This research was supported by a grant from the Office of Economic Research of the Bureau of Labor Statistics, U.S. Department of Labor, NLS Small Purchase Order Program. An earlier version of this paper was presented at the C.V. Starr Center Conference on Technologies and Skills, New York University, December 1994. We thank Boyan Jovanovic, Chris Paxson, Wilbert van der Klaauw, and seminar participants at NBER, Hebrew University, and Tel Aviv University (Econometrics in Tel Aviv 95) for useful suggestions and comments. We also thank Steve Davis, Barbara Fraumeni, John Haltiwanger, Barry Hirsch, Shaul Lach and Sam Kortum for providing us with various data sets used in this paper. Eric Bartlesman's help in matching the different datasets to the NLSY is also acknowledged.

Abstract

Using the National Longitudinal Survey of Youth (NLSY) and five proxies for industry rates of technological change, we study the impact of technological change on post-schooling investments in training among young male workers in the manufacturing sector during the time period 1987 through 1992. We find that production workers in manufacturing industries with higher rates of technological change are more likely to receive formal company training, but not other types of training. While education and training are complements, we show that, at higher rates of technological change, the post-schooling training gap between the more and less educated narrows, and low-skilled non-production workers receive significantly more training than higher-skilled non-production workers. The proportion of individuals receiving training increases with the rate of technological change.

I. Introduction

An issue of increasing interest to researchers and policymakers is how the introduction of new technologies into the workplace will impact workers. In particular, there is concern about how less educated workers will fare in an environment characterized by higher rates of technological change. The observed increase in wage inequality between college and high school graduates in the 1980s might be interpreted to imply that the status of less educated workers will deteriorate with the pace of technological change. But, this prediction ignores other adjustments that may occur in the marketplace, one of which is a change in the post-schooling investment of different education groups.

In this paper, we investigate the impact of technological change on young workers' investments in on-the-job training. Economic theory does not provide a clear prediction on the sign of this relationship. Although higher rates of obsolescence and increased uncertainty will decrease training investments, technological change may reduce the cost of training or increase the value of time in training relative to work. Hence, empirical analysis is needed to determine whether young workers receive more or less on-the-job training in response to technological change, and, in particular, how this relationship depends on the worker's education level.

Economists have long been interested in the impact of technological change on the labor market. In the 1950s, the Bureau of Labor Statistics began its case studies of the impact of "automation" on employment. More recently, researchers' attention has focussed on the effect of technological change on the wage structure (Lillard and Tan, 1986; Mincer, 1989; Allen, 1992; Krueger, 1993; Berman, Bound and Griliches, 1994), the demand for educated workers (Bartel and Lichtenberg, 1987, 1991); inter-country differences in wage structures (Mincer and Higuchi, 1988) and retirement decisions of older workers (Bartel and Sicherman, 1993). But, only two studies, Lillard and Tan (1986) and Mincer (1989) have considered the impact of technological change on young workers and both of these papers have limitations some of which our paper overcome. ₁

One problem with earlier work on training and technological change is the limited training information that was available. We use the National Longitudinal Survey of Youth (NLSY) which is unique in terms of the comprehensiveness of the training information that is reported. Unlike other datasets, it includes detailed information on all formal training spells experienced by the individual, including the actual duration of the training. ₂ With this dataset, we conduct a more comprehensive and reliable study of the training effects of technological change. In addition, the NLSY covers the time period 1979 through 1992, enabling us to provide a more current analysis than previous studies.

The second way in which we improve upon previous research is by utilizing a variety of measures of technological change. Estimating the rate of technological change faced by the worker in his job is very difficult. Since the measurement of technological change outside the manufacturing sector is especially problematic (Griliches, 1994), our analysis is restricted to workers in manufacturing. Even within this sector, however, no single proxy is likely to be perfect. We, therefore, link the NLSY with several alternative datasets that contain proxies for industries' rates of technological change. Specifically, our analysis uses the Jorgenson productivity growth series, the NBER productivity data, the Census of Manufactures series on investment in computers, the R&D/sales ratio in the industry, and the industry's use of patents. Previous studies on training and technological change relied solely on the Jorgenson productivity growth series. Our analysis enables us to examine the robustness of alternative measures of technological change, thereby increasing confidence in the results.

