PRELIMINARY AND INCOMPLETE

The growing share of financial assets that are held and managed by large institutional investors whose trades move prices contradicts the traditional asset pricing paradigm which assumes markets are competitive with small price-taking players. This paper relaxes the traditional price-taking assumption and instead presents a dynamic multi-asset, multi-large participant model of imperfect competition in risky asset markets. Because of imperfect competition, some investors face imperfect market liquidity when rebalancing their portfolios. The paper examines how imperfect competition in asset markets affects equilibrium asset pricing, liquidity, shock absorption, and the transmission of shocks among assets. The paper also presents a framework for examining how news or rumors about some market participants financial distress affects equilibrium asset prices and market liquidity. A simulation analysis of the effects of news and rumors has yet to be completed. * Board of Governors of the Federal Reserve System. The views expressed in this paper are those of the author but not necessarily those of the Board of Governors of the Federal Reserve System, or other members of its staff.


I. Introduction
Mainly forced by a chronic public deficit problem, the Brazilian federal government exerted a great effort to reduce the number of public servants in the second half of the 1990's.One of the main government concerns was with the social welfare impact of such major layoffs.In fact, the design of an efficient public sector downsizing program and the evaluation of its social welfare effects depend heavily on an estimation of the capacity of the private sector to absorb former public workers. 1 Given the existing legal constraints on firing public workers and an overall opposition to public sector reform in Brazil, the federal government typically opted for voluntary job retrenchement schemes.Many state firms, in a step towards privatization, promoted the so-called Voluntary Dismissal Programs (Programas de Demissão Voluntária, VDP), which gave monetary incentives to workers who quit their jobs. 2 a developing country like Brazil, characterized by overstaffing, it is expected that voluntary separation programs would result in an adverse selection outcome.In general, it is expected that the best workers, those with higher reservation wages, opt to leave.On the other hand, the fact that these workers usually have very specific human capital, combined with a possible stigma effect, can reduce the probability of absorption by the private sector.Since all these variables (innate ability, specific human capital and the stigma effect) are unobservable to the econometrician, a method that considers not only how observable characteristics affect the expected wage changes of workers that join a VDP, but also leaves a role for worker unobservables, is desired. 3 1995, Rede Ferroviária Federal S.A. (RFFSA), a huge public firm that had the monopoly on all Brazilian railways, adopted a VDP.From 1995 to the end of 1997 more than 7,000 workers joined the program, while many others opted for early retirement.A first survey with those former employees at RFFSA was conducted in March 1998. 4It revealed that their reinsertion in the private labor market has not been a complete success: for those who were working during the month of the interview, 72% were earning less than at RFFSA and 80% changed occupation.
These results are in a certain way expected.It is a well-documented fact that Brazilian public employees earn on average more than workers at the private sector (see Foguel et al., 2000).
As mentioned above, unobservable factors might have also influenced this outcome.Program participants may have had only public sector experience, and thus, may have only accumulated public-sector-specific human capital.In fact, program participants had an average of 18 years of job tenure at RFFSA.Their previous experience in the public sector may also have stigmatized them.
A comparison between public and private sectors in Brazil and other Latin American countries reveals that wage inequality among workers in the private sector is typically significantly higher than among public employees (see Panizza & Qiang, 2000).. Therefore, it is not surprising that the earnings distribution widened among VDP participants who left the RFFSA.
In fact, for analyzing the changes in the earnings distributions of former RFFSA workers, it is necessary to first understand what happened to the earnings distributions of all workers in the Brazilian labor market.Only with this as a basis for comparison it is possible to investigate the reasons for both the wage decrease and the increased earnings inequality observed for former RFFSA employees.
The main task of this paper is to compare the outcomes of the former RFFSA employees with those in the public and private sectors in Brazil.In this paper, we use the RFFSA survey data set, in combination with information from national household surveys, to study the process of absorption by the private sector of RFFSA workers who joined a VDP.This is accomplished through the use of a decomposition analysis, based on micro-simulations, which attempts to identify the role of observable and unobservable characteristics, as well as their remuneration in the public and the private sector, in explaining the observed changes in the earning distributions of the former RFFSA employees.This paper is organized as follows.The next section describes the data.Section III discusses the overall research methodology.Section IV presents and interprets the empirical results.Section V concludes.

