Frontier estimation of changes in workers' labor market information.
The role of information in the labor market is the subject of much research. Information in the labor market is not perfect or without cost. Search theory has been introduced and applied as a way of motivating the acquisition of information. Several studies use stochastic frontier estimation techniques to estimate the amount of information currently held by workers and to empirically test search theory implications as to whom possesses greater amounts of information [Hofler and Polachek, 1982, 1985; Polachek and Yoon, 1987, 1996; Hofler and Murphy, 1992, 1994; Groot and Oosterbeek, 1994]. Other studies examine the acquisition of information by considering various methods for collecting information such as using job placement services [Black, 1981; Kahn and Low, 1990]. This paper merges the above research by examining changes in employee information between points in time using the frontier approach to estimate information.
The stochastic frontier measure of worker information obtains estimates of worker information by estimating the maximum attainable wage for a worker. Worker information is defined as the percentage of the maximum attainable wages actually earned by the individual. Studies using this measure conclude that individuals with more experience, tenure, or education, who live in standard metropolitan statistical areas (SMSAs), and who join unions, are white or male, possess greater information. In other words, most of the emphasis is placed on the relationship between current characteristics and previous investments in information.
Studies examining information acquisition at a particular point in time consider the relationship between current characteristics and current investments in information. They find that employed male workers with more education, less tenure, who are younger, live in larger cities, or live in counties with lower unemployment rates are more likely to search for a new job [Black, 1981]. Also, workers with lower levels of current information, greater unemployment insurance coverage, more education, less tenure, who are black, or in occupations with greater wage variability are more likely to invest in additional information through the use of labor market intermediaries such as employment services [Kahn and Low, 1990]. The 1985 and 1989 waves of the Panel Study of Income Dynamics (PSID) are used to estimate changes in worker information over time. This paper differs from previous studies using the stochastic frontier approach to estimate information as it concentrates on the relationship between worker characteristics in 1985 and the acquisition of information during the following four years.
A second goal of this paper is to examine the relationship between information acquisition and job mobility. Polachek and Horvath  examine the likelihood of geographic mobility in a human capital framework. They develop several hypotheses relating mobility and information about alternative locations. The likelihood of migration is greatest for those with less current information since investments in additional information are more likely to yield an improvement over some objective function over the current location. In addition, the likelihood of migration is an increasing function of investments in information. Little empirical testing has been performed on the relationship between information and job mobility. This paper fills this gap by examining the relationship between current information and future job mobility and changes in information with and without job changes.
Continued study of this measure of information is important for several reasons. Previous studies examining changes in workers' information rely on easily identified methods of information acquisition, such as the use of civil service, job placement services, employment agencies, or unions. However, much information is gathered through informal networks. Information acquired informally is difficult to measure and may not be captured by previous studies. The use of stochastic frontier estimation to estimate changes in information allows for the consideration of changes regardless of the manner in which it is gathered. Another motivation for this study is to further establish the frontier measure of information as a viable measure of information. While the measure performs well when estimating the stock of information at a point in time, further research is needed to determine whether it is capable of capturing changes in worker information across time.
By concentrating on changes in worker information, a possible concern with previous studies using frontier estimation is also addressed. Analysis with cross-sectional data may result in biased estimates of information if the efficiency term includes unobserved heterogeneity.(1) Estimates of the relationship between information acquired while employed and tenure, education, and experience may be biased if these variables are correlated with typically unobserved factors such as ability.(2) If unobserved factors are time-invariant (with the exception of information), then examining changes in worker information will give a clearer picture of the relationship between information acquisition by employed workers and tenure, education, and experience.
This measure should also be of interest to researchers in fields besides labor economics. For example, Gaynor and Polachek  examine information in the market for physician services. The measurement of buyer and seller information is of interest in many different markets, making the stochastic frontier measurement of information an important tool for a variety of researchers.