Third, unlike the earlier research, we carefully dissect the relationship between technological change and training in order to answer the following questions: (1) How does technological change affect training investments for workers with different levels of education and in different occupational groups? (2) Does technological change increase both entry-level training and training of more experienced workers? (3) Does the pool of trainees increase in response to technological change, or is it mainly the previously trained workers who train more intensively? To our knowledge, this is the first paper to address these important questions. Part II of the paper presents the theoretical framework that guides our empirical work. In Part III, we discuss the data sources for our study, explain the various measures of training and technological change, and present the basic equations that we estimate. Regression results are discussed in Part IV, and a summary is given in Part V.

II. Theoretical Framework

In this section we examine the different channels by which technological change is likely to affect the firm's decision to train its workers or the worker's decision to invest in on-the-job training, as implied by economic theory. ₃ The impact of technological change on the relationship between education and training is also considered. We define technological change as the implementation of new production processes into the workplace. In our empirical work we use various proxies to measure the rate at which these processes are implemented.

There are two mechanisms by which technological change will reduce investments in training. First, an increase in the rate of technological change is likely to accelerate the rate of obsolescence of human capital. According to human capital theory (e.g., Ben Porath, 1967), higher rates of obsolescence will reduce the optimal amount of investment in training at any point in time. Since general human capital is likely to be more immune to the introduction of new work processes, the rate at which an individual's stock of general knowledge and problem-solving skills depreciates will be less than the rate for specific, vocational skills. Technological change should, therefore, lead to a decrease in investments in specific training. The second mechanism by which technological change will reduce training is related to the fact that technological change increases the risk or uncertainty of investment in human capital (see Levhari and Weiss, 1974; and Williams, 1979). While this uncertainty effect impacts the decisions of both individuals and firms, if individuals are more risk averse than firms, the negative effect should be stronger for individuals' investments than firm investments.

Offsetting the negative effects of depreciation and uncertainty are two additional factors which work in the opposite direction. First, technological change might increase the value of time in training relative to its value in work. In that case, employers and workers will find it optimal to increase the amount of on-the-job training, in spite of the loss of time at work. ₄ As in the case of obsolescence, the effect of technological change on the value of training time might vary by the type of human capital, or by level of education. For example, if technological change simplifies the process of learning new skills, the value of time in investment could increase more for the less educated workers, thereby leading to a larger increase in training for these workers. The second positive effect of technological change on training occurs through reductions in the direct costs of training. Technological change could lower the costs of learning devices and other inputs associated with job training, thereby leading to an increase in on-the-job training.

Economic theory, therefore, does not provide a clear prediction with regard to the effect of technological change on the level of on-the-job training. While higher rates of obsolescence and increases in uncertainty are likely to decrease the amount of training, other factors, such as the increase in the value of time in training relative to work, and a reduction in the direct costs of training are likely to increase the amount of job training. Our empirical analysis will show whether the negative or positive effects have dominated in the 1987 to 1992 time period. ₅

We are also interested in analyzing how technological change affects the relationship between education and training. According to human capital theory, more educated workers will train more, simply because human capital is an input in the production of new human capital. In the presence of technological change, however, we may see a weaker relationship between education and training. The discussion above shows that this could happen if the process of learning new skills becomes simpler, thereby increasing the value of time in investment relatively more for the less educated workers. Another reason for a weaker relationship between education and training at higher rates of technological change is that technological change may increase the substitutivity of education and training in the production  of human capital. ₆ The general skills of the more educated may enable them to adapt faster to the new technology, thereby dampening the otherwise positive impact of education on training.

III. Empirical Framework

A. Microdata

We use the main file and the work history file of the 1987-1992 National Longitudinal Surveys of Labor Market Experience of Youth aged 14-21 in 1979 (NLSY) and restrict our analysis to males. The main file is the source of information on personal characteristics such as main activity during the survey week, education, age, race, marital status, health status, etc. An individual enters our sample when he first reports that his main activity during the survey week was "in the labor force." The work history file contains employment related spell data, such as wages, tenure, and separations, constructed from the main NLSY file. For each respondent, employment information is reported for a maximum of five jobs in each survey year. The work history file enables us to distinguish information for each job, especially the reasons for and timing of job transitions. One of these jobs is designated as a "CPS job" and it is the most recent/current job at the time of the interview. Typically it is also the main job. There are a host of important questions that are asked for the CPS job only, such as industry, occupation and firm size. Hence, our analysis is restricted to CPS jobs.