II. Data description
Two data sets are used in this study.The first one, henceforth referred as REDE, contains information on more than 5,000 workers out of around 7,000 who left their jobs at RFFSA through the Voluntary Dismissal Program from 1995 to 1997.The survey was conducted in March 1998 and collected data on several labor market variables, including earnings, employment status, and duration of unemployment and employment spells.It has information on schooling levels, grouped into nine categories, which correspond to the following ranges of years of schooling: 0-3, 4, 5-7, 8,   9-10, 11, 12-14, 15, and more than 15.5 REDE also contains official administrative information for all workers who joined the VDP, including their last wages at RFFSA.The other data set, Pesquisa Nacional de Amostra por Domicílio (PNAD), is the annual Brazilian Household Survey, collected by IBGE.PNAD covers the whole country (except some rural areas) and it is the largest and most important Brazilian household survey, interviewing more than 75,000 households every year, which corresponds to about 300,000 individuals.PNAD collects data every September since 1976, with the exception of Census years and a couple of other years.It contains information on labor, demographic, educational and regional variables and has been widely used in many micro-econometric studies.
In this study, we use information from both data sets only for individuals in the age range of 25-64, with a paid main activity that requires at least 20 weekly hours of work.Two yearly editions of PNAD were selected, 1995 and 1997.These two years were chosen in order to approximately match both the timing of exit from RFFSA and the absorption of these workers by the private sector, as captured by the REDE survey.
Data on earnings correspond to positive monthly labor earnings on the main activity.This variable was properly deflated and evaluated at March 1998, the date of the REDE survey.In the PNAD data set, outliers (more than R$ 250,000 a month) are not considered in the analysis.In the REDE data set, we only use information about workers who switched to the private sector after quitting, as answered in the survey of March 1998.
Since REDE is restricted to some Federation States, only observations in the same geographical range are used in PNAD.In practice, this means that the North Region and some States in the Mid-West are not considered here.Finally, the classification at PNAD for a job at the public sector has the broadest sense, meaning that not only federal public servants are considered as working in the public sector but also any individual who declared to work at that sector with or without a formal labor contract.
Table 1 displays sample means for the most important variables in the two data sets, and the number of observations remaining after the application of the filters described above.

III. Overall Research Methodology
In this section, we describe our methodological approach.The section is divided into four sub-sections.In the first one, the regression model is presented describing the relationship between earnings, observable individual characteristics (such as age, gender and schooling) and unobservable characteristics.The second sub-section briefly discusses the method of comparing distributions using counterfactual micro-simulations.The third sub-section shows how the distribution parameters are estimated and discusses the hypotheses behind the use of regression residuals in the counterfactual earnings distributions.Finally, the last sub-section describes how the earnings distributions at different periods and sectors are compared.

III.1. The earnings equation
In order to estimate the effects of observable and non-observable individual characteristics on earnings,6 the following model is specified: (1) log(y i,t,s,p ) = w i,t,s,p = h 1 (x i,t,s,p ) + h 2 (z i,t,s,p ).
where w denotes log-earnings, x is a vector of observable characteristics and z is a vector of nonobservable characteristics.This additively separable model holds by assumption for all individuals i, at time t, at sector s (public and private), and for both available data sets p (REDE and PNAD).
We also assume that these variables are i.i.d. and that: (2) w i,t,s,p = h 1 (x In practice, six regressions are estimated, since for the PNAD data set there are two sectors (public and private) at each period (1995 and 1997), while for the REDE data set workers are in the public sector (at RFFSA) in 1995 and in the private sector in 1997.

