**The Unreliability of Job Duration Estimates, Current and Past**

Warren C. Whatley and Stan Sedo, University of Michigan

NOTE: The summary which appeared in the October 1997 issue of *The Newsletter of The Cliometric Society *contained graphics and formatting which cannot be accurately reproduced in this version.

Introduction

In this paper we demonstrate that estimates of current and past job duration are systematically biased in ways that can lead to serious confusions about the structure and performance of labor markets. Estimates of job duration are used widely by economists. When looked at by age, they shows young workers moving frequently from employer to employer, eventually maturing into long-term jobs lasting 20 years or more [Hall, (1982), Ureta (1992)]. Looked at historically, changes in estimated job duration have been used to track the evolution from "spot" to internal labor markets [Carter and Savoca (1990), Jacoby and Sharma (1992), James (1994), MacKinnon (1994)]. Comparisons between the United States and Japan normally lead to speculations about the contribution of the nenko system to Japan's postwar growth experience [Hashimoto and Raisian (1985), Temin (1997)]. And recently, economist have shown a renewed interest in job duration in the United States, sparked primarily by the public perception that jobs have become less secure in recent years [Swinnerton and Wial (1995, 1996), Diebold, Neumark and Polsky (1994, 1996), Farber (1995), Jarger and Stevens (1997)].

To our surprise, only one study has analyzed a sample of completed job duration [MacKinnon (1994)]. The others focus on labor turnover or job persistence rate (which can produce misleading indicators of overall trends), or they estimate completed job duration from data on current job duration. Not surprisingly, none of these debates have found consensus. The historical debate is an example. Using incomplete duration data, Carter and Savoca (1990) conclude that one hundred years ago U. S. jobs were approximately as long as they are today. Jacoby and Sharma (1992) conclude that long-term jobs did not spread until after World War I, and James (1994) concludes that the truth is somewhere in the middle of continuity and radical change. Woytinsky (1942) and Ross (1958), using BLS data on worker turnover, find evidence of declining turnover in the 1920s, but it is well known that turnover is concentrated in the lower tail of the duration distribution and the quality of the early turnover data is poor. We are left not knowing if job duration has changed over the past 100 years, by how much or when. Similar ambiguities plague the recent debate on the relationship between down-sizing and job security [See Marcott (1995) and Jeager and Stevens (1997)].

In this paper we use a sample of completed job durations to demonstrate that current duration data produce estimates of completed job duration that are systematically biased. The sample we use is the personnel records of workers hired at the Ford Motor Company between 1919 and 1943. Since the steady-state estimator is the one commonly used to estimate completed tenure, we use the Ford data to calculate the bias in this estimator. We find that the steady-state estimate of average completed tenure misses the sample average tenure by as much as 60% on either side. We then use a few simple measures of employment fluctuations to adjust the steady-state estimator for deviations from steady-state. These variables (hire rates, separation rates and changes in separation rates) remove 30% of the bias. Since BLS data on turnover date back to 1910, these data can be used to remove some of the business cycle effects from a number of historical point-in-time surveys, allowing us to better gauge secular trends.

Historical Changes in Job Duration

National point-in-time surveys of current job duration are available for 1913, 1928 and 1978. The more recent surveys contain broader worker coverage, but taken together the surveys show the limitations of focusing on part of the distribution. For example, the percentage of workers with five or more years of current tenure increases gradually over the period from 32.9 to 39.9%. This slice of the distributions is consistent with the view found in James (1994). The lower tail tells a different story, one of early increases in job stability followed by a return to 1913 levels, and is a pattern consistent with the view found in Carter and Savoca (1990). The upper tail tell yet another story - one of explosion in very long jobs after 1928, which is the development that led Jacoby and Sharma (1992) to conclude that long-term jobs did not spread until after World War I. Finally, the early cross-sections suggest that U. S. workers were becoming more stable before the New Deal.