Results are generally consistent with search theory. In 1985, workers who had greater experience or tenure and had higher levels of education, were white or male, possessed significantly greater information. Individuals who were thinking about changing jobs, actively looking for a new job, or actually changed jobs had less information in 1985. Changes in information between 1985 and 1989 were greater for workers who were thinking about changing jobs, actively looking for a new job, had less experience or tenure, more education, or lived in an area with a low unemployment rate. An even greater information change was found for workers who actually changed jobs between 1985 and 1989. These results provide support for the use of the stochastic frontier measure of information to examine changes in worker information across time.
This paper is organized as follows. The next section presents a brief discussion of search theory. This is followed by the procedure for estimating worker information. Finally, results are presented followed by concluding remarks.
A two-period sequential search model is employed to analyze the relationship between worker characteristics and information. Each worker's characteristics and stock of skills (4)) will generate wage offers during period one in the labor market. Employers will value these characteristics in different manners. It is assumed that these wage offers are generated on the basis of individual characteristics and are increasing functions of these characteristics so that [w.sub.1] = [w.sub.1]([Phi]) and [w.sub.1][prime] [greater than] 0. A worker with characteristics of i in period one and perfect information will receive a potential wage of [w.sub.1]([[Phi].sub.i]). Note that the worker is qualified for all jobs in which [w.sub.1] [less than or equal to] [w.sub.1] ([[Phi].sub.i]).
A worker with perfect information will easily find a job paying [w.sub.1]([[Phi].sub.i]). But information is often incomplete and the gathering of information is a costly process. The worker is face with a distribution of wage offers from which he or she must choose and set a criterion for accepting a particular job offer. This criterion is embodied in the reservation wage ([w.sub.r]), the minimum acceptable wage offer.
A worker will search until he or she receives a wage offer exceeding the reservation wage. This accepted wage will not be greater than the potential wage. Thus, [w.sub.r] [less than or equal to] [w.sub.1] [less than or equal to] [w.sub.1]([[Phi].sub.i]). Hofler and Murphy  use this result to show that the higher a worker sets his or her reservation wage, the lower will be the degree of incomplete information. As a result, factors that systematically determine the reservation wage will, in turn, affect the level of incomplete information [Hofler and Murphy, 1992, p. 514].
The reservation wage is determined so that the marginal cost of receiving an additional wage offer is equal to the marginal benefit of that offer. Benefits include higher lifetime earnings while costs include the out-of-pocket expenses of gathering information as well as the loss of earnings while searching. If the benefits outweigh the costs, then increments to the reservation wage will occur. Factors that increase these benefits more than the associated costs result in a greater investment in information. Previous research indicates that information is greater for workers that have more experience, tenure, or education, live in urban areas, belong to unions, and are white or male.
This analysis is extended to consider the change in a worker's information over a period of time. As mentioned earlier, human capital theory predicts that workers continue to gather information about the labor market while working. A change in jobs occurs when the individual acquires enough information to locate a job paying a wage high enough to entice a job change.(3) If insufficient information is acquired to locate such a wage offer, no job change occurs. However, wages are likely to increase along with the increase in experience and firm tenure. Thus, the wage in period two is likely to be greater than the wage in period one but will be less than or equal to the potential wage in period two, [w.sub.1] [less than or equal to] [w.sub.2] [less than or equal to] [w.sub.2]([Phi]). The potential wage in period two may be greater or less than the potential wage in period one. For example, workers with increased experience have a higher potential wage but a move to a rural area decreases the potential wage.
The investment in information in period two depends on many of the same factors that determine investment in period one. However, instead of considering the reservation wage, the minimum wage that leads to a job change is considered. Workers with greater information in period one are closer to their potential wage in period one. They are less likely to find a wage offer in period two high enough to motivate a job change. Also, the marginal cost of acquiring additional information is likely to be greater for those with more information in period one. As a result, they have less incentive to gather additional information. For example, workers with substantial experience or tenure are less likely to change jobs and also possess more information than younger workers. Workers more likely to change jobs, such as individuals with lower levels of experience and tenure in period one, demand additional information and have a greater flow of information over time. This leads to several testable hypotheses. Workers with less information, experience, or tenure in period one have a greater flow of information in period two. Also, workers with a greater likelihood of changing jobs will invest in more information during period two.
