unemployment duration and business cycle in argentina a ... · roxana maurizio† and ana paula...
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Unemployment Duration and Business Cycle in
Argentina
A Quantile Regression Analysis.
Roxana Maurizio† and Ana Paula Monsalvo‡Universidad Nacional de General Sarmiento (Argentina)
October, 2008
Abstract
Argentina constitutes an interesting case for the analysis of thelabour market given that during the nineties it reached high economicgrowth rates and a stable macroeconomic environment together witha significant raise in unemployment. This dynamic was associated toincreases in the entry flows to unemployment and the average durationof these episodes. The proportion of long-term unemployment alsogrew significantly.
The aim of this paper is twofold. First, to evaluate the presence ofdifferential effects of the business cycle and changes in the productivestructure on unemployment hazard rates along the elapsed unemploy-ment duration of the spells. Second, to test the validity of the propor-tional assumption imposed in most of the studies about unemploymentduration as well as to propose the use of an alternative econometricmethod. Censored quantile regressions will be used in order to esti-mate in a more flexible and robust way the effect of covariates on theconditional distribution of duration. This is the first study in apply-ing this methodology to unemployment duration in Argentina. Theresults indicate that the reduction of the labour opportunities impliedan increase in unemployment duration, especially for those unemployedwith long-term episodes. As a consequence, the long unemploymentspells became even longer during the period under analysis.
Keywords: unemployment duration, censored quantile regression,business cycle, Argentina.
†[email protected]‡[email protected] (+5411 4469 7506)
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JEL: J64, J65, E24
1 Introduction1
Why should the study of unemployment be extended in order to include notonly its incidence (unemployment rate) but also its duration? This questionhas at least two possible answers. The first one is that the unemploymentrate reflects both, the entry flows and the average duration of unemploymentepisodes. For example, a high unemployment rate is consistent with theoccurrence of intense entry flows together with episodes with low durationsor may correspond to a lower incidence of entries in a context of long-termunemployment spells. The second one is the possibility of obtaining anestimation of the complete unemployment duration distribution as well asthe way in which different factors influence it.
From a methodological point of view, the estimation of the conditionaldistribution of unemployment duration requires the application of economet-ric tools different from the usual duration models. In particular, they areneeded in order to solve two important shortcomings. First, the parametricmodels (Weibull and log-logistics, among others) and the semi-parametricCox model estimate the effects of the covariates only in the centre of theconditional distribution. However, this point may not be representative ofthe effect of the covariates in other position of the distribution. Addition-ally, Cox model imposes a proportional hazard rate assumption. This meansthat the effects of covariates remain constant along the duration the unem-ployment episode. In order to avoid these limitations, the censored quantileregression (CQR) appears as a method to model in a more flexible and ro-bust way the relationship between the covariates and the hazard rates aswell as the error distribution.
This paper has two aims: the first one is to evaluate the presence ofdifferential effect of the business cycle and the changes in the productivestructure on unemployment hazard rates along the elapsed unemploymentduration of the spells. The hypothesis here is that the worsening of thelabour market conditions during the nineties had dissimilar effects on theunemployed with different length of the episodes. The second aim is to testthe validity of the proportionality assumption and proposes the use of CQRas alternative method for survival analysis.
The analysis will contribute to improve the knowledge about the Ar-gentine labour market from a dynamic perspective while incorporating anaspect that has not been studied in our country yet such as the impact of the
1A previous version of this paper was presented at “Sextas Jornadas de Mercado deTrabajo y Equidad en Argentina”, Universidad Nacional de General Sarmiento, Argentina,2007. The authors would like to thank Paula Giovagnolli, Walter Cont, Walter SosaEscudero, Guillermo Cruces, Juan Martin Moreno and Martin Lopez Daneri for theirthoughtful comments to a previous version.
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business cycle and other variables on the complete distribution of the unem-ployment duration. Additionally, the results will help to improve the publicpolicy design, with emphasis in the prevention of long duration unemploy-ment, especially in a country characterized by high rates of unemploymentand very scarce insurance coverage.
The paper follows with a review of the international literature aboutunemployment duration. The third section describes the most relevant styl-ized facts related to the macroeconomic regime and to the evolution of un-employment in Argentina. The fourth section details the data source andthe building of the database. The fifth section describes the econometricmethodology. The sixth section analyzes the econometric results from theapplication of the CQR. The last section presents the conclusions.
2 Literature Review
There is vast international literature about unemployment duration. How-ever, there are relatively few and recent studies on the determinants ofunemployment duration in Argentina. This is to a certain extent becausethat such phenomenon has gained more relevance in the nineties and thedatabases needed for this type of analyses became available only at thebeginning of that decade.
These studies were generally based on parametric or semi-parametricspecifications of duration models. In all cases, they have analyzed the tran-sitions from unemployment to employment. Galiani and Hopenhayn (2000)modelled the accumulated risk of unemployment using a model based onthe Cox proportional form (1972).2 Arranz et al. (2000) estimated a dis-crete semi-parametric model for men’s unemployment exit rates based ona log-logistic specification. Cerimedo (2004) used a log-log complementarymodel for discrete duration data. In all the three cases, the baseline hazardfunction is modelled in a non-parametric form through the use of dummyvariables indicating duration intervals. One common assumption in thesestudies refers to the homogeneous effect of the covariates along the condi-tional distribution of duration.
However, there is empirical evidence for Argentina and other countriesthat suggests that this assumption is not valid, at least for some covariates.
Taking this aspect into account, Koenker and Geling (2001) appliedquantile regression (QR) -based on the seminal work of Koenker and Bas-set (1978)- to the survival analysis as an alternative way of modelling thebaseline hazard function and the effect of the covariates in a unified andflexible manner. Koenker and Bilias (2001) used this methodology for theanalysis of unemployment duration based on administrative data in order
2This study also includes an estimation of the conditional probability of exit fromemployment to unemployment.
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to evaluate the impact of different schemes of unemployment benefits on theduration of the spells. One frequent result found for developed countries isthat the insurance prolongs the duration of the episodes. The utilizationof QR allows seeing that such impact is more intensity in the intermediateintervals of duration and less in the extremes.
The type of information used in Koenker and Geling (2001) and Koenkerand Bilias (2001) allowed the estimation of the complete duration of unem-ployment. However, a usual problem of the studies on unemployment dura-tion is that it is not possible to observe the episode until it ends and, there-fore, the data are usually right-censored. Hence, Ludemann et al. (2005)went further and applied CQR (introduced by Powell, 1984 and 1986) tostudy the unemployment duration in Germany. They found that the increaseof the episodes’ duration was not generalized but was mainly concentratedin older individuals. Also, the greater the wage before unemployment, theshorter the episode’s duration, a phenomenon that increase in the upperquantiles of the distribution.
In the analysis of unemployment sometimes could be more interesting tofocus on the hazard rate rather than unemployment duration. In this sense,Fitzenberger and Wilke (2005) proposed a way to estimate the exit ratesfrom unemployment by applying the methodology suggested by Machadoand Portugal (2002) and Guimaraes et al. (2004). The authors found evi-dence that the proportional assumption is violated for some covariates. Thisis reflected in the fact that the hazard functions for the different groups ofunemployed workers are not parallel but cross each other.3
Machado et al. studied the changes in the distribution of unemploymentduration in the United States applying CQR. Moreover, based on the de-composition method of Machado and Mata (2005), they estimated the effectof changes in the covariates’ distribution and in the conditional distributionof duration. Contrary to what was expected, changes in the labour forcecomposition are not as important and changes in the distribution of the un-employment duration are mainly due to two opposite effects: an increase inthe transition rates between jobs and a greater sensitivity of unemploymentduration to the rate of unemployment. As a result, the shortest episodesshortened even more, whereas the longest ones became longer.
Finally, Fitzenberger and Wilke (2007) estimated the effect of unem-ployment benefits’ duration and value on the unemployment duration andthe post-unemployment wages in Germany. They used censored Box-Coxquantile regression and found that the effect of an increase in the benefit’sduration is greater in the highest quantiles of the distribution.
Summing up, these few and recent studies based on the QR method show
3They found that the difference in the exit probabilities between single and married,and winter and summer were not constant along the distribution of the unemploymentduration. Bover et al. (1996) also found similar results when comparing those with andwithout unemployment insurance.
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the advantages of using this econometric tool in the survival analyses. Inthis paper we will apply this methodology in order to estimate the effect ofcovariates on the conditional distribution of duration without imposing theproportionality assumption a priori.4 As mentioned, this is the first studythat applies this methodology to the analysis of unemployment duration inArgentina.