The NLSY is particularly well suited for a study of employee training because of the vast amount of information on the subject that is recorded. ₇ Data on a maximum of seven different training programs taken at any time since the last interview are included. Beginning with the 1988 survey, data on the following items are available for each of the seven training programs: starting and ending dates of the training program, ₈ the number of weeks that the individual attended the program, what type of program it was (e.g. apprenticeships, company training, technical/vocational training off the job, (such as business college, nurses programs, vocational and technical institutes, barber or beauty school, a correspondence course)), government training; and how many hours he usually devoted per week to this program. In the NLSY, company training encompasses three types of training: (1) training run by the employer, (2) training run at work, not by employer, and (3) company training outside of work.

Prior to 1988, detailed information on type of private sector training, as well as the weeks and hours per week spent in training, were only recorded if the training spell lasted at least four weeks. In other words, for the 1979 through 1986 time period, the researcher can measure incidence of private sector and government training, but it is impossible to determine if the private sector training was company-provided training, an apprenticeship program, or obtained in other ways such as a vocational/technical institute, business college, or correspondence course. In addition, even if the training spell lasted at least four weeks, the measure of training duration provided in the pre-1988 surveys is extremely unreliable because it is based on the starting and ending dates of the training program. ₉ In 1987, no training questions were asked. However, training information for 1987 can be imputed from the 1988 data, thereby enabling us to add one more year of data to our analysis; the regressions we report cover the time period 1987 through 1992.

Table 1 reports the incidence and duration of private sector training, by education and size of firm, for the manufacturing sector for the 1988 through 1992 time period. Incidence and duration are calculated on an annual basis. The data show that, on average, 17 percent of the individuals reported receiving private-sector training during the "twelve" month period between consecutive surveys. ₁₀ Median duration of training (for workers with positive hours) was 40 hours, i.e. about one week, and the mean duration was 142 hours, or, approximately, three-and-one-half weeks.

The probability of receiving private-sector training increases monotonically with education. The relationship between training duration and education is not monotonic; as we show below, this occurs because of the association between type of private sector training and education level.

The detailed data from the 1988 through 1992 surveys can be used to calculate the distribution of private sector training across three categories: (1) Company, or in-house, training; (2) Apprenticeships; and (3) Other training, such as training received in a business college, a nurses program, a vocational or technical institute, a barber or beauty school, or a correspondence course. For the entire sample, approximately 76% of private sector training is provided by the company. This percentage ranges from a low of 54% for the lowest education group to a high of 95% for the highest education group. Company training has a median duration of 40 hours for all education groups. This is considerably shorter than the median duration of apprenticeships, and somewhat shorter than the duration of other private sector training. Thus, although more educated individuals are more likely to receive private sector training, their training duration is shorter because their skills are acquired in company training programs rather than apprenticeships or other outside programs.

We distinguished large from small firms based on whether the number of employees in the individual's firm had at least 1000 employees. The data in Table 1 show that the incidence of company-provided training in large firms is 20% compared to only 7.7% in small firms, confirming the earlier findings of Barron, Black and Loewenstein (1987). The positive effect of firm size on the incidence of training holds for all education groups.

B. Measures of Technological Change

In order to estimate the model outlined in Part II, we require a measure of the rate of technological change faced by the individual in his place of work. In the absence of such information, we link the NLSY with several alternative datasets that contain proxies for the industry's rate of technological change. ₁₁ Below we describe each of these measures and analyze their strengths and weaknesses. Since no single proxy is a perfect measure, we feel it is important to use several alternative measures in our analysis. If similar results are obtained with different measures, we can have more confidence in the reliability of the findings. ₁₂

The five measures of technological change that we use are (1) the total factor productivity growth series calculated by Jorgenson et.al. (1987) and updated through 1989, (2) the NBER total factor productivity growth series, (3) 1987 Census of Manufactures' data on investment in computers, (4) the R&D/sales ratio in the industry as reported by the NSF, and (5) the number of patents used in the industry. Each of these measures has advantages and disadvantages as we describe below.