These distributions are not adjusted for business cycle effects, and they measure current tenure only, not completed tenure. We do not know how the state of the labor market at the time of the surveys influences the distributions, nor do we know how the upper tails fill out eventually. Salant (1977) shows that the upper tail can be estimated if we assumes that the flow of workers is in a steady-state - meaning that job spells begin and end at rates independent of calendar time. In a steady-state, exactly half of all workers will be more than halfway through their jobs and exactly half of all workers will be less than half way through their jobs, making average completed tenure twice average current tenure.

Ackerlof and Main (1981) double average current tenures for 1963-1978 and produces estimates of average completed tenures in the range of 17-18 years for white men, 11-12 years for white women, 14 years for nonwhite men and 10-12 years for nonwhite women. Carter and Savoca (1990) estimate 13 year jobs on average for 1892 San Francisco workers, and 19 years if San Francisco had the capital:labor ratio of 1980, thus their view of continuity. All of these estimates assume a steady-state, as is the case for any econometric model that imposes a functional form on current tenure in order to estimate a distribution of completed tenure.

The Ford Data

We use the Ford records to see if the steady-state assumption biases estimates of completed tenure. The Ford sample contains the complete work histories of workers employed between 1919 and 1947. We limit the sample to workers hired between January 1, 1919 and January 1, 1944 in order to eliminate end-of-sample truncation on job durations. Information on a variety of worker characteristics such as race, marital status and age are recorded in the files. A detailed description of the data is found in Foote and Whatley (1993). We use only the representative sample because it best represents worker flows, which we use later to measure deviations from steady-state. Complete information is available for 1,899 representative workers. Mean completed duration is 127 days, with a standard deviation of 216 days. The average age at hire is 28.2 years. Six and a half percent of the sample is black and 49.5% are married.

We conduct point-in-time surveys of Ford workers on the first day of each quarter. To provide a context for the Ford sample, we compare the sample weighted average of current tenure at Ford with other point-in-time surveys of current tenure. These comparisons show that between 1913 and 1928 factory jobs in Detroit were shorter than factory job elsewhere in the U. S., and Ford jobs were extremely short. This can be expected when employment grows as fast as grew in Detroit during this period, and employment at Ford grew even faster [Maloney and Whatley (1995)]. Still, we do not want to overemphasize the impact of new hires on the observed current job tenure at Ford. By the 1920s Ford was no longer a progressive employer, but had become known as the "man killing place" where the rule was "put out or get out."

The Steady-State Bias

For each quarterly point-in-time survey we calculate average completed tenure (SEW) and the steady-state estimate of it (2T), where T is average current tenure. The difference between the two (2T-SEW) is the steady-state bias. A plot of the percentage bias shows that it is generally negative in the 1920s and positive in the 1930s, with the steady-state estimator underestimating completed tenure by as much as 60% in the 1920s and 1940s and overestimating it by as much as 65% in the 1930s.

How sensitive is the steady-state bias to deviations from steady-state? Since a steady-state is a situation where hire rates and separation rates are constant, we use changes in these rates as first-order approximations of deviations from steady-state. Deviations from steady-state prior to a survey are measured by three variables. NEWQT-1 is the percentage of the work force newly hired in the quarter preceding the survey. It controls for changes in worker arrival rates. HAZ-1 is the worker separation hazard for the quarter preceding to the survey. It controls for changes in worker separation rates. When NEWQT-1 increases, holding HAZ-1 constant, a point-in-time survey will capture a disproportionately large number of new workers at the beginning of their job spells, causing the steady-state predictor to underpredict average completed duration. When HAZ-1 increases, holding NEWQT-1 constant, a point-in-time survey will capture the typical worker more than half way through his spell of employment, causing the steady-state predictor to overpredict average completed tenure. If the additional hires are entering an environment of declining job duration then a higher arrival rate might not lead to much overprediction. We include the variable DDUR-1 to control for these cohort effects. It measures the percentage change in average completed duration over the two quarters preceding the survey.

Deviations from steady-state after the survey are captured by DHAZ, which is (HAZt+1 - HAZt). If workers begin leaving more quickly in the future then the steady-state predictor will overpredict their average completed tenure.