II.2. Comparing two distributions using counterfactual micro-simulations
In this sub-section, we show how we use the information from log-earnings equations to compare two distinct labor income distributions.Consider the log-earnings of an individual i at the triple (t 0 ,s 0 ,p 0 ).In order to facilitate notation, say m 0 = (t 0 ,s 0 ,p 0 ).Then using (3) (4) Now define: (5) Equation ( 5) simulates what would be the earnings of an individual i at the triple m 0 = (t 0 ,s 0 ,p 0 ) if she is paid β β m1 instead of β β m0 for her observable characteristics, where β β m1 is the vector of the rates of return on human capital variables at the triple m 1 = (t 1 ,s 1 ,p 1 ).This is usually referred as a "price effect".As this can be generalized for every individual i at the triple m 0 , we come up with a "simulated" earnings distribution, with its own mean and inequality measures.
The same is true for equation ( 6), which "simulates" what would be the earnings of a worker i if she faces not only the "prices" of observable characteristics at the labor market described by m 1 but also receives the "prices" for her unobservable characteristics at that market, which is given by ε j,m1 .The implementation of that "simulated" labor earnings distribution is not as trivial as the former one, since it now involves not only the price effect, but also a complex choice of how the ε's should be allocated to each worker.We keep it to sub-section III.3 the description of the method of allocating the residuals used in this paper.
The previous equations allow us to compare the earnings distribution of workers at a labor market characterized by m 0 with workers at m 1, using the "simulated" earnings as intermediate steps.
In order to see that note that using (4): Then, (8) Equation ( 7) shows the familiar "controlled individual wage gap" expression, now commonly used in the literature (see, for instance, Foguel et al., 2000, and Panizza and Qiang,   2000).For every individual i, given her own observable characteristics, the controlled wage gap is the difference between her actual log-earnings and the log-earnings she would have obtained at labor market m 1 , that is, w i,m0 -w SIM1 i,m0 .According to (7), this controlled wage gap turns out to be just the difference in the coefficients of both regressions times the vector of the observable characteristics for the individual i at m 0 .
Equations ( 8) and (8a) show how to decompose the "gross individual wage gap", that is, the difference in log-earnings between two individuals, i and j, who are in two distinct labor markets, m 0 and m 1 , respectively.Equation ( 8) reveals that this difference can be decomposed in three parts.
The first one is the just mentioned controlled wage gap.The second component is the individual version for the so-called "composition effect": it is the part of the gross wage gap that reflects differences in the observable characteristics of two distinct workers.Finally, the last term reflects earnings differences that can be attributed to unobservable characteristics.As shown in the next sub-section, this last term reflects either qualitative differences in those unobservable characteristics or differences in their "prices" at each labor market, or both.Now consider the first and second moments of the four distributions, w m0 , w m1 , w SIM1m0 and w SIM2m0 .Note that we have dropped the subscripts i and j, making use of the i.i.d.assumption.After computing the first moment, the equation for the gross mean wage gap becomes: The first term on the right hand side is the mean version for the controlled wage gap and the second term is the analogous composition effect.The differences between ( 9) and ( 8) are basically that (9) computes the wage gap for means of two different labor income distributions and because of that the third term in (8) vanishes, since The variance of log-earnings is one of the two measures of inequality used in this paper.Its population expression for equations (4), ( 5) and ( 6) are (under the homoscedasticity assumption): Equation (10) gives the traditional formula for the variance decomposition in a between where K is the number of observable variables.
Equations ( 10a) and (10b) are analogous formulas to (10), giving the variances for the "simulated" log-earnings w SIM1 and w SIM2 .Similarly to the first moment equations, these two equations are used to decompose the effects of a difference in variances in three parts: a price effect on the observables; a composition effect; and a price effect on the unobservables.Therefore, the difference between (10a) and ( 10) gives the effect on inequality of a change in the returns of the observables.The difference between (10b) and (10a) gives the effects of a change in the returns of the unobservables.Finally, the difference between equation ( 10) with another group subscript, say m 1 , and equation (10b) gives the effects of a change in the variance of the observables (composition effect).

III.3. Estimation procedures
The earnings equations can be estimated by ordinary least squares, since (a) the regression function is assumed to be linear and separable; (b) the errors are assumed to be uncorrelated with regressors; and (c) identically and independent distributed.
For estimating changes in means and variances, one needs to have an estimate for E[exp(x)], the vector of the means for the observables.A natural choice is E N [exp(x)], the sample means.9Note that exp(.) is used since earnings, y = exp(w), are the variable of interest.
The variance decomposition analysis described in the previous subsection has two steps.
First, the actual and simulated distributions w i,m0 , w j,m1 , w SIM1i,m0 and w SIM2i,m0 are calculated.Then, the respective measures of inequality for each distribution are computed.These measures are the variance of the log-earnings (Var[w m ]) and the Theil-T index, which formula is described in the appendix.
The method of allocating the residuals in the simulated distributions, based on Juhn, Murphy and Pierce (1993), is as follows.First, the errors ε are estimated by the regression residuals e.Second, for estimating w SIM2i,m0 and its component e j,m1 , a crucial hypothesis is required.
Since an individual j from m 1 is not observed at m 0 , there are several ways of designating the e j,m1 that will be allocated to the individual i as her unobserved component in w SIM2i,m0 .The way used here is to sort each residual distribution in an ascending order and then match the residuals according to their ranking in those orderings.In other words, workers with residuals between the p th and the p+1 th percentiles of the residual distribution at m 0 are assigned the residuals between the p th and the p+1 th percentiles of the residual distribution m 1 .As a practical matter, since the sample sizes typically differ, we rearrange the observations for each labor market m into 100 different groups.Each group corresponds to a quantile of the residual distribution at m and has received average values.
This method of allocating the residuals entails the hypothesis that the unobserved characteristics at m 1 have the same distribution at m 0 .The only difference between the unobserved characteristics in two distinct labor markets is basically their "prices" at each market.To illustrate with an example, this assumption means that if ability is an unobservable variable,10 ability is assumed to have the same distribution in both the public and private sectors.The only difference is that one sector remunerates better this unobserved ability than the other.Therefore, for the purpose of this study, computing differences between w SIM1m0 and w SIM2m0 is relevant in the sense that it allows measuring the role of specific labor environments and unmeasured characteristics on earnings inequality.

