of the
findings reported here. First, the effective rate of protection was computed (using the tariff
series and inputoutput matrices for Mexico) and used in place of the raw tariff series in
estimating (10'). As the results presented in Table VI indicate, this does not change the
results in any significant quantitative or qualitative way. Second, given that many of the
right hand side variables were only observed on an annual basis, (10') was estimated using
annually averaged observations (on income risk as well as the right hand side variables).
These results, presented in Table VII, are also very similar to the ones we have reported
before. More precisely, we calculated the average quarterly 2 for each year and used these
averages as the left hand side variable in (10'). Since in this case averaging reduces to a
greater extent the variation in the left hand side variable, the degree of fit is now higher.
To ensure that the dramatic nominal exchange rate devaluation undertaken by the Mexican
25
authorities at the end of 1994 did not drive our results, (10') was estimated by dropping
observations from the years 1995 and 1996. These results are also reported in Table VIII.
As is evident, dropping observations from the years immediately following the exchange rate
crisis in Mexico does not alter our results.
An additional point concerns the lagged effects of policy changes. Note that we measure
tariff changes as the change between the beginningofyear tariffs of two subsequent years.
The corresponding change in income risk measures the average effect over a total of a two
year period. Thus, a tariff change implemented at the beginning of 1988 could affect income
risk in the last quarter of 1989, and this change in income risk would still be taken into
account in our specification (10'). Estimation results (not reported here but available upon
request) with specifications in which we included lagged tariff changes (and other lagged
independent variables) on the righthandside of (10') did not support the inclusion of such
lags.
Finally, experimenting with other specifications with additional interactive and nonlinear
terms did not reveal any significant or systematic patterns in the data.
IV. Income Risk and Welfare
The preceding discussion has outlined our approach to estimating the relationship between
trade policy and income risk. We now turn to the analysis of the link between income risk
and welfare, which is provided by a simple dynamic model with incomplete markets along
the lines of Constantinides and Duffie (1996) and Krebs (2004). The model extends the basic
insights of the large literature on the permanent income hypothesis to a generalequilibrium
setting with isoelastic preferences and incomplete markets.31 It remains tractable enough
31Deaton (1991) and Carroll (1997) provide a quantitative analysis of the consumptionsaving problem
26
to permit closedform solutions for equilibrium consumption and welfare, yet is rich enough
to provide a tight link to the empirical analysis. Clearly, our goal here is not to provide a
complete assessment of the effects of income risk on welfare taking into account all possible
channels, but rather to articulate a simple framework that allows us to obtain indicative
estimates of welfare change through the income risk channel.
The model features longlived workers that make consumption/saving choices in the face of
uninsurable income shocks. These income shocks are permanent, which implies that "self
insurance" through borrowing or own saving is an ineffective means to smooth out income
fluctuations. In other words, the effect of permanent income shocks on consumption is
substantial.32 In accordance with Constantinides and Duffie (1996) and Krebs (2004), we
consider an exchange economy. Thus, we rule out by assumption any effect of changes in
income risk on aggregate output. In this section, we briefly discuss the basic assumptions of
the model and state the main welfare results. All derivations are relegated to the Appendix.
IV.1. Model
Time is discrete and open ended. Income of worker i employed in industry j in period t is
denoted by y~ijt. Income is random and defined by an initial level y~ij and the law of motion
0
y~ij,t+1= (1 + µj,t )(1 + ij,t )y~it ,
+1 +1 (11)
where µj,t +1 is a mean growthrate effect common across workers in the sector and ij,t +1 is
with permanent income shocks in a partial equilibrium context (exogenous interest rate).
32 Krebs (2003a) considers a production economy with only permanent income shocks, and shows again that
selfinsurance is highly ineffective. Thus, the result that selfinsurance is not very effective does not depend
on the zero aggregate saving feature of endowment economies, even though we will make it to simplify the
analysis. Notice also that there are differences between the current analysis and the work by Constantinides
and Duffie (1996) and Krebs (2004). First, Constantinides and Duffie (1996) and Krebs (2004) focus on the
asset price implications of market incompleteness, whereas the current analysis explores the welfare effects.