The Jorgenson total factor productivity series has been used extensively in previous research (e.g., Bartel and Sicherman (1993), Lillard and Tan (1986), Tan (1989), Mincer and Higuchi (1988) and Gill (1990)) because it has been shown to be highly correlated with technological change. Griliches and Lichtenberg (1984) showed that for the time period 1959-1976 there was a significant relationship between an industry's intensity of private R&D expenditures and subsequent growth in productivity. Lichtenberg and Siegel (1991) also found that this relationship existed at the company level in the 1970s and 1980s. In using the Jorgenson productivity growth series, technological change is measured as the rate of change in output which is not accounted for by the growth in the quantity and quality of physical and human capital. One problem with this approach is that technological change may not be the only cause of productivity growth. Other factors, such as fluctuations in capacity utilization and non-constant returns to scale, are also likely to affect productivity growth. In order to control for these effects, the empirical analysis will include controls for the industry unemployment rate and the rates of entry and exit of firms in the industry. The Jorgenson series is currently available for the time period 1947 through 1989. The main advantage of the Jorgenson series is that changes in the quality of the labor input are carefully used to correctly measure net productivity growth. Also, the new Jorgenson series utilizes the BEA constant-quality price deflator; the earlier series underestimated productivity growth in high-tech industries (e.g. the computer industry) since quality improvements were not incorporated into the output price index. The major disadvantage of the Jorgenson series is that the data are reported for only 22 broad industry categories in the manufacturing sector, equivalent to two-digit SIC categories.

The NBER productivity database contains annual information on total factor productivity growth for 450 (four digit) manufacturing industries for the time period 1958 through 1989. The advantage of the NBER database over the Jorgenson database is its narrow industry categories yielding data on approximately 100 three-digit industries in manufacturing. The disadvantage is that the productivity growth measure was not adjusted for changes in labor quality.

The third measure of technological change that we use is investment in computers. During the 1980s, there was an enormous growth in the amount of computer resources used in the workplace. Indeed, it has been argued (see Bound and Johnson, 1992) that the most concrete example of technological change in the 1980s was the "computer revolution". ₁₃ Hence the extent to which firms invest in information technology can serve as a good proxy for the rate of technological change at the workplace. Using data from the 1987 Census of Manufactures, we calculate the ratio of investment in computers to total investments. ₁₄ The advantages of this measure are that (1) unlike data on R&D expenditures, it measures use  (not production) of an innovation and (2) it is available for several hundred four-digit industries in the manufacturing sector, which reduces to approximately 100 three-digit industries for the NLSY sample.

A fourth proxy for technological change is the ratio of company R&D funds to net sales reported by the National Science Foundation (1993) for industries in the manufacturing sector. The advantage of this variable is that it is a direct measure of innovative activity in the industry, but as indicated above, the innovative activity refers only to the industry in which the innovation originates, not the industry where the innovation is actually used.

The fifth measure of technological change is obtained from the dataset constructed by Kortum and Lach (1995) on the number of patents used  in two-digit manufacturing industries. Patent data are generally collected by technology field but Kortum and Lach (1995) propose a method for converting the number of patents per technology field into the number of patents used per industry. Their data are available for the time period 1957-1983. Since our analysis begins in 1987, we need a measure of patents used that is closest to that year. We could use the number of patents employed by the industry during the 1980s, but the likelihood of an innovation being patented has differed historically across technology fields, and hence, across industries. In order to control for these systematic differences in the likelihood of patenting across industries, we construct the following variable for each two-digit manufacturing industry: the number of patents used by the industry during the years 1980 through 1983, divided by the number of patents used by the industry during the 1970s. The main advantage of proxying technological change by "use of patents" is that, like the computer investment variable discussed earlier, it measures the direct use  of innovations. The disadvantage is that the data are only reported for twenty manufacturing industries.