III.4. Decomposing changes in the earnings distribution
In the previous sub-sections, we have shown how to decompose the differences in means and of inequality measures of two distinct distributions in several components.Another insightful way of comparing differences between two parameters of distinct distributions is the differences-indifferences method.In this case, a third distribution is used and one uses the fact that a difference in ).This method can be useful when the goal is to identify partial effects that otherwise would be confounded.
In this case, one can decompose the differences in parameters of two specific distributions into several distinct partial effects.In this paper, the main interest is the difference between the distributions (1995, public, REDE) and (1997, private, REDE).It is possible to decompose it into 4 steps.For example, one could compare the RFFSA employees with all workers in the public sector in 1995; then examine how the public sector evolved between 1995 and 1997; and finally compare the public and private sectors in.1997.In fact, there are two ways of doing this decomposition, which are described below: ( The difference between cases 1 and 2 is therefore in steps 2 and 3.In case 1, step 3 measures the temporal evolution of earnings on the private sector while step 2 compares the private and the public sector in 1995.In case 2, step 3 measures the difference between the public and the private sector in 1997 while step 2 captures the temporal evolution of earnings in the public sector.

IV. Estimation results
This section presents the results of the decomposition analysis.First, log-earnings regressions are estimated.Then, we compute each difference in means and in variances of the distributions in equation ( 11), including all 4 steps in the two cases considered.Finally, we decompose the differences in means into a controlled wage gap (a price effect on the observables) and a composition effect; and the differences in variances into a price effect on the observables, a composition effect, and a price effect on the unobservables.
Table 2 shows the log-earnings equation estimates for the six regressions described above.
All coefficients have the expected sign and are significantly different from zero at the 5% level, with the exceptions of age and the dummy for 5-7 years of schooling in the (1997, private sector, REDE) regression.Note: The dependent variable is log-earnings.Standard errors are in parentheses.
Table 3 presents the decomposition effects for the differences in means.The table reveals that the absorption by the private sector of those workers who left RFFSA through the VDP was painful.The first row of the table shows that those workers have their average wages reduced from monthly R$ 967 to R$ 757 and that decrease was mainly due to a price effect.The simulated average earnings of a worker who got a job in the private sector in 1997, but with observed average characteristics of those who left RFFSA in 1995, fell from R$ 967 to R$ 543.This corresponds to a controlled wage gap of R$ 425 a month, which means that the rates of return of those observed characteristics were much less valued in the private sector relative to RFFSA.
The composition effect, on the other hand, played a compensatory role of R$ 214.This means that the workers that got a job in the private sector were those with better-evaluated observable characteristics.
Table 3 also reports that RFFSA workers were better paid than other workers in the public sector in 1995.In this case, there is both a price effect and a composition effect, contributing 54% an 46%, respectively, in explaining the gross wage differential.In fact, as shown in Tables 1 and 2, the composition effect operates in favor of RFFSA workers not because of better productive characteristics but due to a combination of a higher percentage of men at RFFSA and a discrimination effect against women.
It can also be seen from Table 3 that the public-private wage gap fell dramatically between 1995 and 1997.The controlled wage differential of R$ 64 or approximately 10% of the average earnings in the public sector in 1995, decreased and became negative R$ 24 in 1997.This means that the wage premium paid at the public sector disappeared in this period. 11As the same Table 3 reveals, this was due to a sharp real wage reduction in the public sector (R$ 89 decrease in the controlled wage gap) and not to significant better payments in the private sector (R$ 4 increase in the controlled wage gap).