Second, Constantinides and Duffie (1996) and Krebs (2004) consider a onesector economy. In contrast,
the current model has multiple sectors (industries) that differ with respect to the amount of income risk
households have to bear. Finally, we assume that households can save, but not borrow.
27
an individualspecific shock to the growth rate of income. We assume that log(1 + ij,t ) +1
is normally distributed with time and industrydependent variance j,t . Although the 2
+1
distribution of individualspecific shocks may change over time, the shocks are unpredictable
in the sense that current and future shocks are uncorrelated. To ensure that workers are
exante identical, we also assume that the distribution of shocks is identical across workers.
Each worker begins life with no initial financial wealth. Workers have the opportunity to
save at the common interest rate rt, but they cannot borrow. Hence, the sequential budget
constraint of worker i reads
aij,t+1 = (1 + rt)aijt + y~ijt  cijt (12)
aijt 0 , aij = 0 .0
Here cijt denotes consumption of worker i employed in industry j in period t and aijt his
asset holdings at the beginning of period t (excluding interest payment in this period).
Workers have identical preferences that allow for a timeadditive expected utility represen
tation:
U({cijt}) = E tu(cijt) . (13)
t=0
c1
Moreover, we assume that the oneperiod utility function, u, is given by u(c) = , = 1,
1
or u(c) = log c, that is, preferences exhibit constant degree of relative risk aversion .33
IV.2. Welfare
33The model can easily be extended to allow for an endogenous laborsupply decision. Suppose, for
example, that y~ijt = wjthijtlijt, where wjt is the wage rate per effective unit of labor, hijt is the stock of
human capital (general and specific) of worker i, and lijt is the number of hours worked. Suppose further that
hijt is stochastic and that idiosyncratic shocks to hijt are unpredictable (permanent) as in Krebs (2003a,b).
Then a straightforward extension of the argument made in the appendix shows that the optimal labor choice,
lijt, is independent of idiosyncratic shocks to hijt if preferences over consumption and leisure are homothetic
with respect to consumption (as assumed above) and multiplicative in consumption and leisure. That is,
permanent shocks to the hourly wage rate of workers will not change labor supply, and the welfare formula
(13), respectively (14), is still valid.
28
In the Appendix, we derive an explicit formula for equilibrium welfare that depends on the
preference parameters and and the income parameters µjt and jt, where jt is the
2 2
variance of the lognormally distributed income shocks . We also show that the variance
jt of the income process (11) can be identified with the variance 2jt of the permanent
2
component of our empirical specification (1). This provides a tight link between the empirical
results obtained in Section II and the welfare analysis conducted in this section. We now
briefly outline and discuss the main welfare results.
For simplicity, assume that the income parameters are time and industryindependent:
µjt = µ and 2jt = 2. Suppose further that trade reform changes the tariff rate from
to (1 + ) permanently, and that this change in the tariff rate leads to a corresponding
permanent change in income risk from 2 to (1 + )2. Clearly, the change in income risk
2 corresponds to the longrun effect that is associated with the level term, , on the
righthandside of our regression equation (10). We can find the welfare effect of the change
in risk, , by calculating the compensating variation in lifetime consumption, c. That
is, we can ask by how much we have to change consumption in each period and state of the
world to compensate the household for the change in income risk. In the appendix we show
that this compensating differential, expressed as percent of lifetime consumption, is given by
1
1  (1 + µ)1 exp(.5(  1)(1 + )2)
1
c =  1 if = 1
1  (1 + µ)1 exp(.5(  1)2)
2
c = exp  1 if = 1 . (14)
(1  )2 2
Equation (14) shows how to translate longrun changes in labor income risk, , into equiv
alent changes in lifetime consumption, c. It provide the answer to the following question:
how much lifetime consumption are risk averse workers willing to give up in return for not
having to experience the increase in income risk that is caused by a change in trade policy.