Following the previous argument, the condition of the labor market in period two is also an important factor in determining the costs and benefits of acquiring information. Areas with low unemployment rates are more likely to have job openings and, therefore, an increased likelihood of finding an acceptable wage offer. Thus, workers in areas with low unemployment rates invest in additional information. Individuals with greater search ability have greater returns to search time and invest in more information. Last, workers with a lower discount rate place a greater emphasis on the future and spend a greater amount of time in period two investing in information.
The Estimation of Information
Stock of Information
Two general methods are used in the literature to estimate information. The first uses the variance in wages (or prices) as a measure of information [Stigler, 1962; Stigler and Kindahl, 1970; Von Hoomissen, 1988; Lach and Tsiddon, 1992]. Workers facing a greater variance in the distribution of wages are considered to have less information than workers facing a narrower distribution in wages. However, this measure does not take into account that wages vary for a wide variety of reasons, including differences in worker characteristics such as education and experience. This lead to an alternative measure of information based on the work of Aigner et al. . Consider the following equation:
[Mathematical Expression Omitted], (1)
where: the dependent variable represents the individual's maximum potential wage offer; X is a vector of independent variables; v is a disturbance distributed as [Mathematical Expression Omitted]; i represents individuals; and t denotes 1985 or 1989. A worker with perfect information about the labor market is able to locate a job paying his or her potential wage. However, the vast majority of workers search with limited information. In this case, the worker usually accepts a wage below his or her potential maximum. The difference between the observed wage and the potential wage depends on the level of information held by the worker. Those workers who invest more in search activities are closer to their potential wage, while those who invest less are farther from their potential wage.
By reconsidering (1) one arrives at:
[Mathematical Expression Omitted], (2)
where [u.sub.it] [less than or equal to] 0. If [u.sub.it] = 0, the worker has achieved his or her maximum wage. Thus, [u.sub.i] is considered an individual-specific estimate of incomplete information. Combining (1) and (2) leads to:
[Mathematical Expression Omitted], (3)
where [[Epsilon].sub.it] = [v.sub.it] + [u.sub.it].
In order to convert the estimates of incomplete information into a measure of information, compute the percentage of potential wages actually earned by each worker in year t:
[Mathematical Expression Omitted]. (4)
Workers with more information have a figure closer to one while workers with less information are closer to zero. As discussed above, Hofler and Polachek [1982, 1985], Polachek and Yoon [1987, 1996], Hofler and Murphy [1992, 1994], and Groot and Oosterbeek  use the frontier estimation to compute worker information.
Changes in Information Stock
Since this paper seeks to determine how both the level of information in 1985 and change in information between 1985 and 1989 vary based on individual characteristics, a frontier for a combined cross-section time-series sample of workers from 1985 and 1989 is estimated. The frontier is used to estimate a worker's potential wages in 1985 and 1989. Potential wages vary for individuals over time due to changes in worker characteristics. Actual wages are compared to potential wages to calculate individual-specific estimates of information at both points in time. By subtracting the level of worker information in 1985 from the level in 1989, the net change in information over the time period is estimated:
[CHANGE.sub.i] = [INFO.sub.i,89] - [INFO.sub.i,85]. (5)
Workers who move closer to their potential wage have a positive information change, while those moving away from their potential wage have a negative change in information. It is important to note that an increase in wages is not sufficient to increase estimated information. Wages must increase more than potential wages in order for worker information to increase.
There are several alternatives to the estimation procedure used in this paper. Given the use of panel data, a fixed effects model could be estimated that includes intercepts for each individual. Pitt and Lee  and Schmidt and Sickles  consider the firm-specific intercepts to represent estimates of firm-specific efficiency. For wage regressions, the individual-specific intercepts might be interpreted as estimates of information. Polachek and Yoon  and others note that the unobserved heterogeneity literature tends to interpret individual-specific intercepts as the effects of unobserved individual characteristics such as ability and motivation. Polachek and Yoon  develop a model to estimate information while netting out individual-specific effects. However, their estimation procedure only measures information at the market level and does not measure information for each individual.