3 Macroeconomic Performance and Labour Mar-
ket during the Nineties
After decades of macroeconomic instability, the stabilization plan ,“Con-vertibility Plan”, introduced in 1991 was based on the establishment of afixed exchange rate and the convertibility of the national currency with theAmerican dollar. From this year onwards, important progress was madetowards macroeconomic stability: inflation was rapidly controlled and GDPgrew significantly, especially during the first half of the decade.5
During this whole period it is possible to identify three differentiatedphases. The first lasted from the beginning of the currency board up to1994 and it was characterized by high economic growth rates that only re-sulted in a weak creation of employment. Although the high growth ratesof the first years contributed to the increase of employment in non-tradablesectors, the trade opening and the exchange rate appreciation seriously at-tempted against the employment creation in the industrial sector.6 At thesame time, the reduction of the price of capital goods in relation to labourmade it possible to incorporate embodied technology to an economy thathad experienced a low level of investment during the eighties. This pro-cess was registered jointly with a rise in the participation rate which alsocontributed to the increase of unemployment. All these facts strongly weak-ened the employment requirement, with the consequent increase of openunemployment rates, even when the economy exhibited, at the beginningof the 90’s, a vigorous growth (Figure 1). On the poor performance of thelabour market, the second phase started with the recession of the middle ofthe decade (associated to the “tequila effect”), which severely worsened thegeneral conditions of the labour market, raising unemployment to 20,2% inMay 1995 in Greater Buenos Aires (GBA), and 18,4% in total urban centres
4Following to Lancaster (1990, chapter 7): “There is no known economic principlethat implies that hazard functions should be proportional and the few non-stationarystructural transition models that have been derived do not generally lead to proportionalhazard models”.
5For more details about convertibility, see, for instance, Damill et al. (2002).6The manufacturing industry started to show an important net loss of jobs since the
beginning of the decade: between 1991 and 1994 employment registered a 10% reduction,while output expanded 30%. Between 1991 and the end of 2001 the employment loss wasaround 40% (data coming from the Industrial Survey).
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Figure 1: GDP (at constant 1993 prices) and unemployment rate.May 1991-October 2002
2000
0022
0000
2400
0026
0000
2800
0030
0000
GD
P
510
1520
25
01 Jan 91 01 Jan 94 01 Jan 97 01 Jan 00 01 Jan 03Period...
Unemployment rate GBA Unemployment rate Total Urban Center
GDP
(Figure 1). Once the external difficulties were overcome, the economy grewagain between 1996 and mid-1998, and this time the employment creationgrew more in line with the expansion of output. Throughout this secondphase the unemployment rate showed a decreasing trend, although the levelswere clearly higher than those of the first phase.
Finally, as from mid-1998 and until the convertibility collapse at the be-ginning of 2002, the economy went through a recessionary phase that gavean additional impulse to the unemployment growing trend and dramaticallyworsened the labour precariousness. In October 2001, the last figure beforethe macroeconomic regime change, the open unemployment rate in GBAwas 19% and 18.3% in total urban centres (Figure 1). Unemployment keptgrowing until May 2002 -as a consequence of the final crisis of the convert-ibility and the shift in the macroeconomic regime-; from then on, it startedto decrease systematically.7
The dynamics of unemployment just mentioned were associated to changesin both the entry flows and the average duration of the episodes. However,along the whole period, the rise in the incidence of unemployment had more
7It seems important to highlight the high similarity between the unemployment trendsregistered in GBA and in all the urban centres as a whole, for which there is data onlysince 1995 (we discuss this below) This is important because in this paper we focus theanalysis on GBA.
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to do with the growth of the entry rate (146%)8 than with the rise in theduration (43%).9 During the first phase, the rise in unemployment camealong with a significant growth of entry rates together with an increase inthe duration of the episodes. This can be seen in Figure 2, which showsdifferent indicators aimed at capturing the behaviour of duration. In par-ticular the indicators “incomplete duration of the ongoing episodes”10, the“average complete duration of all the episodes”, the “unemployment sur-vival median” and the “percentage of long-term unemployment”11, they allreflect the growing difficulties that the unemployed workers had to leave thisstate.12
Figure 2: Unemployment duration and unemployment rate.Greater Buenos Aires 1991-2002. Index 1991=100
010
020
030
040
0
1991 2002year
Unemployment rate Income average durationSurvival median Average Duration (steade state)
In the second phase, the decline in unemployment rates took place to-
8The entry rate is computed as the percentage of unemployed with a duration equalor lower than one month over the total labour force.
9Under the steady-state assumption, the average complete duration of all the episodes,measured in months, is equal to the ratio between the stock of unemployed and the flow ofentry to unemployment (proxied as those unemployed with an up-to-one-month duration).See Layard et al. (1991).
10They are those episodes observed at the moment of the interview.11Defined as the percentage of unemployed with duration of one year or more over the
whole unemployed.12It is important to highlight that this rise in duration was registered despite the increase
in the entry flow to unemployment which, ceteris paribus, should push down the averageduration.
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gether with a reduction of the complete duration of the episodes and ofthe survival median. However, the incomplete duration of the episodes andthe percentage of long-duration unemployed continued to grow until 1996and begun to decrease only in the following years. The latter could bedue to the decline of the entry flows or to the fact that in this context ofemployment growth the unemployed of shorter duration were able to getjobs quicker than those unemployed with longer duration. Finally, duringthe recessionary phase (between 1999 and 2002), the increase in the rate ofunemployment took place together with a rise in duration, a trend that isshown by all the indicators (although with a lag in some cases).
To sum up, throughout the period there is an inverse relationship be-tween the economic cycle and the unemployment rate, except for the firsthalf of the convertibility regime. On the other hand, there is a direct re-lationship between the unemployment rate and several measures of dura-tion (except for some cases during the second phase), thus indicating aninverse effect between the cycle and the duration of episodes as from themid-nineties. At the same time, even though the dynamics of unemploy-ment incidence and its duration have had the same sign, the intensity hasbeen different, being higher in the first case. Nevertheless, the proportion oflong-term unemployment has also increased significantly. All this evidenceserves as a general framework for the more detailed analysis of the changesthat took place in the whole distribution of unemployment duration (up tothis point we have only analyzed the average duration), which we carry outbelow.
4 Source of Information
Data used in this paper come from the regular household survey of Ar-gentina, the Permanent Household Survey (EPH) carried out by the Na-tional Statistical Office (INDEC), which covers urban areas and collects in-formation especially on labour market variables. Until 2003, it was carriedout twice a year in 28 urban centres, during May and October. However, theanalysis will be restricted to Greater Buenos Aires for the period 1991-2002,given the lack of micro-data for other surveyed areas for the whole period.13
Although the EPH is not a longitudinal survey, its rotating panel sam-ple allows drawing flow data from it. In particular, a selected householdshould be interviewed in four successive moments or waves. Consequently,by comparing the situation of an individual in a given wave to that of thesame person in the following one (i.e. five or six months later), it is possible
13In 2003 the survey underwent methodological changes (from “EPH Puntual” to “EPHContinua”) and produces since then quarterly labour market data. These methodologi-cal changes implied a discontinuity in the labour market series, including unemploymentduration, making comparison difficult. For this reason the analysis ends in October 2002.
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to assess if he/she has experienced changes in diverse variables, includingoccupational variables. In order to have enough observations, transitions ofthe entire period (1991-2002) were pooled. For the same reason, panels fromtwo successive waves have been built, instead of using the four waves due toloss of observations that would occur in the latter case.
Additionally to using the panel structure of the sample, this paper alsouses retrospective information in order to apply duration models. Specifi-cally, we restricted the sample to those individuals that were unemployedin the first of those two interviews. All those people are asked regardinghow long she/he has been in this state. From this information only theincomplete duration of the episode can be drawn. However, the fact of be-ing able to observe the individuals in two successive waves allows knowingwhich of these episodes comes to an end during the period of observation.In these cases, an approximation of the complete duration can be known.For those episodes still in progress at the time of the second interview, theduration is right censored because the only fact that we know is that thecomplete duration is at least (i.e. longer than) the elapsed duration in thelast observation.14
It is important to highlight that given the different behaviour of thetransitions from unemployment to employment with respect to the exitsto inactivity, it does not seem convenient to analyze the exits from unem-ployment to these two destinations jointly.15 In addition, given that one ofthe aims of this paper is to relate the unemployment duration (and the exitsfrom this state) to the economic cycle, we decided to focus on the transitionsfrom this state to employment only.16 The final sample has 6,525 individ-uals. The characteristics of the population in the sample are presented inTable 1.