Notice that (14) is the result of an exante welfare calculation under rational expectations.
29
More specifically, (14) assumes that workers do not know who will lose and who will gain
from trade reform, but they know to what extent trade reform creates winners and losers
(the effect of trade reform on the income risk parameters is known exante).
The welfare expression (14) assumes that the change in 2 is permanent. However,we are
also interested in the welfare effect of an increase in income risk from 2 to (1 + )2 for
n periods. In this case, the welfare effect is given by
1
1  x 1
c = 1  x n+1 + xx n  1 if = 1 (15)
1  x
(1  n)
c = exp 2  1 otherwise
2(1  )2
where we introduced the following notation:
x = (1 + µ)1 exp .5(  1)2
x = (1 + µ)1 exp .5(  1)(1 + )2 .
The welfare expressions (14) and (15) have some intuitive properties. First, the welfare effect
of a change in income risk is a nonlinear and increasing function of the initial level of income
risk. Put differently, if workers are already exposed to a large amount of income risk, then
increasing income risk hurts a lot. This property explains why the welfare effects we find in
this paper (see below) are so much larger than the welfare cost of business cycles found in
the macroeconomic literature (Lucas, 2003). Second, the welfare effects are increasing in the
riskaversion parameter : the more riskaverse the workers are, the stronger is the welfare
effect of a change in income risk. Finally, the welfare effects are the same for all workers
regardless of their wealth. This property is the result of the joint assumption of homothetic
preferences and an income process defined as in (11).
IV.3. Results
30
The welfare expressions (14) and (15) form the basis for our quantitative welfare analysis of
trade reform. In order to conduct such an analysis, we need information about the income
parameters µ, 2, and and the preferences parameters and . Our empirical analysis
provides estimates of the income parameters. We estimate an average value of a quarterly
variance, 2, of of .008 (averaged across industries and over time), and this is also the value
we use in all welfare calculations reported below. Similarly, we choose a quarterly growth
rate µ = .005 to match the average growth rate in aggregate real income in Mexico over the
relevant sample period. For the preference parameters, we choose a quarterly discount factor
of = .99 and a degree of risk aversion of = 1 (logutility) for the baseline economy. These
values for the preference parameters are in line with the values used in the macroeconomic
literature (Cooley (1995)). However, we also report the welfare results for a higher degree
of risk aversion ( = 2).
We conduct the following exercises. Starting from a tariff level of = .10, which is roughly
the average tariff level in our data set, we consider the welfare consequences of reducing the
tariff level to = .05. Our empirical analysis in section III suggests that this tariff reduction
has two effects for industries with high import penetration. First, there is a shortrun effect
that leads to an increase in income risk for one year (four quarters), and in this section we
evaluate the welfare cost of this shortrun effect. Second, there is an "interaction effect", and
we report the welfare cost corresponding to this effect as follows. We compute the welfare
cost of a shortrun increase in income risk following a real exchange rate appreciation of ten
percent with the tariff level also at ten percent, and then compare this welfare cost of the
same exchange rate appreciation with the cost that obtains when the prevalent tariff level
were five percent instead. Finally, we consider the welfare effect of a change in income risk
due to a downturn in the economy, with the growth rate of GDP lowered by five percent,
and again see how this is altered if the tariff level were lowered by five percent.