Case Step
Finally, the last row of Table 3 reveals that workers who left RFFSA received, on average, R$ 329 a month more than workers in the private sector as a whole in 1997.This is mostly due to a composition effect, which contributes with 92% of the observed total wage gap.In fact, these workers have, on average, higher levels of observed human capital characteristics (like more years of schooling) than the private sector as a whole, besides having a larger proportion of males.
Table 4 presents the results of the earnings inequality decompositions, for the two measures used: the variance of log-earnings and the Theil-T index.Since the variance of log-earnings is a measure that depends on the value of the mean of a distribution, we only comment the results based on the Theil-T indicator, which has the property of independence from the mean.
Table 4 reveals that the earnings distribution became much more uneven for those former RFFSA workers.The Theil index jumps from 0.11 to 0.39.The simulated distributions decomposition shows that a larger dispersion for the price of the unobservables is mostly responsible for this result.In fact, the observables price effect has an almost insignificant impact on the earnings distribution, increasing the Theil index from 0.11 to 0.12.The unobservables price effect, on the other hand, makes the inequality measure jump to 0.58. Theil-T

Case
Step In fact, workers at RFFSA were in an environment with very low levels of inequality even when compared with the public sector as a whole.As expected, this was also due to a small dispersion on payments to unobservables at RFFSA, since an individual firm probably values less unobservable dimensions than the entire private or public sector do.
Another interesting result reported in Table 4 is the lower public sector earnings inequality relative to the private sector, which is also observed in most countries.Note, however, that there was a sharp increase in the public sector's Theil index from 0.11 to 0.26 between 1995 and 1997, which might be reflecting a differentiated ability of some categories of public workers to obtain nominal wage increases (see footnote 10).
Finally, we notice that there is no big difference between the measures of earnings inequality among former RFFSA workers when compared to the private sector as a whole.In fact, this last result completes our picture of what resembles a full and fair absorption of former RFFSA workers by the private sector in Brazil, at least as given by the first two moments of simulated distributions.Not only average wages were typical of workers in the private sector with identical observed characteristics, but also wage dispersion was very similar.

V. Concluding remarks
The objective of this paper was to study the process of absorption by the private sector of RFFSA workers who joined a Voluntary Dismissal Program.The results presented clearly reveal that the move to the private sector of these former RFFSA workers caused a decline in average wages and an increase in wage dispersion.However, it is by no means a symptom of discrimination against former public employees at the private sector.In fact, it seems that the previously accumulated general human capital of these workers was decisive for their remuneration at the private sector, and that their lack of private sector-specific human capital did not prevent them from being fairly paid.
All results show that these workers were paid accordingly to their embodied observable characteristics and faced the same "prices" for those characteristics that any other worker in the private sector would face on average.Also, the increase in wage dispersion brought them to levels of earnings inequality that are not significantly different from that existing in the private sector as a whole.
As an aside conclusion, this study finds that the public-private sector wage gap rapidly eroded between 1995 and 1997.However, the inequality in both sectors has not changed over the selected years.It is also important to mention that in order to explain the gap in the inequality between the public and private sectors, the important factor that should be taken into consideration is the within-group component, or, in other words, the differences in the "prices" of the unobservable characteristics.

APPENDIX: The Theil Inequality Indicator
We present here the Theil-T index formula.Let X be the variable of interest and ω the weights or the relative frequency of each value of X.Then, the X distribution has the following Theil-T index: For further references on that inequality measure see, for instance, Bourguignon (1979).

A summary of the new estimation procedures and results to be incorporated in the next version of the paper (sessions III and IV):
III. Estimation Procedures a. "Differences-in-differences" approach: i) Oaxaca Decomposition: Then estimate the Controlled Wage Gap as: i.: ) Pooling m 0 and m 1 (estimating gamma coefficient): Then estimate γ γ by OLS, for instance.
iii) Pooling m 0 and m 1 and using Propensity Score (estimating rho coefficient): , assuming some functional form for F(.) (for instance, logistic distribution).The fitted value, ) ( ˆX p , is the estimated P-score.

Semi
vector of individual log-earnings had m 1 had the X's attributes of m 0 but the actual wage structure of m 1 .Analogy applies to *