Data on movements coming from this source face limitations. Some ofthese derive from the sampling design itself: 25% of the sampling panel isrenewed in each wave, thus allowing comparing only 75% of the sample.Yet, this does not hinder the aim of the paper due to the possibility ofpooling the data in order to work with enough observations. Nonetheless,it should be taken into account that the effective proportion of individualsand households that are actually matched using panels from two successivewaves is lower than 75% due to attrition. Therefore, even if the number
14Those cases for which durations were not declared were excluded. They representedless than 1% of the sample.
15For example, it can be seen that as unemployment duration grows, the probabilityof exit to an occupation diminishes, while the probability to enter economic inactivityincreases, thus showing markedly different behaviours. This could be reflecting a certain“discouraged worker” effect or a reduction in the monetary resources for the search ofjobs.
16The economic cycle could also have an impact on the decision to exit unemploymentand enter inactivity. However, due to constraints of space and because it is not centralfor the aims of this paper we do not analyze this phenomenon.
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of observations left in the pooled panels is still sufficient, the mentionedphenomenon may introduce biases in the sample if the loss of data is non-random. Given the lack of information, these potential biases have not beencorrected in this paper. Another difficulty arises from the fact that not everymovement can be captured when matching two successive waves because atransition is identified by comparing two observations in a five or seven-month span. Individuals could have been through two or more symmetricalmovements during the inter-wave period -e.g. exiting from unemploymentout of the labour force and then returning to unemployment. These changescould occur without being identified implying thus an underestimation ofthe transitions.
Given the fact that in Argentina unemployment episodes are relativelyshort the effect of the longitudinal bias -associated to the fact that at a givenmoment in time long episodes have more probability than short ones of beingobserved-, is expected to be small. However, in a country with low coverageof unemployment insurance it is possible to suppose that those workers whostay longer unemployed (and thus have higher probability of being observed)have characteristics that differ from those who had to rapidly shelter ininformal, precarious occupations due to the impossibility of continuing theactive search for a better quality occupation.
Nevertheless, despite these limitations, this source of information allowsanalyzing adequately the behaviour of unemployment duration and unem-ployment risk, as well as the effect that the business cycle and other factorshave on these variables.
5 Methodology
Standard duration models are frequently used in empirical survival analysis.However, in spite of the great utility of these models, they only allow to studythe effect of the covariates in the centre of the conditional distribution. Inaddition, these models impose the proportional-hazards assumption wherethe covariates affect proportionally the survival function. That is, the effectof the covariates in the exit rate is supposed to be constant throughout theconditional distribution of the duration.17
Quantile regression (QR) methods are being increasingly used as an al-ternative to duration models in survival analysis not only in labour studiesbut also in financial analysis and biometrics, among others. This methodallows the specification of the relationship between the covariates and thehazard rates as well as the error distribution in a flexible and robust way.Unlike the Cox model and the Accelerated Failure Time model, QR does notimpose a proportional effect of the covariates on the hazard, assumptionsthat may not be empirically valid.
17Proportional Cox Model is a clear example of this specification.
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In particular, as the classical linear regression method, from which ispossible to estimate models for conditional mean functions, QR proposes aprocedure for modelling an entire range of conditional quantiles of distri-bution, including the median. Following Koenker and Geling (2001), underproportionality assumption, QR models would estimate a family of parallelconditional quantile functions indicating that the covariates only have a purelocation shift effect. However, QR is more robust and flexible than the pro-portional hazard model or accelerated failure models, due to its possibility ofcapturing diverse effects at different quantiles of the duration distribution.
Nevertheless, in comparison to duration models, QR has three impor-tant drawbacks. On the one hand, it cannot take account of time-varyingcovariates. On the other hand, unlike mixed proportional hazard models,QR models have not been extended to account for unobserved heterogeneity.Finally, by QR models only simple risks can be estimated and no frameworkfor competing risks has been developed yet. In spite of these disadvantages,this paper will be based on QR for the modelization of unemployment dura-tion in order to capture diverse effects at different quantiles of the durationdistribution without imposing any restriction a priori.
The estimating procedure has two parts. First, the estimation of thechanges of quantiles of the conditional distribution in response to the varia-tion of the covariates, following Powell’s methodology of CQR (Powell, 1984and 1986). Second, the obtention of hazard functions from the applica-tion of the simulation method proposed by Machado and Portugal (2002),Guimaraes et al. (2004) and Fitzenberger and Wilke (2005).
5.1 Censored Quantile Regression
As mentioned, Koenker and Basset (1978) introduced QR as a method toobtain a robust estimation of the effect of different covariates over quantilesof the dependent variable.18
In order to describe the application of the method in the survival analysisframework, let yi be the unemployment duration. This is modelled in a log-linear way, as follows:
lnyi = x′
iβ + µi (1)
with i: 1,2,3,...,Nwhere x represents a k covariates vector, β is a k coefficients vector and
µ is a random variable with E(µ /x) = 0. From this specification is possibleto identify as parameters the effect of the covariates over the conditionalmean of the distribution:
18Here we will not present an exhaustive analysis of quantile regression, and their modi-fication in order to take into account right censoring, but only the most important aspectsrelated to the aims of this paper.For more details about these models, see, for example,Fitzenberger and Wilke (2005), Ludemann et al.(2005).
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E(lnyi
xi
) = x′
iβ (2)
These parameters are obtained by OLS (the conventional optimizationproblem of minimization of the error) or by Maximum Likelihood in the casethat some error distribution is supposed.
Similarly, from QR the full range of conditional quantile functions ofthe log of unemployment duration are modelled as a linear function of thecovariates in each τ -quantile:
lnyi = x′
iβ(τ) + µi(τ) (3)
Given any random variable t with continuous and monotonic distributionfunction F(t), the τ -quantile is defined as the value Q(x) that satisfies:
F (Q(τ)) = τ (4)
where τ ∈ (0,1) and denotes that the -quantile is the value of the supportof the distribution that accumulates τ% of total observations.
Also, due to it is supposed that Qτ (µi(xi)) = 0 , that is, the τ -quantileof the distribution of the error conditional to the covariate vector is zero.Therefore:
Qτ (lnyi/xi) = x′
iβ(τ) (5)
where Qτ (lnyi/xi) denotes the τ -conditional quantile of the logarithm ofthe duration of the unemployment given x. Therefore, for each covariate avector of coefficient β(τ) is estimated resolving the following minimizationproblem:
minβτ∈RK
n∑
k=1
ρτ (yi − x′
iβχ(τ)) (6)
Where ρτ = z (τ − I [yi − x′
iβ(τ)]), I[*] is the ’check function’ whichadopts value 1 if [yi − x′
iβ(τ)] < 0 and 0 otherwise.
Finally, equivariance property to monotone transformation of the con-ditional quantile function allows us re-writing the expression [5] directly interms of unemployment duration, given the covariates set:
Qτ (yi/xi) = ex′
iβ(τ) (7)
Until now, complete duration of the spells was supposed from which thecoefficient β(τ) can be estimated following to Koenker and Basset (1978).However, data used in this paper does not allow the direct application ofthis method because of right censoring. Therefore, some modifications are
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necessary in order to take this fact into account applying CQR, as wassuggested by Powell (1984, 1986).
Specifically, with right censoring, the observed duration yi will be de-termined by yi = min(y∗i , yci) being y∗i the true elapsed unemploymentduration and the censor point for each spell. Then, CQR is obtained by theminimization of a function similar to [6], as shown next:
1
N
∑
i=1
ρτ (ln(yi) − min(y∗i , yci)) (8)
Powell (1984, 1986) shows that the CQR estimator, ˆβ(τ), is√
N -consistentand asymptotically normal distributed. Additionally, [8] is a more generalmethod than the proposed by Koenker and Basset (1978) due to the inclu-sion of [6] as a special case where yci → ∞.
5.2 Hazard Function estimation based on Quantile Regres-
sion
As mentioned, often in empirical duration analysis it is more relevant toestimate the effect of the covariates on the hazard rate than the impact ofthe covariates on duration itself. In the context of QR there are differentmethods to obtain the estimated conditional hazard functions. Among them,the one proposed by Machado and Portugal (2002), Guimaraes et al. (2004)and Fitzenberger and Wilke (2005) appears as the most appropriate.