31
Table IX reports the effects of a trade reform that lowers tariff rates from ten percent to five
percent for industries with high levels of import penetration. As indicated in Table IX, this
would raise 2 for one year following the reform from a mean level of 0.08 to 0.013 (here
we use our regression results from equation (10') reported in Table VI). The corresponding
welfare cost of this change is calculated to be 0.98 percent of permanent consumption if
the coefficient of risk aversion is = 1, and this cost increases to 1.96 percent of lifetime
consumption if we choose = 2 instead.34 Now consider the indirect effects of trade policy as
measured by the interaction terms in (10'). As noted above, an exchange rate appreciation
of ten percent raises 2 for a year from 0.008 to 0.011 if the tariff level is ten percent. This
translates into a welfare cost of 0.59 percent of lifetime consumption if = 1 and 1.18 percent
if = 2. If the tariff rate were lowered to five percent, however, 2 rises to 0.014 and the
corresponding welfare costs are 1.18 and 2.36 percent of lifetime consumption, respectively.
Finally, if the tariff rate is ten percent, a cyclical downturn in the economy (a drop in g by
five percent) raises 2 for a year from 0.008 to 0.010, and the corresponding welfare cost is
calculated to be 0.39 percent of lifetime consumption if = 1 and 0.78 percent with = 2.
In contrast, if the tariff rate were lowered to five percent, 2 rises to 0.013 instead, and the
corresponding welfare costs are 0.98 and 1.96 percent of lifetime consumption, respectively.
Thus, our calculation suggest that both the shortrun direct effects of tariff reforms and the
indirect effects of the level of the tariff in amplifying the effects of macroeconomic shocks
are economically significant.
As we have mentioned before, the limited time series dimension of our income data might
lead us to overestimate the amount of permanent labor income risk Mexican workers face.
34Although the welfare formula (15) is nonlinear in , this nonlinearity is not very pronounced for
moderate degrees of risk aversion. For example, if = 4, then the welfare cost of this shortrun change in
2 is 4.16% of lifetime consumption. Notice also that the results reported in Table IX assume n = 4 since
we use quarterly risk and preference parameters and the increase in income risk lasts for four quarters (one
year).
32
Consequently, the welfare results reported in Table IX might overstate the true cost of
trade liberalization. We therefore also calculate the welfare effects for an economy in which
the average income risk, 2, and all changes in income risk, 2, are scaled down by a
factor of 0.7. The factor 0.7 is derived from the fact that the estimate of income risk, 2,
obtained by Carroll and Samwick (1997), Gourinchas and Parker (2002), Hubbard, Skinner
and Zeldes (1994), and Storesletten, Telmer and Yaron (2004) using income data with a
very long panel dimension is roughly 70 percent of our estimate of income risk using a much
shorter panel dimension (see our discussion in Section II.5 for details). Using the scaled
down values for income risk and income risk changes, we find the following welfare cost of
a five percent tariff reduction for a degree of risk aversion of = 1. First, the oneyear
increase in income risk immediately following the tariff reduction is equivalent to a decrease
in lifetime consumption by .68 percent. Second, a five percent decline in GDP growth leads
to an increase in income risk that is equivalent to a loss of lifetime consumption of .27 percent
before the tariff reduction, and this loss increases to .68 percent after the tariff reduction
(that is, the difference is .41 percent). Thus, although the welfare cost of trade liberalization
are somewhat smaller than for the baseline case, they are still quite substantial.
VI. Conclusions
This paper studies empirically the relationship between trade policy and individual income
risk. The analysis proceeds in three steps. First, longitudinal data on Mexican workers
are used to estimate individual income risk in various manufacturing sectors. Second, the
variation in income risk and trade barriers  both over time and across sectors  is used
to arrive at estimates of the relationship between trade policy and individual income risk.
Finally, using the estimates of this relationship between trade policy and income risk, a simple
dynamic general equilibrium model with incomplete markets is used to obtain estimates of
the corresponding welfare effects.
33
Our findings can be summarized as follows. First, for industries with high levels of import
penetration, trade policy changes have a significant shortrun effect on income risk. Second,
the effect of the tariff level on income risk is insignificant. Third, while the tariff level has
an insignificant mean effect, it nevertheless changes the degree to which macroeconomic
shocks affect income risk. Finally, the welfare costs associated with the estimated increases
in income risk are substantial.