Also worth noting is the potential criticism that this measure of information is based on a regression residual. Polachek and Robst [forthcoming] examine the relationship between frontier estimates of information and independent measures of worker information available in the National Longitudinal Survey of Young Men . They find a significant positive relationship between the two measures of information. Thus, despite the fact that the frontier measure is based on a residual, it provides a reasonable measure of worker information.
Data and Sample
The data used in this study are from the PSID. The PSID was began in 1968 and follows over 5,000 families at a time in annual surveys. This paper concentrates on the 1985 and 1989 waves. The time span is chosen to balance the desire to look at people over a length of time while maintaining a reasonable sample size. Individuals between the ages of 18 and 60 in 1985 who are employed in both sample years are included in this study.
There are 1,481 men and 1,194 women in the sample. Variable means are reported in Table 1. Consistent with many other studies, women tend to have lower levels of experience, tenure, unionization, and wages than men. Women are more likely to be in clerical and service occupations, while men are more likely to be in managerial and crafts occupations. One-quarter of both men and women are thinking about changing jobs, while 15 percent are actively looking for a new job. Thirty percent of women and 28 percent of men change jobs between 1985 and 1989.
TABLE 1 Variable Means Women Men 1985 1989 1985 1989 Age 36.38 40.34 35.21 39.16 Education 12.97 12.97 12.82 12.82 Experience 14.23 17.27 16.79 21.12 Tenure 6.40 8.46 8.11 10.08 SMSA size 2.78 2.76 2.56 2.50 Wage 1.81 1.88 2.14 2.19 White 0.65 0.65 0.71 0.71 Married 0.72 0.72 0.85 0.87 Children 1.12 1.07 1.29 1.34 Union 0.18 0.18 0.28 0.27 Unemployment Rate 6.62 5.10 6.69 5.11 Professional 0.23 0.25 0.20 0.19 Managerial 0.09 0.09 0.12 0.14 Sales 0.03 0.03 0.02 0.02 Clerical 0.31 0.31 0.06 0.05 Craftsmen 0.02 0.02 0.24 0.25 Operatives 0.11 0.11 0.22 0.21 Laborers 0.02 0.01 0.08 0.07 Service 0.19 0.19 0.07 0.07 Thinking of changing jobs 0.25 - 0.26 - Actively looking for a new job 0.15 - 0.15 - Changes jobs 0.30 - 0.28 - Number of observations 1,194 1,194 1,481 1,481 Notes: Data from 1985 and 1989 waves of the PSID. Variable definitions: age, education, experience, tenure are in years; SMSA size is a bracketed variable indicating the size of the largest city in the county; wage = the natural log of hourly wages deflated by the Consumer Price Index; white = dummy variable, 1 denoting the individual is white; married = dummy variable, 1 indicating the individual is married; children = the number of children ages 0-17 living in the household; union = dummy variable, 1 indicating the respondent's job is covered by a union contract; unemployment rate = the county unemployment rate; professional, managerial, sales, clerical, craftsmen, operatives, laborers, and service are dummy variables denoting occupation; thinking of changing jobs = dummy variable, 1 denoting the individual is thinking of changing jobs; actively looking for a new job = dummy variable, 1 indicating the individual is doing something to search for a new job; changes jobs = dummy variable, I if the individual changes jobs between 1985 and 1989.
Table 2 contains the estimated frontier. The coefficients are similar to countless earnings functions found in the literature and compare to ordinary least squares (OLS) results which are also provided. Education, experience, and tenure are all positively related to wages. Men earn more than women, whites more than blacks, and union jobs pay more than nonunion jobs. The county unemployment rate is included to capture changes in local economic conditions, while a dummy variable for 1989 is included to control for changes in national economic conditions and other external factors that may have changed productivity over time. Neither variable is significant. The primary difference between the frontier results and OLS lies in [Sigma] and [Gamma].(4) The significance of [Gamma] implies that [[Sigma].sub.u] is not equal to zero and workers possess incomplete information.