Appendix B contains the industry means of the various proxies for technological change followed by a correlation matrix. Each listing is presented in rank order so that we can observe whether the five proxies produce similar patterns regarding high and low technological change industries in the manufacturing sector. We find that some industries appear at the top or near the top of each measure's list. Using the Jorgenson data, non-electrical machinery has the highest rate of technological change and electrical machinery is tied for second place with petroleum refining. The computer investment data provides information for more detailed industries; the three industries with the highest computer share of investment, electronic computing equipment, radio, T.V., and communication equipment, and office and accounting machines, are members of the broader non-electrical machinery and electrical machinery categories. For the NBER productivity measure, electronic computing equipment has a significantly larger value than the other manufacturing industries. The R&D/sales ratio data show "office, computing and accounting machines" as the top-ranking industry. For the patent variable, office and computing machines and communication and electronics rank at the top.

The fact that the two or three industries that we generally think of as "high-tech" industries rank at the top for all five measures of technological change is evidence that the five variables are good indicators of technological change. One might be attempted to generalize from these cases and conclude that, since all five proxies appear to be measuring the same thing, perhaps only one proxy should be used for the analysis. A closer look at the five listings indicates, however, that they each contribute unique information about the differences in the rates of technological change in the manufacturing sector. For example, according to the computer investment measure, leather products has a relatively high rate of technological change, but this is not captured by the other proxies. By comparison, petroleum refining ranks high for the Jorgenson and NBER productivity measures and the patent variable, but not for the other three proxies. Additional comparisons of the five listings also demonstrate that, in many cases, the rankings are dissimilar.

The correlations among the five measures, presented at the end of Appendix B, show that no two measures are perfectly correlated, and, therefore, there is no redundancy in using all of them in our analysis. The correlations between the different measures range from .3 to .7, which is consistent with our argument that each proxy is likely to capture a different aspect of technological change. ₁₅ If all proxies produce similar results about the impact of technological change on training, confidence in our conclusions will be significantly enhanced.

C. Matching the Microdata and Industry Measures of Technological Change

Since our NLSY panel covers a short time span (1987-1992) and there is a high degree of randomness in annual changes in the technological change measures that are available on an annual basis, it is impossible to conduct a true time-series analysis. Our analysis therefore relies on cross-section variations in technological change. All of the measures that we use have a common trait, i.e. they are proxies for the industry  rate of technological change. We recognize that an industry measure of technological change may not have the same impact for all of the occupations in that industry. For example, an innovation in the industry's production processes may have little or no impact on clerical employees. By matching an industry measure of technological change to all of the individuals in that industry we are less likely to find a strong effect of technological change. Hence, our empirical results are likely to be underestimates  of the true relationship. ₁₆ We deal with this issue by conducting separate analyses for production and non-production workers, since in most cases production workers are more likely to be affected by technological change in the manufacturing sector.

In order to match the different measures of technological change to the industrial classification used in the NLSY (the Census of Population classification), we use industry employment levels as weights whenever aggregation is required. When we utilize the Jorgenson and NBER productivity growth measures, we characterize industry differences in the rate of technological change by using the mean rate of productivity growth over the most recent ten-year time period, i.e. 1977-1987. In the case of investment in computers, we use data from 1987 as described earlier. The R&D/sales ratio for each industry is calculated as a three-year moving average for the three year period prior to the year of analysis, e.g. averaging data for 1984-1986 for the 1987 NLSY, etc. For the patent data, we calculate the number of patents used during the time period 1980-83 divided by the number used during the 1970s. Hence, with the exception of the R&D variable, we use a fixed time period measure of technological change which may act like a fixed effect for each industry, capturing other fixed attributes of the industry. We deal with this problem by including several industry characteristics in the regressions which we believe may influence the relationship between training and our measures of technological change. They are: the annual industry unemployment rate obtained from Employment and Earnings, annual measures of percent unionized in the industry compiled from the CPS by Hirsch and MacPherson (1993), and the annual rates of job creation and job destruction for both start-up and continuing establishments in the industry constructed by Davis and Haltiwanger (1992).