As we have pointed out before, the welfare results reported in this paper have to be inter
preted with caution keeping in mind several limitations of our analysis. More specifically,
we focus exclusively on the link between trade policy and individual income risk, and do not
study how trade reform affects the mean of income growth. Second, our welfare calculations
do not allow for the possibility that an increase in income risk might lead to a simultaneous
rise in insurance opportunities (endogenous market incompleteness). Third, we follow a long
standing tradition in economics and measure risk by the variance (second moment) of the
relevant distribution, which is justified if (as assumed in this paper) the economic variables
of interest are (log)normally distributed. Finally, the Mexican household survey we use to
implement our general approach is a rotating panel that follows individual workers for five
quarters over time, which means that the panel dimension of our income data is somewhat
limited. In short, the welfare results presented here do not show that trade liberalization
is necessarily costly, but they do provide strong evidence that any comprehensive welfare
analysis of trade liberalization ought to take into account the cost of increased labor market
risk.
34
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38
Appendix
In this appendix, we construct the equilibrium and derive the welfare expressions. Notice first that
the Euler equation associated with the consumption/saving problem of household i reads
 
cijt (1 + rt +1)E[cij,t (A1)
+1Fijt] ,
where Fijt is the information that is available to household i in period t and (A1) holds with
equality if aijt > 0. The Euler equation (A1) says that the utility cost of saving one more unit
of consumption is greater than or equal to the expected utility gain of doing so. If we rule out
international borrowing and lending, then the domestic interest rate is determined by the saving
decisions of domestic households only.35 In this case, domestic asset market clearing reads:
aijt = 0 . (A2)
i,j
Suppose the interest rate is
1  1 .
rt
+1 = minj (A3)
(1 + µj,t
+1 ) E (1 + ij,t +1 ) Fijt
Notice that the righthand side of (A3) does not depend on i because of our assumption that the
distribution of ij,t +1 is independent of i and Fijt. Clearly, at the interest rate (A3) the Euler
equation (A1) holds for all households i if they all choose aijt = 0 and cijt = y~ijt. Moreover,
a tedious but straightforward argument show that expected lifetime utility is finite and that a
corresponding transversality condition holds if (Krebs, 2004)
(1 + µj,t+1 )1 E (1 + ij,t
+1)1 < 1 . (A4)
Thus, the plan aijt = 0 and cijt = y~ijt is individually optimal for all households. Since aijt = 0
satisfies market clearing, we have found an equilibrium.
We now turn to the welfare analysis. For simplicity, suppose that tariff rates and income parameters
are constant over time and equal across industries: jt = , µjt = µ, and jt = 2. If cijt = y~ijt
2
and there are no aggregate fluctuations, then expected lifetime utility (13) becomes
c1i
0
Ui = if = 1
(1  ) (1  (1 + µ)1 E[(1 + )1 ])
1
Ui = logci +
0 (log(1 + µ) + E[log(1+ )]) otherwise (A5)
1  (1  )2
35Clearly, an alternative interpretation is that the model describes a small open economy with exogenous
interest rate that is at least as low as (A3).
39
where the expectation is taken over idiosyncratic shocks (over the random variable ) and for
simplicity we dropped the industryindex j on cij . Using the assumption that N(.52, 2),
0
integration over income shocks yields
c1i
0
Ui = if = 1 (A6)
(1  ) (1  (1 + µ)1 exp (.5(  1)2))
1
Ui = logci +
0 log(1 + µ)  2/2 otherwise .