They have proposed a method of estimation of the conditional hazardfunction implied by the estimated quantile regression based on a resamplingprocedure.19 In particular, this procedure consists in obtaining empiricallythe hazard function following three main steps. First, to simulate data basedon the estimated quantile regressions for the conditional distribution of theduration Ti. Second, given that unemployment duration is a positive ran-dom continuous variable, the density function and the distribution functioncan be estimated directly from simulated duration data. Third, the hazardfunction for each quantile of conditional distribution is obtained as the ratiobetween the density function and the survival function. The procedure is asfollows:
1. Generate M independent random draws τm , m = 1, , M from auniform distribution U(τI , τS), where I, S are the bottom and the toplimits of distribution support, respectively.20
2. For each τm the QR model is estimated and M vectors β(τm) areobtained.
19Following Fitzenberger and Wilke (2005), this procedure is more appropriated than alinear approximation of the hazard rates between the different τ -quantiles.
20In general, the limits are chosen in light of the type and the degree of censoring in thedata.
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3. For a given value of the covariates x0 M simulated durations are ob-tained as:21
T ∗
m = qm(Ti/x0) = e
(
x′
0ˆβ(τm)
)
with m= 1,2,...,M
4. Based on the sample T ∗ the conditional density function f∗(t|x0) andthe conditional distribution function F ∗(t|x0) are estimated.
5. Finally, from the density function and the distribution function, thehazard function is obtained as follows:
λ0(t) =(τS − τI)f
∗(t|x0)
1 − τI − (τS − τI)F ∗(t|x0)(9)
where the conditional density function is obtained using the kernelestimator:
f∗(t|x0) =1
Mh
M∑
m=1
K((t − T ∗
m)/h) (10)
where h is the bandwidth and K(.) the kernel function.22
6 Econometric Results
First of all, the Cox Model is applied in order to obtain an initial test of thevalidity of the proportional-hazards assumption. Then, the results from QRand the empirical hazard functions for each covariate will be analyzed.
In both cases, the effect of the macroeconomic situation on the proba-bility of exit from unemployment (one of the most important dimension tobe analyzed) will be estimated alternatively through different specifications:(a) dummy variables representing each wave of the EPH for the period be-tween May 1991 and October 2002;23 (b) dummy variables corresponding tothe three economic phases pointed out in section 3; (c) a dummy variablethat takes value equal one in the case of a negative yearly rate of economicgrowth (“recession”); and (d) the rate of unemployment.
21This step is supported by Integral Transformation Theorem that impliesT ∗
m = F−1(τm)22For more detail about kernel estimator for density function, see, for instance, Silver-
man (1986)23Due to the lack of information necessary to build the panels, it was not possible to
include the wave of October 1992.
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6.1 Proportional hazard assumption
Before examining the result of the test a first analysis of the covariates’ ef-fect on the unemployment exit rate will be made, particularly focusing inthose that capture the effect of the economic cycle. Table 2 to Table 5 showthe Cox proportional model estimates corresponding to each specification.There are three important results obtained from alternative (a).24 On theone hand, it can be seen that the coefficients of the year-wave dummy vari-ables are statistically significant (except for the year 1992), and all of themshow a negative sign, thus indicating a reduction in the exit rates with re-spect to 1991. This was expected, for in that year unemployment registeredthe lowest value of the series. On the other hand, when the coefficients areanalyzed in greater detail, it can be seen that they fit very well the dif-ferent phases of the economic cycle, especially from the second half of thenineties. In fact, from 1996 to the end of 1998 there is a reduction in thenegative gap of exit rates with respect to 1991. From then on, the oppositeprocess appears, especially during the last years of the series, associated tothe macroeconomic crisis.
Additionally, in the first phase (until 1994), consistently to what wasmentioned, the estimated coefficients show a different behaviour than thebusiness cycle. In particular, in this expansive phase the estimated prob-abilities of exiting unemployment to employment diminish. On the otherhand, these results are compatible with the dynamics of the unemploymentrate. Finally, a strong asymmetry can be seen in the behaviour of exit prob-abilities given that, despite of during the economic recovery after the 1995crisis the rates of economic growth were similar to those of the first phase,the probabilities of exiting unemployment were significantly lower. Again,this is correlated to the growing unemployment rates.
This scenario is consistent with specification (b), in which the variablesindicating the periods are also statistically significant and negative (the base-line category corresponds to the first period). From that specification it fol-lows that in these two phases the probability of exiting unemployment repre-sented, approximately, 75%25 of the probability experienced in the first halfof the nineties. No significant differences are registered between the secondand third phase. Moreover, specifications (c) and (d) confirm again the roleplayed by the macroeconomic and labour situation on the unemploymentexit rates.
As a result, from the different specifications we can conclude that thebusiness cycle (particularly after the productive restructuring) turns out tobe a relevant factor in determining the probability of ending of an unemploy-ment spell. This evidence makes it possible to continue analyzing this effect
24The baseline category is year 1991.25The relative risk is obtained as exp(β). This is the average value, which is assumed
to be constant along the conditional distribution of duration.
15
more deeply, based on the QR method. In order to do so, we work withspecification (b) and (c) only because, on the one hand, the dummy vari-ables for the different phases correctly represent what happened throughoutthe whole decade; and, on the other hand, because it is a more parsimo-nious specification than alternative (a) considering the dimension of thecoefficient matrix obtained with this method in this specification. Besides,working with dummy variables instead of continuous variables as in the caseof (d) makes it possible to building empirical hazard functions for each subperiod or business cycle phases and compare them.
The rest of the variables included in the regressions (we will not ex-haustively discuss its results here) present, in general, the expected signsin all the specifications (Table 2 to Table 5).26 Men and household headshave greater probabilities of exiting unemployment than women and non-household heads, respectively. This may be the result of a more activesearch and a higher acceptance of job offers, given the responsibility theyhave within the households, especially in the case of household heads. Inthe case of gender, a certain degree of segregation against women could beoperating, thus reducing the job offers they get.27 Age does not presenta monotonous relationship with exit rates, where a positive relationship isobserved up to 40 years old (which is not always statistically significant) andthen a negative relationship, indicating greater difficulties to enter jobs bothfor young people and for older adults.28 The presence of underage childrenin the household is associated to higher exit rates, which could be indicating,among other factors, that the need to receive an income in order to face thehousehold’s requirements becomes more urgent. A higher family income iscorrelated with higher exit rates, which may be associated with the fact thatthis entails greater financial support for the search of jobs, given the poorcoverage of the unemployment insurance in the country.
A higher educational level is associated to lower probabilities of exitingunemployment. Even though a detailed analysis of this result goes beyondthe scope of this study, it could be argued that it is related, on the one hand,to an attempt on the part of the individual to get a job with attributesadequate to his skills or with higher reservation wages, which makes thesearch period longer. On the other hand, it could be related to the factthat in a context of jobs destruction, the obsolescence of general human
26The baseline category: women, non-household heads, younger than 26 years old, withcomplete primary school, that do not search for a job to cover the household’s basic needs,and live in households with no underage children. We did not include the unemploymentinsurance among the covariates due to its poor coverage in Argentina. During the nineties,the latter covered less than 10% of the unemployed.
27It is important to remember that exits to inactivity are not considered in the analysis.Was this destination included, it could substantially change these results given that womenand non-household heads are more intermittent in the labour force.
28In the case of young people, the inclusion of exits to inactivity could also alter theresults.
16
capital and, in particular, of specific human capital could have played a role,which reduces the probabilities of getting a job. Finally, those unemployedthat search for jobs to cover the household’s basic budget register higherprobabilities of getting a job, which could be reflecting the need to performa more active search for jobs.
Once the residuals of these regressions are obtained, it is possible to per-form the test of the proportional-hazards assumption based on the scaledSchoenfeld residuals.29 From Table 6 to Table 9 (corresponding to each spec-ification) it can be seen that the hypothesis is globally rejected in all thefour specifications of the model. However, when the dummy representingeach waves are individually evaluated, the hypothesis is rejected in certainmonth-years only (October 1998, May 2000 and May 2001, in which thecoefficient of is statistically different from zero). The hypothesis is not re-jected for the period variables in specification (b), in the case of the dummyindicating recession in specification (c) and for the unemployment rate inspecification (d). Hence, these results seem to be indicating a proportionaleffect of such variables on the exit rate from unemployment.
However, following the suggestion by Therneau and Gramsch (2000),when analyzing the residuals’ graph as a function of time (Figure 3) strongnon-linearities are observed in almost all cases; for instance, in the caseof both subperiods. Given that the test measures the linear correlationbetween these two variables, the non-linear relationship would be leadingnot to reject the proportional hypothesis when, in fact, it seems to persista behaviour in the residuals which, although not captured by these modelswould be indicating that the assumption is not valid, at least in some cases.On the other hand, in the case of the variable representing the presence ofchildren in the household the graph suggest that the correlation betweenthe residuals and time is null. This would be consistent with the test, whichfails to reject the proportional-hazards assumption.