[TABULAR DATA FOR TABLE 2 OMITTED]
The mode formula of Jondrow et al.  estimates the information held by individuals in 1985. The average of the modes for various groups is compared to determine who has greater information. When the sample is broken into two groups, t-statistics are computed under the null hypothesis that the average information for each group is equal. The t-test is appropriate for large samples since the sampling distribution of the difference between means can be assumed to be normal. When there are more than two groups, analysis of variance tests are performed under the null hypothesis that all means are equal. When the null hypothesis is rejected, multiple t-tests are performed to determine which means are significantly different. When the sample is divided into more than two groups, relatively equal sample sizes in each group are maintained when deciding where to split the sample.
Average information is calculated for the entire sample and for various groups. The average worker earned 95.68 percent of his or her potential wage in 1985. Similar to previous studies, information is significantly greater for workers who are white males and have more education, experience, or tenure. Consistent with the theory of Polachek and Horvath , results indicate that information is significantly lower for workers who are thinking of changing jobs, actively looking for a new job, or actually change jobs between 1985 and 1989.(5)
In order to estimate the change in information, the level of information for each worker in 1989 is computed. The change in information is defined as the difference between the worker's information in 1985 and 1989. The average worker in this sample increases their information by .03 percentage points to 95.71 percent of their maximum. Clearly this is a measure of the net investment in information and not the gross investment in information. Some of the stock of information in 1985 will depreciate and may or may not be replaced. Thus, some workers have a decline in information between 1985 and 1989.
This paper first examines whether workers with a greater likelihood of mobility invest in more information. Workers that are potentially more mobile include those who are actively seeking a new job, changing jobs, or changed jobs during the sample period and those with less initial information, experience, or tenure.
The change in information between 1985 and 1989 is calculated for those actively seeking a new job in 1985. Individuals who were not considering changing jobs had an estimated level of information of 95.89 in 1985 and 95.68 in 1989. Thus, individuals had a change in information of-.0021. This compares to estimates for job seekers of .9452 in 1985 and .9542 in 1989, a change in information of .0090. Thus, individuals who were actively looking for a new job had a significantly greater change (increase) in information between 1985 and 1989 than those not actively seeking a new job.
Workers thinking of changing jobs in 1985 had an estimated level of information of .9472 in 1985 and .9542 in 1989, an increase of .0070 in their ratio of actual to potential earnings. On the other hand, workers not thinking of changing jobs had an initial level of information equal to .9581 in 1985 and this level subsequently fell by .21 percentage points to 95.81 percent of potential earnings in 1989. Thus, workers thinking of changing jobs in 1985 had a significantly greater change (increase) in information between 1985 and 1989 than those not thinking of changing jobs.
Additional evidence for the relationship between mobility and information can be obtained by considering workers who actually change jobs between 1985 and 1989. Individuals who actually change jobs in the sample period increased their information by .73 percentage points from 94.50 percent in 1985 to 95.23 percent of their maximum earnings in 1989. Workers who did not change jobs experienced a decrease in information from .9625 in 1985 to .9593 in 1989, a decrease of .0032 in their ratio of actual to potential earnings.
Next, the relationship between a worker's initial information and investment in additional information is considered.(7) The sample was ranked based on the stock of information in 1985 and segmented into three categories of equal size. Significant support was found for an inverse relationship between the level of information in 1985 and the change in information between 1985 and 1989. Those with the least initial information had an increase of .0192 in their ratio of actual to potential wages, while those with the greatest initial information had a decline of .0133. In addition, the group means were significantly different in each possible comparison.
In order to test the impact of different levels of experience on the change in information between 1985 and 1989, the sample was divided into three categories: workers with up to 10 years of experience, those with greater than 10 years up to and including 20 years, and workers with greater than 20 years of experience. Individuals with less experience had significantly different changes in information than workers with greater experience. Workers with 10 or less years of experience had an increase of .56 percentage points to 95.83 percent of their maximum while those in categories of 11 to 20 and greater than 20 years of experience had a decrease in their ratio of actual to potential wages of .0029 (from .9597 to .9568) and .0017 (from .9573 to .9556), respectively. Thus, changes in information were significantly greater for individuals with less experience in 1985. Nearly identical patterns were revealed when considering worker tenure in 1985.