1  (1  )2
Equation (A6) shows how welfare depends on income risk, 2, which in turn depends on tariff rates,
. Thus, the welfare expression (A6) can be used to calculate how trade reform affects welfare
through its effect on income risk. Clearly, this change in income risk induced by trade reform
corresponds to the longrun effect that is associated with the level term, jt, on the righthandside
of our regression equation (10) and (10'). In order to get numbers for these welfare changes with
economically meaningful units, we calculate the percentage change in initial consumption, ci , that
0
is necessary to compensate the worker for the change in risk. More precisely, for any ci , 2, and
0
, we are searching for the percentage change in initial consumption, c solving
U(ci , 2) = U (1 + c)ci , (1 + )2
0 0 (A7)
Notice that because of our random walk assumption, any increase in initial consumption, ci , 0
amounts to an increase in consumption for all future dates and events (lifetime consumption). Using
(A6) and (A7), we find the welfare expression(14). Notice that expression (14) is independent of
ci , that is, the welfare change expressed in percentage changes of lifetime consumption is the same
0
for all workers.
So far, we have calculated the welfare effect of a permanent increase in 2. However,we are also
interested in the welfare effect of an increase in income risk from 2 to (1 + )2 for n periods.
In this case, expected lifetime utility of workers without the increase is still given by (A6), and
expected lifetime utility with the increase is:
n
Ui = tE [(cit)1 ]
+ tE [(cit)1 ]
1  1 
t=0 t=n+1
E[(cit)1 ] =
c1i
t
0 (1 + µ)(1 )t E[(1 + )1 ]
t = 0, 1, . .., n (A8)
1 

n (tn)
E[(cit)1 ] =
c1i
0 (1 + µ)(1 )t E[(1 + )1 ]
E[(1 + )1 ] t = n + 1, n + 2, . . .
1 
where log(1 + ) N(2/2, 2) and log(1 + ) N(2(1 + )/2, 2(1 + ). A similar
expression holds for the case of log utility. We define again the welfare cost of trade reform, c,
as the increase in average consumption that is necessary to compensate workers for the (nperiod)
increase in income risk. Using this definition and evaluating the expression (A8), we find the welfare
expression (15) in section IV.
40
Finally, let us discuss the link between the specification of the income process (1)(3) in the Section
II and the income process (11) used in the Section IV. Recall that we assume that log(1 + ) in
(11) is normally distributed. More specifically, we assume log(1 + ij,t 2 2
+1 ) N(j,t ).
+1/2, j,t+1
The term .5j,t 2 2 , a property
+1 ensures that the mean of income growth is independent of j,t +1
that is useful since it allows us to vary income risk without changing the mean growth rate. Notice
that this type of specifying the distribution of income shocks is standard in the asset pricing and
macroeconomic literature (Carroll, 1997, and Constantinides and Duffie, 1996). To understand the
economic meaning of this assumption, notice that with this specification we have E[ij,t +1] = 0 and
2 2
var[ij,t+1 ] = ej,t (ej,t
+1 +1  1) using the standard formula for lognormal distributions (see, for
example, Campbell, Lo, and MacKinlay 1997). Thus, any increase in j,t 2 ],
+1 increases var[ij,t+1
but leaves E[ij,t +1 ] unchanged. Taking the logarithm in (11), we find
log y~ij,t+1 = log y~ijt + log(1 + µj,t
+1) + log(1 + ij,t+1) (A9) .
Thus, income follows a logarithmic random walk with drift log(1 + µj,t +1 ) and heteroscedastic
error term log(1+ ij,t +1 ). Comparison of (A9) with the econometric specification (1)(3) suggests
that we relate log(1 + ij,t +1 ) in (A9) with the innovation term of the permanent, unpredictable
component of income changes in (1):
log(1 + ij,t 2
+1 ) = ij,t+1 j,t /2 (A10) .
+1
In (A10) we introduce the term j,t 2 /2 to ensure that both random variables have the same
+1
mean. Taking the variance in (A10) we find
j,t
2 (A11) .
+1 = 2j,t +1
Thus, our empirical measure of income risk, 2, coincides with our theoretical measure of income
risk, 2. This shows that we can use our empirical estimates of 2 obtained in Section II when
evaluating the welfare expressions (14) and (15) in Section IV.