Hence, the results obtained up to here would be suggesting a non propor-tional effect of the business cycle on hazard rates. This evidence strengthensthe need to go further in the estimations that capture these differential im-pacts on the distribution of duration, as we do in the following section.
6.2 Quantile Regression
In this section we present the econometric results from the application of QR(Table 10 for alternative b and Table 11 for alternative c).30 In particular,
29The null hypothesis of the test is that the variable’s effect on the exit rate remainsconstant along the duration (and thus the effect is proportional). This hypothesis is testedby stating that the correlation between the scaled Schoenfeld residuals and time is null(ρ = 0).
30Estimations were carried out using the CRQ package of the program R (Portnoy, 2003,2008).
17
we analyze the coefficients’ values for 6 different taus: 0.1, 0.2, 0.4, 0.5(median), 0.6 and 0.7. In addition, as a comparison, we present the resultsof the Weibull model. Unlike the previous section, the dependent variablehere is the duration in unemployment (as stated in [7]) and not the exitprobability, and thus we expect the signs of the coefficients to be the oppositeto the ones obtained up to here. In particular, a positive sign indicates ahigher duration in unemployment and therefore a lower probability of exit.
6.2.1 Business cycle and unemployment duration
Based on the Weibull model31 we observe that the dummy variables forboth periods (Alternative b) are statistically significant and have a posi-tive sign. The QR results indicate that the coefficients’ positive sign holdfor the different quantiles, thus reflecting the fact that the increase in du-ration was general for all unemployment spell.32 However, what is moreimportant is that the coefficients’ value of each of the two period variablesdoes not remain constant but rather increases with the position in the dis-tribution. In fact, the coefficients corresponding to the lower quantiles aresignificantly lower than the higher ones, thus suggesting that the increasein the episodes’ duration was verified with greater intensity in the upperextreme of the distribution. The estimate from the alternative (c) confirmsthese results: dummy of recession is positive and increasing with the quan-tiles of the conditional distribution of duration. This, in turn, means thatduring the period long unemployment spells became even longer.
In Figure 4 we present the set of coefficients obtained with the differ-ent taus for each covariate, and also the intervals with a 95% of confidencelevel obtained from the bootstrapping method (with 500 repetitions). Thehorizontal line drawn in each graph represents the null hypothesis: if theconfidence interval contains the number zero, the coefficient is not statisti-cally significant. In the case of the variables Period 1995-1998 and Period1999-2002 and dummy of recession, the graphs clearly show a growing andsignificant trend of the coefficients (only in the first quantiles of the variablePeriod 1999-2002 the confidence interval contains number zero), which al-lows us to conclude that the worsening of the labour market situation wasmore severe in spells with long duration unemployment.
One possible explanation for this behaviour could be related to the pro-ductive restructuring process that Argentina went through, particularly dur-ing the first years of the nineties and, as it was mentioned, involved a deepchange in the sectoral pattern of the economic growth. Particularly, it couldbe argued that dismissed workers of the manufacturing sector (especiallythose with long tenure) were not absorbed by the productive sectors grow-
31The control group is the same than in previous regressions.32Also here the coefficients are statistically significant with the only exception of quantile
0.1 for the 1999-2002 period.
18
ing in both the first and second phase, and thus they accumulated time inthe unemployment. Let us remember that the increase in the duration ofthe longest episodes had begun to be evident in the second period, whenGDP was growing and the unemployment rate was decreasing. Hence, suchargument could account for the increase in duration of some episodes evenin this expansive phase of the business cycle.
Some of the evidences presented in Table 12 seem to be consistent withthis hypothesis. In the first place, the table shows the distribution of theunemployed by the last job’s activity sector and by the duration in un-employment. There can be noticed a strong rise in the proportion of theunemployed with a 2-or-more-years duration coming from the manufactur-ing industry over the total of unemployed with the same duration. In fact,this is the activity sector that experiences the biggest changes in this indica-tor. The opposite happens with the shorter episodes of unemployment (oneyear or less), within which the manufacturing activities gradually lost im-portance; this could be associated to the reduction in the stock of employedin the manufacturing industry. On the other hand, the Table 12 shows thevariations in the median and other percentiles of duration in unemploymentby activity sector between 1991-1994 and 1995-1998. It can be seen that themajor increases occur in the manufacturing sector, especially in the higherpercentiles. Then, both indicators would be accounting for the greater rela-tive difficulties to get a job faced by individuals previously employed in themanufacturing industry; this, in turn, would have contributed to the higherduration of these unemployment episodes.
Finally, as indicated in section 5, once the conditional duration basedon QR is estimated, it is possible to obtain the empirical hazard functionsfor each of the covariates.33 In Figure 6 we present only some of them. Ineach graph we compare the probabilities of exiting unemployment for twoindividuals that are equal in all the observable attributes except for the onethat is being evaluated. In order to do so, it was necessary to define the setof characteristics on which those functions are estimated. The effect of theperiod variables was estimated separately for men and women.
In both cases it can be clearly seen that the hazard functions are notparallel but they rather present very different behaviours. In particular, thegap in the exit rates between the first period, on the one hand, and theother two, on the other hand, does not remain constant but rather increaseswith duration, with certain fluctuations. Moreover, the most importantdifferences are verified between the first years of the nineties and the rest ofthe period, while the hazard functions of the second and third phase are verysimilar. Similar results are obtained in the case of the recession variable.In particular, the gap in the exit rates between an expansion and recession
33For the estimation of the density functions needed to build the hazard functions wechose to use an adaptative kernel Epanechnikov with an optimum bandwidth.
19
phase also increases with the unemployment duration.
6.2.2 Effects of other covariates
The results obtained for the rest of the variables are also interesting (Table10 and Table 11). In the case of the gender variable the gaps in unemploy-ment duration between men and women gradually widen, while the smallestdifferences can be seen in the inferior bound of the distribution. This meansthat in the first months of unemployment the differences between men andwomen are not very important, while unemployment duration increases, theprobability of getting a job for a man becomes higher compared to that ofwomen.
A similar behaviour is noticed for household heads, although in this casewe observe a certain gap reduction in the superior quantiles. In the case ofage there is a shift in the sign of the coefficients: these are (in most cases)negative at the beginning and then become positive; many of them are notstatistically significant. In any case, the significance is greater in the higherquantiles and in the superior intervals of age. It is worth to remember thatthe proportional test rejected the null hypothesis for many age intervals inthe different specifications.
The results of the Weibull model also indicate that as education increasesthe duration in unemployment also does. However, the intensity differs byquantile. In general, as from the level complete secondary school or higher itis observed that the duration gaps diminish as the quantile increases (whatis clearly seen in Figure 5). Under the reservation wages assumption or thesearch for a better matching, these results would be suggesting that thesefactors have a stronger impact in the first intervals of duration. The resultsare also consistent with those of the test indicating the non acceptance ofthe proportionality for the complete secondary school or higher educationallevel.
Finally, both for the case of family incomes and the reason for searchingfor a job it is observed that the gaps diminish along duration. In the firstcase, this could be indicating that higher household incomes make it possibleto do a more active search in the first months of unemployment but that thisfinancial source decreases or runs out as time passes in this state. In anycase, the differences between quantiles do not seem to be very important.In the second case, this means that the differences in the intensity of thesearch according to the motive of the search are stronger during the firstmonths in unemployment and then they diminish. In both cases, the testindicated no proportionality.
Therefore, the evidence obtained in this paper from the application ofQR would be indicating that the proportional assumption is not confirmedby the data. Hence, the results obtained from duration models are notrepresentative of what happened in the different intervals of duration in
20
unemployment in the period considered.
7 Concluding remarks
The hypothesis about the differential impact of the worsening in labourconditions during the nineties across unemployed with different elapsed du-ration was confirmed. In fact, the empirical evidence suggests that both theproductive reconstruction process during the first year of the convertibil-ity plan and the macroeconomic instability during the second part of thatdecade implied an increase in unemployment duration, especially for indi-viduals with more difficulties to get a job even in the positive business cyclesubperiod. Therefore, the long unemployment spells became longer. Most ofthem, coming mainly from the manufacture sectors, had no access to train-ing programs in order to facilitate their re-insertion to the new productivestructure.
From a methodological point of view, the proportionality assumption isnot empirically supported not only in the case of the effect of the businesscycle but also in the case of the other covariates. These findings implied theneed of allowing the estimated coefficients to vary over the quantiles of theduration distribution and to change their sign. Thus, quantile regressionappears as a more robust and flexible econometric technique for durationanalysis.
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[2] Bover, O., M. Arellano, and S. Bentolila, (1996) Unemployment duration,benefit duration and the business cycle, Estudios Econmicos 57, Bancode Espana.