Changes in information for individuals thinking of changing jobs, actively looking for a new job, and those who actually change jobs coupled with identified patterns of information changes for individuals with various levels of experience and tenure suggest a clear link between the likelihood of mobility and investments in information. Those workers who are more likely to change jobs will make greater investments in information than workers who are less likely to change jobs.
The relationship between information and tenure merits further discussion. Years of tenure was used to stratify the sample into three groups with relatively balanced sample sizes. Categories were constructed as workers with zero to three years, greater than three years and up to and including eight years, and greater than eight years of tenure. The level of information increases from .9487 to .9606 when comparing the zero to three years group with the greater than three to eight years group in 1985. However, the change in information between 1985 and 1989 was much smaller than expected at .0044 for the zero to three year group. This suggests that cross-sectional estimates of the relationship between information and tenure may be biased due to unobserved heterogeneity. Workers with greater ability acquire information at relatively low cost. Thus, the positive relationship between information and tenure in cross-sectional estimates may reflect information increases for workers with greater ability. Cross-sectional estimates of the relationship between information and experience do not appear to be biased, as the changes in information between 1985 and 1989 are consistent with the greater information for more experienced workers in 1985.
Workers with more schooling were also found to have greater increases in their information. For example, workers with less than 12 years of schooling had a decline in information of .20 to 94.98. Alternatively, workers with greater than or equal to 16 years of schooling had an increase in their information by .74 percentage points to 95.99 percent of potential earnings. This is consistent with the idea that individuals with more schooling are generally more future-oriented, suggesting an incentive to acquire additional information. This finding also indicates that there is a positive relationship between education and information acquisition by employed workers when taking unobserved time-invariant factors into account.
The condition of local labor markets is another important factor in the acquisition of information. Workers in counties with low unemployment rates acquire more information than individuals in counties with high unemployment rates. Workers facing unemployment rates of 4 percent or less acquired .28 percentage points more of their potential wage to received 96.00 percent of their maximum. On the other hand, workers facing rates of unemployment greater than 8 percent experienced a decline in the ratio of actual to potential wages of .35 percentage points to 95.41 percent.
Comparisons between men and women, whites and blacks, union and nonunion, married and single workers, and SMSA and nonSMSA residents produced insignificant differences. Kahn and Low  find that blacks are more likely to use labor market intermediaries than whites and suggest this indicates blacks are shut out of informal networks. If blacks are more likely to use formal networks, results showing no difference in the change in information for blacks and whites appear to support the idea that whites have greater access to informal networks. The benefits to acquiring additional information may be greater for nonunion workers as workers in union jobs are generally less likely to change jobs than nonunion workers [Sicherman and Galor, 1990]. However, unions may provide a low-cost method for workers to acquire additional information. Workers in SMSAs have greater potential benefits to acquiring additional information but workers in small communities are likely to acquire more information through low-cost, informal methods.
To provide greater support for these results, the same analysis was performed for the 1976 and 1980 waves of the PSID. The results were similar to those reported above. Also, separate frontiers for 1985 and 1989 were estimated. Again, the change in information is greater for those with less tenure, experience, or information and those who are thinking of getting a new job or are actively looking for a new job in 1985. Also, those who changed jobs between 1985 and 1989 acquired greater amounts of information. However, the change in information was greater for those with less education and no significant difference was found based on county unemployment rates. This paper reports results from the single-regression approach, as the changing nature of the sample may make comparisons between the two one-sided error terms troublesome. In particular, the 1985 sample ranges from ages 20 to 60, while the 1989 sample ranges from ages 24 to 64. Also, given the fairly short time span, substantial changes in the returns to worker characteristics are unlikely.
The measurement of labor market information is the subject of several recent articles. The goal of this paper is to examine changes in workers' information across time. Previous studies attempt to measure the acquisition of information by whether a worker uses labor market intermediaries such as civil service, job placement services, employment agencies, or unions. While this is useful, many workers acquire information without the use of intermediaries or through informal methods that are difficult to measure. Stochastic frontier techniques are used to estimate employee labor market information in 1985 and 1989. By comparing information at two points in time, the net change in information is computed. Results are consistent with previous research examining the acquisition of information [Black, 1981; Kahn and Low, 1990].