41
Table I: ENEU Worker Survey  Summary
(19871998)
Variables
Mean Age 32
Mean Years of Education 8
Fraction High School and Above 17
Fraction Wage Earners 65
Fraction Self Employed 25
Table II: Estimates of Persistent and Transitory Income Shocks
Annual Averages (19871998)
Year 2 2 Sample Size
87 0.011 0.096 19136
(0.003) (0.002)
88 0.005 0.101 35397
(0.003) (0.002)
89 0.004 0.103 28203
(0.002) (0.001)
90 0.014 0.098 35167
(0.002) (0.001)
91 0.001 0.103 37344
(0.002) (0.001)
92 0.006 0.106 54022
(0.001) (0.001)
93 0.007 0.112 78741
(0.001) (0.001)
94 0.006 0.110 121716
(0.001) (0.001)
95 0.014 0.118 164212
(0.001) (0.001)
96 0.000 0.107 172766
(0.001) (0.001)
97 0.006 0.104 172870
(0.001) (0.001)
98 0.008 0.097 158707
(0.001) (0.001)
Figures shown are annual averages (across industries and quarters) of the point estimates of the persistent
shock 2 and the transitory shock . The figures in parentheses are the averages of the corresponding
2
standard errors. Sample size denotes the numbers of workers surveyed in the respective year.
Table III: Estimates of Persistent and Transitory Income Shocks
Industry Averages (19871998)
Industry 2 2 Industry 2 2
311 0.013 0.131 352 0.020 0.111
(0.0004) (0.0003) (0.0025) (0.0019)
313 0.012 0.088 353 0.002 0.081
(0.0007) (0.0005) (0.0009) (0.0007)
321 0.005 0.097 356 0.006 0.079
(0.0006) (0.0005) (0.0016) (0.0011)
322 0.012 0.124 369 0.011 0.113
(0.0008) (0.0006) (0.0014) (0.0011)
323 0.008 0.107 371 0.003 0.110
(0.0022) (0.0015) (0.0031) (0.0025)
324 0.004 0.088 381 0.006 0.125
(0.0002) (0.0001) (0.0006) (0.0004)
331 0.004 0.120 382 0.002 0.098
(0.0027) (0.0020) (0.0015) (0.0011)
332 0.019 0.121 383 0.008 0.056
(0.0017) (0.0013) (0.0002) (0.0002)
341 0.004 0.102 384 0.004 0.073
(0.0016) (0.0012) (0.0002) (0.0001)
342 0.011 0.134 390 0.005 0.143
(0.0016) (0.0012) (0.0062) (0.0047)
351 0.012 0.107
(0.0029) (0.0023)
Figures shown are averages over time of the point estimates of the persistent shock 2 and the transitory
shock for the respective industries. The figures in parentheses are the averages of the corresponding
2
standard errors.
Table IV: Trade Policy and Income Risk  Panel Estimates
Variables 2 2
vs vs
0.043 0.140
(0.060) (0.051)
0.035 0.017
(0.044) (0.031)
· Dn 0.090 0.109
(0.047) (0.047)
e 0.621
(0.207)
g 1.208
(0.414)
· e 0.539
(0.184)
· g 1.055
(0.370)
Time Effects Included
Industry Fixed Effects Included Included
N 945 945
R2 0.058 0.044
Figures in parentheses are robust standard error estimates obtained by allowing for heteroscedasticity,
contemporaneous correlation of errors across industries and serial correlation within industries.