[3] Cerimedo, F. (2004) Duracion del Desempleo and Ciclo Economico en laArgentina, Working Paper N 8, CEDLAS, Argentina.
[4] Cox, D. (1972) Regression Models and Life-Tables, Journal Royal Sta-tistical Society.
[5] Damill, M., R. Frenkel and R. Maurizio, (2002) Argentina: A decade ofcurrency board. An analysis of growth, employment and income distribu-tion, Employment Paper 2002/42, International Labour Office, Geneva.
[6] Fitzenberger, B. and R. Wilke, (2005). Using Quantile Regression forDuration Analysis, IZA Discussion Paper N 05-65.
21
[7] Fitzenberger, B. and R. Wilke, (2007) New insights on unemploymentduration and post unemployment earnings in Germany: Censored Box-Cox Quantile Regression at Work, IZA Discussion Paper N 2609.
[8] Galiani, S. and H. Hopenhayn, (2000) Duracion y riesgo de desempleoen Argentina, Documento de Trabajo FADE N 18, Argentina.
[9] Guimaraes, J., J. Machado and P. Portugal, (2004) Has long becomelonger and short become shorter? Evidence from a censored quantile re-gression analysis of the changes in the distribution of U.S. unemploymentduration, Universidade Nova de Lisboa.
[10] Jenkins, S., (2006) hshaz: STATA module estimate discrete time(grouped data) proportional hazards models., Statistical SoftwareComponents S444601, Boston College Department of Economicshttp://ideas.repec.org/c/boc/bocode/s444601.html
[11] Koenker, R. and G. Bassett, (1978) Regression Quantiles Econometrica,46, 33-50.
[12] Koenker, R. and Y. Bilias, (2001)Quantile Regression for DurationData: A Reappraisal of the Pennsylvania Reemployment Bonus Experi-ments Empirical Economics, 26, 199-220.
[13] Koenker, R. and O. Geling, (2001) Reappraising Medly Longevity: AQuantile Regression Survival Analysis, Journal of the American Statis-tical Association, 96(454), 458-468.
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[16] Ludemann, E., R. Wilke and X. Zhang, (2005) Censored Quantile Re-gression and the Length of Unemployment Periods in West-Germany,ZEW Discussion Paper 04-57.
[17] Machado, J. and P. Portugal, (2002) Exploring Transition Data throughQuantile Regression Methods: An Application to U.S. UnemploymentDuration, Statistical data analysis based on the L1-norm and relatedmethods. 4th International Conference on the L1-normand RelatedMethods. Ed. Yadolah Dodge.
[18] Machado, J. and J. Mata, (2005) Counterfactual decomposition ofchanges in wage distributions using quantile regression, Journal of Ap-plied Econometrics, 20, 445-465.
22
[19] Machado, J., P. Portugal and J. Guimaraes, (2006) U.S. UnemploymentDuration: Has Long Become Longer or Short Become Shorter?, IZADiscussion Paper N 2174.
[20] Portnoy, S., (2003)Censored Regression Quantiles, Journal of the Amer-ican Statistical Association, 98(464).
[21] Portnoy, S.,with contributions from T. Neocleous and R. Koencker,(2008) crq: Censored Quantile Regression, The R Project for statisticalcomputing. http://www.r-project.org/ .
[22] Powell, J. (1984) Least Absolute Deviations Estimation for the CensoredRegression Model, Journal of Econometrics, 25, 303-325.
[23] Powell, J., (1986) Censored Regression Quantiles, Journal of Economet-rics, 32, 143-155.
[24] Silverman, B., (1986) Density Estimation for Statistics and DataAnal-ysis, Chapman and Hall.
[25] Therneau, T. and P. Grambsch, (2000) Modeling Survival Data: Ex-tending the Cox Model, Editorial Springer.
23
Figure 3: Scaled Schoenfeld residuals vs. Time
Time
Bet
a(t)
for
per_
gral
2
15 91 300 730
−0.
60.
01995−1998
Time
Bet
a(t)
for
per_
gral
3
15 91 300 730
−0.
80.
0
1999−2002
Time
Bet
a(t)
for
a199
31
15 91 300 730
−1.
00.
0
May 1993
Time
Bet
a(t)
for
a200
11
15 91 300 730
−3.
0−
1.0
May 2001
Time
Bet
a(t)
for
a199
43
15 91 300 730
−1.
50.
0
October 1994
Time
Bet
a(t)
for
rece
sion
15 65 230 610
−0.
60.
00.
6
Recession
Time
Bet
a(t)
for
zmen
or6_
gral
15 91 300 730
−4
04
Children in the household
Time
Bet
a(t)
for
tasa
des.
gral
15 91 300 730
−1.
00.
0
Unemployment rate
24
Figure 4: Estimated coefficients from Quantile Regression.
Coefficients relates to business cycle
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
−0.
20.
00.
20.
40.
6
tau
1995−1998
95% boot: 2.906*IQR
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.2
0.4
0.6
0.8
1.0
tau
1999−2002
95% boot: 2.906*IQR
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
−0.
10.
10.
20.
30.
4
tau
Recession
95% boot: 2.906*IQR
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.02
0.06
0.10
tau
Unemployment rate
95% boot: 2.906*IQR
25
Figure 5: Estimated coefficients from Quantile Regression.
Other Covariables
0.0 0.2 0.4 0.6
34
56
78
tau
Intercept
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−1.
0−
0.6
−0.
2
tau
Gender
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−1.
0−
0.6
−0.
2
tau
Household head
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
6−
0.2
0.2
0.6
tau
Age: 25−30
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
6−
0.2
0.2
0.6
tau
Age: 31−40
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
40.
00.
40.
8
tau
Age: 41−45
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
0.0
0.5
1.0
1.5
tau
Age: 46−50
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
50.
00.
51.
0
tau
Age: 51−55
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
50.
51.
5
tau
Age: more than 55
95% boot: 2.906*IQR
26
Figure:5 Estimated coefficients from Quantile Regression.Other Covariables(continued)
0.0 0.2 0.4 0.6
−0.
6−
0.2
tau
Children in the household
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
6−
0.2
0.2
tau
Incomplete primary
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
40.
00.
2
tau
Incomplete secondary
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
40.
00.
4
tau
Complete secondary
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
20.
20.
61.
0
tau
Incomplete university
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
0.0
0.5
1.0
tau
Complete university
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
0015
−0.
0005
tau
Per capita familiar income
95% boot: 2.906*IQR
0.0 0.2 0.4 0.6
−0.
6−
0.4
−0.
20.
0
tau
Search to cover the budget
95% boot: 2.906*IQR
27
Figure 6: Empirical hazard functions estimated from CQR
.006
.008
.01
.012
.014
.016
Haz
ard
func
tion
10 20 30 40 50Unemployment duration
1991−1994 1995−1998
1999−2002
Men*
.004
.005
.006
.007
.008
.009
0 20 40 60 80Unemployment duration
1991−1994 1995−1998
1999−2002
Women*
* Houseold head, with children, search to cover basic budget
Hazard function by subperiod.0
07.0
08.0
09.0
1.0
11.0
12H
azar
d fu
nctio
n
10 20 30 40 50Unemployment duration
Expansion Recession
Men*
.004
.004
5.0
05.0
055
.006
.006
5
20 40 60 80Unemployment duration
Expansion Recession
Women*
* Household head, with children, search to cover basic budget
Hazard function by phases of the business cycle
28
Table 1: Descriptive analysis of final sample. Total unemployed.