In addition, results indicate that applying frontier estimation to cross-sectional data may result in biased estimates of the relationship between information and tenure. However, unobserved heterogeneity does not appear to cause problems with the relationship between information and experience. Overall, the stochastic frontier estimation of information appears to provide a reasonable method for examining the information changes across time. This allows researchers to easily examine changes in information using most panel data sources without requiring specific questions concerning a worker's acquisition of information.
Further research is needed on employee investments in information. Of particular interest may be the ability of workers to take information between jobs. Similar to on-the-job training, it is expected that labor market information will contain aspects which are particular to occupations and industries, while other aspects may apply to the labor market in general.
Estimation of (3) is achieved through the use of maximum likelihood. u is assumed to be distributed half-normal [Mathematical Expression Omitted], and truncated at zero from above, [u.sub.it] [less than or equal to] 0. The distribution of [Epsilon] is parameterized as:
f([Epsilon]) = 2/[Sigma]f([Epsilon]/[Sigma])[1 - F([Epsilon][Lambda][[Sigma].sup.-1])], (6)
where [Mathematical Expression Omitted], and f([center dot]) and F([center dot]) are the standard normal density and distribution functions, respectively. The estimate of u is obtained via maximum likelihood and the following likelihood function:
ln L ([w.sub.0]/[Beta], [Lambda], [[Sigma].sup.2]] = N ln [-square root of 2]/[-square root of [Pi]] + N ln [[Sigma].sup.-1] + [summation over it] ln [1 - F([[Epsilon].sub.it] [Lambda][[Sigma].sup.-1])], (7)
which is the same likelihood function used in frontier production functions. From these results, estimates of [Beta], [Lambda], and [[Sigma].sup.2] are obtained.
The techniques of Jondrow et al.  can be used to obtain two individual specific estimates of incomplete information:
[Mathematical Expression Omitted], (8)
[Mathematical Expression Omitted], (9)
where E([u.sub.it]/[[Epsilon].sub.it]) is the mean and M([u.sub.it],[[Epsilon].sub.it]) is the mode for each individual in year t.
1. Polachek and Yoon  find that unobserved heterogeneity is an important component of information but they do not examine the effect of unobserved heterogeneity on the relationship between information and worker characteristics.
2. There exists some debate over the relationships among ability, education, and tenure. For example, Altonji and Shakotko  and Ruhm [1990b] argue there exists a positive relationship between ability and tenure, while Topel  does not find support for such a relationship. Griliches and Mason  and Blackburn and Neumark  find a positive relationship between ability and education, while Ashenfelter and Krueger  do not find support for such a relationship.
3. Job mobility may be either between or within firms. Obviously not all job changes result in higher wages. Workers who are laid off may accept a lower wage offer. Ruhm [1990a] finds that workers approaching retirement often change jobs and occupations and also receive lower wages on their new job.
4. Reported tenure for job changers may understate the potential wages in 1989 for workers who changed jobs between 1985 and 1989. Thus, tenure was redefined to equal tenure in 1985 plus 4. The dummy variable for 1989 became negative and significant. However, there were no significant differences in the information comparisons reported in Table 2.
5. Union workers have more information than nonunion workers. Results indicate no significant differences in information between married and single workers or SMSA and nonSMSA respondents.
6 Detailed tabular presentation of the magnitudes of both the stock and change in information in the discussion that follows is available from the authors upon request.
7. Kahn and Low  do not have a measure of a worker's current information. They use experience, tenure, education, race, gender, and union coverage as proxies for current information. While this may be reasonable given the stochastic frontier results discussed above, a more direct test of this hypothesis was performed utilizing estimates of a worker's current information.
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John Robst and Kimmarie McGoldrick, State University of New York-Binghamton and University of Richmond.
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|Author:||Robst, John; McGoldrick, Kimmarie|
|Publication:||Atlantic Economic Journal|
|Date:||Dec 1, 1997|
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