Table V: Industry Average Characteristics (1997)
Industry Age Education Wage
311 32.11 7.98 14.52
313 31.45 9.76 24.80
321 33.31 8.69 17.09
322 30.02 8.44 13.50
323 29.76 7.82 17.42
324 29.55 7.14 15.66
331 30.83 8.77 14.40
332 30.99 8.31 17.44
341 30.05 8.69 18.31
342 31.68 10.77 23.55
351 34.41 11.93 50.63
352 32.75 11.22 30.06
353 38.54 11.83 41.58
356 30.27 9.16 19.43
369 33.98 7.79 19.27
371 36.31 11.07 47.89
381 32.20 8.85 18.51
382 30.98 10.50 25.91
383 28.81 9.60 23.19
384 29.40 10.12 24.90
390 29.93 9.05 13.92
Age and education are average age and education of the labor force measured in years. Wage denotes
the average monthly wage in thousands of Pesos.
Table VI: Trade Policy and Income Risk  Effective Rates of
Protection
Variables 2 2
vs vs
0.019 0.109
(0.043) (0.045)
0.009 0.015
(0.032) (0.026)
· Dn 0.076 0.098
(0.042) (0.042)
e 0.463
(0.179)
g 0.935
(0.345)
· e 0.397
(0.157)
· g 0.807
(0.307)
Time Effects Included
Industry Fixed Effects Included Included
N 945 945
R2 0.058 0.042
Figures in parentheses are robust standard error estimates obtained by allowing for heteroscedasticity,
contemporaneous correlation of errors across industries and serial correlation within industries.
Table VII: Trade Policy and Income Risk  Annual Estimates of
2
Variables 2 2
ERP
0.132 0.103
(0.061) (0.056)
0.017 0.007
(0.038) (0.028)
· Dn 0.094 0.081
(0.035) (0.038)
e 0.635 0.485
(0.229) (0.231)
g 1.162 0.910
(0.537) (0.447)
· e 0.549 0.413
(0.204) (0.200)
· g 1.010 0.781
(0.486) (0.400)
Industry Fixed Effects Included Included
N 252 252
R2 0.13 0.14
Figures in parentheses are robust standard error estimates obtained by allowing for heteroscedasticity,
contemporaneous correlation of errors across industries and serial correlation within industries.
Table VIII: Trade Policy and Income Risk  Robustness§
Variables 2 2
AD Excluded 9596 Excluded
0.133 0.150
(0.052) (0.055)
0.034 0.028
(0.031) (0.032)
· Dn 0.113 0.116
(0.048) (0.046)
e 0.608 0.540
(0.212) (0.226)
g 1.126 1.303
(0.425) (0.466)
· e 0.531 0.472
(0.188) (0.199)
· g 0.985 1.123
(0.379) (0.414)
Industry Fixed Effects Included Included
N 809 861
R2 0.04 0.045
§Figures in parentheses are robust standard error estimates obtained by allowing for heteroscedasticity,
contemporaneous correlation of errors across industries and serial correlation within industries. In the first
column (marked `AD Excluded'), observations from industries with high levels of antidumping protection
were excluded. In the second column (marked `9596 Excluded'), observations from the years 1995 and 1996
have been excluded. See Section VI for a detailed discussion.
Table IX: Welfare Effects¶
Change in 2 Welfare Change Welfare Change
(Æ2 = 0.008) =1 = 2
Trade Reform
reduced by five percent 0.005 0.98 1.96
(0.002) (0.39) (0.79)
Macroeconomic Factors
( level = ten percent)
g lower by five percent 0.002 0.39 0.78
(0.001) (0.20) (0.40)
e appreciation by ten percent 0.003 0.59 1.18
(0.001) (0.20) (0.39)
Macroeconomic Factors
( level = five percent)
g lower by five percent 0.005 0.98 1.95
(0.001) (0.29) (0.59)
e appreciation by ten percent 0.006 1.18 2.36
(0.002) (0.40) (0.80)
¶Welfare changes are measured in compensating variation terms and denote the change in lifetime con
sumption necessary to compensate agents for the short term (one year) increases in 2 (relative to its sample
mean of 0.008) that result under the exercises being considered. denotes the coefficient of relative risk
aversion. Standard errors for the estimated welfare effects were obtained by simulation.