Greater Buenos Aires. 1991-2002Observations Percentage
Final sample 6,525 100%
GenderMen 4,045 62%
Women 2,480 38%Household position
Head 2,464 38%Other 4,061 62%
Educational levelIncomplete primary 691 11%Complete primary 2,003 31%
Incomplete secondary 1,579 24%Complete secondary 1,180 18%
Incomplete university 709 11%Complete university 363 6%
AgeYounger than 20 1,314 20%
21-29 1,218 19%26-30 686 11%31-40 1,138 17%41-45 576 9%46-50 523 8%41-55 460 7%
Older than 55 593 9%Sub-periods
1991-1994 1,043 16%1995-1998 2,948 45%1999-2002 2,534 39%
Children in the householdYes 1,851 28%No 4,674 72%
Search for jobs to cover the households basic budgetYes 2,103 32%No 4,422 68%
Unemployment durationEqual or less 1 month 1,868 29%
2 months 998 15%3 months 654 10%4 months 391 6%5 months 358 5%6 months 499 8%7 months 158 2%8 months 157 2%9 months 70 1%
10 months 87 1%11 months 21 0%12 months 722 11%
More than 12 months 542 8%Right censoring 3,242 50%
29
Table 2: Alternative a. Cox Proportional ModelExit rate from unemployment to employment
Greater Buenos Aires 1991-2002Covariates Coefficient p-value
Men 0.3755 0.0000Household’ head 0.3247 0.0000Educational levelIncomplete primary or less 0.0911 0.1400Incomplete secondary -0.0373 0.4500Complete secondary -0.1964 0.0004Incomplete university -0.2676 0.0001Complete university -0.3667 0.0000Age26 to 30 0.1557 0.011031 to 40 0.0703 0.210041 to 45 -0.1144 0.120046 to 50 -0.3162 0.000151 to 55 -0.4183 0.0000More than 55 years old -0.4914 0.0000Month-YearMay 1992 0.0643 0.7200May 1993 -0.3545 0.0210October 1993 -0.4972 0.0016May 1994 -0.4866 0.0018October 1994 -0.7493 0.0000May 1995 -0.6751 0.0000October 1995 -0.7997 0.0000May 1996 -0.8247 0.0000October 1996 -0.7799 0.0000May 1997 -0.6540 0.0000October 1997 -0.6289 0.0000May 1998 -0.6136 0.0000October 1998 -0.4745 0.0011May 1999 -0.5651 0.0001October 1999 -0.6178 0.0000May 2000 -0.4602 0.0012October 2000 -0.5500 0.0001May 2001 -0.9133 0.0000October 2001 -1.0657 0.0000May2002 -0.9462 0.0000October 2002 -0.8221 0.0000Children in the household 0.1883 0.0000Search to cover the households budget 0.2060 0.0000Per capita familiar income 0.0003 0.0000
Observations 6,525
30
Table 3: Alternative b. Cox Proportional ModelExit rate from unemployment to employment
Greater Buenos Aires 1991-2002Covariates Coefficient p-value
Men 0.3646 0.0000Household’ head 0.3252 0.0000Educational levelIncomplete primary or less 0.1192 0.0530Incomplete secondary -0.0297 0.5400Complete secondary -0.2041 0.0002Incomplete university -0.2612 0.0001Complete university -0.3527 0.0000Age26 to 30 0.1580 0.009631 to 40 0.0584 0.300041 to 45 -0.1439 0.052046 to 50 -0.3186 0.000151 to 55 -0.4276 0.0000More than 55 years old -0.5070 0.0000Period1995 - 1998 -0.2514 0.00001999 - 2002 -0.2747 0.0000Children in the household 0.1845 0.0000Search to cover the households budget 0.2047 0.0000Per capita familiar income 0.0003 0.0000
Observations 6,525
31
Table 4: Alternative c. Cox Proportional ModelExit rate from unemployment to employment
Greater Buenos Aires 1991-2002Covariates Coefficient p-value
Men 0.3851 0.0000Household’ head 0.3540 0.0000Educational levelIncomplete primary or less 0.1184 0.0600Incomplete secondary -0.0243 0.6200Complete secondary -0.2113 0.0001Incomplete university -0.2568 0.0001Complete university -0.3149 0.0003Age26 to 30 0.1622 0.007931 to 40 0.0504 0.380041 to 45 -0.1465 0.050046 to 50 -0.2930 0.000351 to 55 -0.4349 0.0000More than 55 years old -0.5107 0.0000Recession -0.1269 0.0004Children in the household 0.1774 0.0000Search to cover the households budget 0.1695 0.0003Per capita familiar income 0.0003 0.0000
Observations 6,525
Table 5: Alternative d. Cox Proportional ModelExit rate from unemployment to employment
Greater Buenos Aires 1991-2002Covariates Coefficient p-value
Men 0.3662 0.0000Household’ head 0.3207 0.0000Educational levelIncomplete primary or less 0.1040 0.0910Incomplete secondary -0.0388 0.4300Complete secondary -0.2010 0.0003Incomplete university -0.2604 0.0001Complete university -0.3597 0.0000Age26 to 30 0.1454 0.017031 to 40 0.0597 0.290041 to 45 -0.1244 0.092046 to 50 -0.3211 0.000151 to 55 -0.4305 0.0000More than 55 years old -0.5038 0.0000Unemployment rate -0.0502 0.0000Children in the household 0.1896 0.0000Search to cover the households budget 0.2127 0.0000Per capita familiar income 0.0003 0.0000
Observations 6,525
32
Table 6: Test of the proportional-hazards assumptionExit rate from unemployment to employment
Greater Buenos Aires. 1991-2002Alternative (a)
Covariates rho chisq p-value
Men -0.0221 1.5800 0.2090Household’ head -0.0161 0.8610 0.3540Educational levelIncomplete primary or less 0.0013 0.0060 0.9380Incomplete secondary -0.0006 0.0010 0.9750Complete secondary 0.0463 6.9100 0.0086Incomplete university 0.0474 7.1400 0.0076Complete university 0.0428 5.8800 0.0153Age26 to 30 -0.0372 4.4600 0.034731 to 40 -0.0365 4.4900 0.034141 to 45 -0.0309 3.1400 0.076446 to 50 -0.0490 7.9900 0.004751 to 55 -0.0243 1.9400 0.1640More than 55 years old -0.0439 6.4900 0.0109Month-YearMay 1992 -0.0315 3.2900 0.0697May 1993 -0.0149 0.7230 0.3950October 1993 -0.0155 0.7850 0.3760May 1994 -0.0244 1.9400 0.1640October 1994 -0.0186 1.1300 0.2880May 1995 -0.0187 1.1400 0.2860October 1995 -0.0089 0.2600 0.6100May 1996 -0.0207 1.4000 0.2370October 1996 -0.0115 0.4300 0.5120May 1997 -0.0175 1.0100 0.3160October 1997 -0.0200 1.3000 0.2540May 1998 -0.0326 3.4900 0.0616October 1998 -0.0408 5.4500 0.0196May 1999 -0.0228 1.7000 0.1920October 1999 -0.0248 2.0100 0.1560May 2000 -0.0355 4.1100 0.0426October 2000 -0.0232 1.7600 0.1840May 2001 -0.0506 8.3400 0.0039October 2001 -0.0201 1.3200 0.2500May2002 -0.0011 0.0037 0.9520October 2002 -0.0191 1.1900 0.2750Children in the household -0.0075 0.1860 0.6660Search to cover the households budget -0.0390 4.8000 0.0285Per capita familiar income -0.0528 5.7000 0.0169
GLOBAL 116.0000 0.0000
33
Table 7: Test of the proportional-hazards assumptionExit rate from unemployment to employment
Greater Buenos Aires. 1991-2002Alternative (b)
Covariates rho chisq p-value
Men -0.0264 2.2195 0.1360Household’ head -0.0110 0.4020 0.5260Educational levelIncomplete primary or less 0.0008 0.0021 0.9640Incomplete secondary -0.0012 0.0043 0.9470Complete secondary 0.0516 8.5307 0.0035Incomplete university 0.0493 7.6318 0.0057Complete university 0.0413 5.4512 0.0196Age26 to 30 -0.0446 6.4134 0.011331 to 40 -0.0400 5.3768 0.020441 to 45 -0.0324 3.4125 0.064746 to 50 -0.0516 8.8463 0.002951 to 55 -0.0271 2.3933 0.1220More than 55 years old -0.0510 8.7425 0.0031Period1995 - 1998 0.0041 0.0553 0.81401999 - 2002 -0.0149 0.7223 0.3950Children in the household -0.0065 0.1413 0.7070Search to cover the households budget -0.0412 5.3822 0.0203Per capita familiar income -0.0481 4.5565 0.0328
GLOBAL 95.1364 0.0000
34
Table 8: Test of the proportional-hazards assumptionExit rate from unemployment to employment
Greater Buenos Aires. 1991-2002Alternative (c)
Covariates rho chisq p-value
Men -0.0229 1.6413 0.2000Household’ head 0.0017 0.0092 0.9240Educational levelIncomplete primary or less 0.0033 0.0344 0.8530Incomplete secondary 0.0075 0.1800 0.6710Complete secondary 0.0497 7.7459 0.0054Incomplete university 0.0587 10.5977 0.0011Complete university 0.0514 8.3015 0.0040Age26 to 30 -0.0426 5.7307 0.016731 to 40 -0.0500 8.2973 0.004041 to 45 -0.0408 5.3573 0.020646 to 50 -0.0501 8.2112 0.004251 to 55 -0.0312 3.1256 0.0771More than 55 years old -0.0440 6.3850 0.0115Recession -0.0062 0.1215 0.7270Children in the household -0.0087 0.2460 0.6200Search to cover the households budget -0.0470 6.9527 0.0084Per capita familiar income -0.0466 4.0540 0.0441
GLOBAL 85.7430 0.0000
Table 9: Test of the proportional-hazards assumptionExit rate from unemployment to employment
Greater Buenos Aires. 1991-2002Alternative (d)
Covariates rho chisq p-value
Men -0.0238 1.7914 0.1810Household’ head -0.0123 0.5044 0.4780Educational levelIncomplete primary or less 0.0016 0.0082 0.9280Incomplete secondary -0.0009 0.0027 0.9590Complete secondary 0.0507 8.2197 0.0041Incomplete university 0.0477 7.1346 0.0076Complete university 0.0423 5.6895 0.0171Age26 to 30 -0.0417 5.5973 0.018031 to 40 -0.0388 5.0575 0.024541 to 45 -0.0319 3.2859 0.069946 to 50 -0.0509 8.5739 0.003451 to 55 -0.0283 2.6102 0.1060More than 55 years old -0.0507 8.6147 0.0033Unemployment rate 0.0222 1.6762 0.1950Children in the household -0.0087 0.2485 0.6180Search to cover the households budget -0.0426 5.7128 0.0168Per capita familiar income -0.0511 5.2680 0.0217
GLOBAL 93.4181 0.0000
35
Table 10: Quantile Regression Model and Weibull Model. Unemployment durationGreater Buenos Aires 1991-2002
Alternative b.