We use OLS to regress the percentage steady-state bias (BIAS) on the measures of deviations from steady-state produce, one model including DDUR-1 and one excluding it. All of the variable except DDUR-1 have independent and significant effects on the steady-state bias, with all of the estimated coefficients having the expected signs. These simple variables explain 25-33% of the variance in BIAS.

One of our goals is to adjust point-in-time surveys for the state of the labor market. Our discussion, therefore, focuses on the model that excludes DDUR-1 because point-in-time surveys do not contain information on completed duration. In this model, the coefficient on NEWQT-1 is -.5116, so the average hire rate for the sample period (40.2%) causes the steady-state predictor to underpredict completed tenure by -20.5%. The maximum arrival rate causes an underprediction of -42.6%. The coefficient on DHAZ is 19.768, so the bias due to quarterly shifts in the survival function ranges from -65.23 to 82.04%. According to these results, steady-state estimates of completed tenure are extremely sensitive to fluctuations in hire and separation rates.

Sample Effects

We present results for one company, so it is reasonable to ask how representative these might be. Should we expect similar biases in other point-in-time surveys, like those used by Carter and Savoca and James, or the Current Population Surveys, or the BLS surveys? If the economy-wide flow of workers looked like Ford's then our sample would be representative of the economy, but Ford jobs were much shorter. Do deviations from steady-state at Ford have a large effect on BIAS at Ford because Ford jobs were short? The answer is no. Average job length does influences the sensitivity of BIAS to deviations from steady-state, but in the opposite direction.

Consider two steady-state worker flows, one with an average job duration of five years and one with an average job duration of ten. Both have the same steady-state employment levels, implying that the worker arrival and separation rates are twice as high in the short duration regime. Now suppose both regimes want to double the steady-state employment level. If the separation rates do not change, then both regimes must double their steady-state hire rates. Which regime has more bias in the steady-state estimate of completed tenure during the transition to the new steady-state?

First note that the long duration regime is more likely to be out of steady-state at any point in time because it take ten years to reach the new steady-state while the short duration regime will take only five. Second, the steady-state bias during the transition period is larger in the long duration regime. One year after the transition begins, the steady-state estimator in the long duration regime will underpredict the average completed duration of the additional hires by 80% [(2-10)/10]. In the short duration regime it will underpredict it by only 60% [(2-5)/5].

The same logic applies to changes in separation rates. For any deviation from steady-state, the longer the average duration, the larger the bias in the steady-state estimate of completed duration. If anything, the coefficients at Ford underestimate economy-wide sensitivity to deviations from steady-state.

However, economy-wide fluctuation in hiring and separation rates are not as great as those at Ford because the economy faces a less elastic labor supply. Wage adjustments during expansions and contractions should dampen macro fluctuations in worker flows. The greater variance in hiring and separation rates at Ford has helped us estimate the coefficients with greater precision. The coefficients for the economy would probably be larger but more difficult to estimate.

If fluctuations in the economy-wide worker flow were never more than half a standard deviation from the Ford means, and if we applied these milder fluctuations to the smaller Ford coefficients, then the implied steady-state bias for the economy would still range from -21 to 26%. Ackerlof and Main's steady-state estimate of completed tenure is approximately 17 years in 1973. Carter and Savoca's estimate is 13 years for 1892 San Francisco workers. Given our range of possible error, these estimates are consistent with a tremendous rise in average duration over the 80 year period (from 10 years to 21 years) or a surprising decline over the same period (from 16 years to 13 years).

Conclusion

These are rough calculations, but they demonstrate the importance of considering the impact of labor market conditions on tenure data collected by point-in-time surveys. Additional estimates of the sensitivity of BIAS to labor market fluctuations can be gotten from other samples of completed duration, and these will improve the level of confidence in the admissible range of sensitivity. BLS turnover data dating back to 1910 can then be used to purge some of the business cycle effects from point-in-time surveys of current tenure, allowing us to better identify secular changes in completed tenure.

Tables 1-4, Figure 1 NOT AVAILABLE