TAUS WEIBULL
Covariates 0.1 0.2 0.4 0.5 0.6 0.7
Men -0.346 (**) -0.437 (**) -0.531 (**) -0.488 (**) -0.514 (**) -0.481 (**) -0.469 (**)Household’ head -0.162 -0.354 (**) -0.532 (**) -0.520 (**) -0.462 (**) -0.495 (**) -0.411 (**)Educational levelIncomplete primary or less -0.041 -0.114 -0.287 (**) -0.190 (*) -0.236 (*) -0.254 (*) -0.138 (*)Incomplete secondary 0.035 0.084 0.007 0.157 (**) 0.015 -0.038 0.037Complete secondary 0.340 (**) 0.462 (**) 0.343 (**) 0.363 (**) 0.221 (**) 0.106 0.250 (**)Incomplete university 0.591 (**) 0.520 (**) 0.419 (**) 0.473 (**) 0.311 (**) 0.381 (**) 0.364 (**)Complete university 0.811 (**) 0.699 (**) 0.554 (**) 0.504 (**) 0.368 (*) 0.457 (**) 0.501 (**)Age26 to 30 -0.217 (*) -0.197 (*) -0.190 (**) -0.163 (**) -0.282 (**) -0.192 -0.180 (**)31 to 40 -0.327 (**) -0.149 -0.154 -0.048 -0.054 0.006 -0.04241 to 45 -0.327 (**) -0.078 0.172 0.366 (**) 0.320 (**) 0.458 (**) 0.218 (**)46 to 50 -0.200 (*) 0.169 0.353 (**) 0.495 (**) 0.568 (**) 0.907 (**) 0.451 (**)51 to 55 -0.152 0.220 0.704 (**) 0.780 (**) 0.800 (**) 0.866 (**) 0.577 (**)More than 55 years old -0.101 0.072 0.608 (**) 0.889 (**) 1.075 (**) 1.151 (**) 0.722 (**)Period1995 - 1998 0.177 (*) 0.215 (**) 0.424 (**) 0.373 (**) 0.413 (**) 0.458 (**) 0.336 (**)1999 - 2002 0.119 0.190 (**) 0.440 (**) 0.361 (**) 0.463 (**) 0.537 (**) 0.389 (**)Children in the household -0.258 (**) -0.233 (**) -0.273 (**) -0.284 (**) -0.247 (**) -0.181 (*) -0.249 (**)Per capita familiar income -0.001 (**) -0.001 (**) -0.001 (**) -0.001 (**) 0.000 (**) 0.000 (**) 0.000 (**)Search to cover the households budget -0.313 (**) -0.443 (**) -0.288 (**) -0.307 (**) -0.298 (**) -0.118 -0.267 (**)Constant 3.795 (**) 4.451 (**) 5.234 (**) 5.522 (**) 5.896 (**) 6.058 (**) 6.040 (**)
Observations 6,525* significant at 10%; ** significant at 5%
36
Table 11: Quantile Regression Model and Weibull Model. Unemployment durationGreater Buenos Aires 1991-2002
Alternative c.
TAUS WEIBULL
Covariates 0.1 0.2 0.4 0.5 0.6 0.7
Men -0.182 (**) -0.384 (**) -0.546 (**) -0.469 (**) -0.565 (**) -0.439 (**) -0.483 (**)Household’ head -0.347 -0.437 (**) -0.528 (**) -0.560 (**) -0.499 (**) -0.531 (**) -0.443 (**)Educational levelIncomplete primary or less -0.015 -0.098 -0.244 -0.243 (*) -0.200 -0.307 -0.146 (**)Incomplete secondary 0.023 0.077 0.090 0.125 0.060 -0.019 0.026 (**)Complete secondary 0.290 (**) 0.456 (**) 0.404 (**) 0.364 (**) 0.317 (**) 0.119 0.262 (**)Incomplete university 0.550 (**) 0.490 (**) 0.510 (**) 0.404 (**) 0.417 (**) 0.281 0.343 (**)Complete university 0.741 (**) 0.673 (**) 0.515 (**) 0.431 (**) 0.394 (*) 0.323 0.417 (**)Age26 to 30 -0.209 (*) -0.179 -0.145 -0.180 (*) -0.254 (**) -0.226 (**) -0.191 (**)31 to 40 -0.340 (**) -0.153 -0.089 -0.093 0.018 -0.132 -0.037 (**)41 to 45 -0.270 (*) -0.121 0.189 0.318 (*) 0.403 (*) 0.420 (**) 0.209 (**)46 to 50 -0.194 0.098 0.371 (**) 0.366 (**) 0.526 (**) 0.690 (**) 0.383 (**)51 to 55 -0.240 0.214 0.767 (**) 0.789 (**) 0.784 (**) 0.703 (**) 0.568 (**)More than 55 years old -0.070 0.093 0.767 (**) 0.868 (**) 0.979 (**) 0.991 (**) 0.675 (**)Recession 0.070 0.046 0.165 (**) 0.170 (**) 0.181 (*) 0.129 0.157 (**)Children in the household -0.223 (**) -0.226 (**) -0.239 (**) -0.255 (**) -0.187 (*) -0.166 (**) -0.228 (**)Per capita familiar income -0.001 (**) -0.001 (**) -0.001 (**) -0.001 (**) 0.000 (**) 0.000 (*) 0.000 (**)Search to cover the households budget -0.315 (**) -0.400 (**) -0.269 (**) -0.288 (**) -0.202 -0.108 -0.203 (**)Constant 3.873 (**) 4.599 (**) 5.423 (**) 5.792 (**) 6.053 (**) 6.477 (**) 6.235 (**)
Observations 6,525* significant at 10%; ** significant at 5%
37
Table 12: Industry of the last job (unemployed workers)Greater Buenos Aires 1991-2002
Distribution of unemployment by industry of their last job (%)Total Duration ≥ 1 year Duration ≥ 2 year
Industry 91-94 95-98 99-02 91-94 95-98 99-02 91-94 95-98 99-02
Manufacture 25 20 18 27 25 19 12 26 25Construccion 17 21 24 10 5 12 36 2 11Trade 19 19 19 19 24 24 12 23 21Transport 9 7 7 13 7 7 4 6 4Finacial services 5 7 7 4 10 7 4 11 6Educ. and health 1 2 3 3 3 5 8 4 6Domestic services 8 11 10 8 14 12 24 12 13Other industries 16 13 12 17 13 14 0 15 13
Total 100 100 100 100 100 100 100 100 100
Porcentual variation of unemployment duration between 1991-1994 and 1995-1998Industry of the last job
Percentile Manufacture Construcction Trade Transport Fin.Serv. Educ-Health
1.0% 75% 0% 0% -50% 0% -77%5.0% 58% 0% 50% -14% 0% -67%10.0% 14% -33% 67% -50% 40% -67%25.0% 50% -5% 100% 0% 100% -67%
50.0% 33% 50% 33% 0% 13% -33%
75.0% 67% 0% 67% -14% 83% -53%90.0% 17% -14% 0% 0% 50% -50%95.0% 100% -25% 0% 33% 50% 0%99.0% 100% 0% 50% -58% 50% 50%
Average duration 61% -3% 25% -16% 48% -37%
38