Another issue is that the standard errors of our estimated coefficients may be biased downwards because industry-level shocks may be correlated across individuals within a given industry. In order to deal with this issue, we re-estimated all the models reported in this paper, using linear probability random effect models. None of the findings reported here were changed in a significant way. We chose to present the Logit estimates because a linear model is an inappropriate specification in the case of a discrete choice model, even though the estimation results are often similar to those obtained by maximum likelihood estimation (See Dhrymes, 1978, pp. 331-334).

D. Econometric Models

1. The Likelihood of Company Training

Our econometric analysis is restricted to company training because, as was shown in Table 1, three-quarters of private-sector training is provided by the firm. We do provide some evidence of the impact of technological change on other forms of private-sector training and contrast these effects with those for company training.

In order to estimate the effect of technological change on the likelihood of company training, we adopt a simple Logit framework. In each period, between two surveys, an individual will face one of the following two alternatives described by j: Engage in company training (j=1), or not (j=0).

The choice j  occurs when the latent variable , where

where i is the individual index, t is time, j is the alternative, X_itj is a vector of individual, job, and industry characteristics that may vary over time. The vector X includes the following variables: marital status, race, years of education, residence in an SMSA, years of experience and its square, tenure and its square, union membership, whether or not the individual is employed by a large firm, the industry unemployment rate, union coverage in the industry, and job creation and destruction in the industry. T_it  is the rate of technological change in the industry in which the individual is working at time t. ₁₇ This specification treats technological change as an exogenous variable. It is possible that the decision to adopt a technology will depend on the trainability of a firm's workforce, making technological change an endogenous variable. However, since we measure the rate of technological change at the industry level, using multi-year means, it is reasonable to assume that firms and workers treat these measures of technological change as exogenous.

Assuming that e is logistically distributed ₁₈ gives rise to a logit model in which the underlying probabilities are

In order to identify the parameters, the normalization is imposed and the estimated parameters are obtained by maximum likelihood.

2. Hours of Company Training

In order to estimate the effects of technological change on the amount  of time spent in company training, we adopt a standard Tobit model. As McDonald and Moffitt (1980) show, the Tobit coefficients measure the effects of the covariates on the dependent variable (hours of training), resulting from both the change in the likelihood of being above the limit (getting training), and from the change in the value of the dependent variable (hours of training) if it is already above the limit. In Appendix D, we outline the Tobit model and describe the decomposition procedure suggested by McDonald and Moffitt. The independent variable used in the Tobit models are the same as those used in the Logit regressions.

IV. Results

A. Incidence of Company Training

A summary of the estimates from our logit models on the incidence of company training in the manufacturing sector is shown in Table 2. Complete regression results for one model are given in Appendix C where we see the typical patterns regarding the effect of education, firm size, and other characteristics on the incidence of training. ₁₉ In this section, we detail the relationship between technological change and the incidence of training; in all of our specifications, we control for four additional industry characteristics: the unemployment rate, percent of workers who are union members or covered by a union contract, the annual rate of job creation, and the annual rate of job destruction.

Table 2 The Effects of Technological Change on the Likelihood of Company Training in the Manufacturing Sector*
	All		Production		Non-Production
I. Jorgenson TFP	25.26 (.002)	.021	32.95 (.004)	.018	9.56 (.457)	.013
II. Share of Investment in computers	2.11 (.09)	.010	3.90 (.058)	.012	-.02 (.99)	-.0002
III. NBER TFP	2.36 (.10)	.006	5.99 (.022)	.01	.002 (.999)	.00001
IV. R&D to Sales ratio	.0805 (.001)	.021	.1622 (.0001)	.026	.0289 (.378)	.012
V. Use of Patents	6.13 (.005)	.016	10.85 (.0025)	.018	1.267 (.661)	.005
Number of observations	3856		2541		1312
*In parentheses, below the logit coefficients, are estimated probability that the coefficient is not different from zero. To the right of each estimated coefficient is the derivative (dP/dX), multiplied by standard deviation of measure of technological change. The derivative is calculated as where is the mean incidence of training in the sample. The values for the standard deviations are: .0086 for jorgenson's TFP, .05 for Investment in computers, .026 for growth in investment in computers, .027 for the NBER TFP, .86 for the Yale measure, 2.57 for the R&D to sales ratio, and .027 for use of patents. The mean rates of training for the sub-samples in the regressions are .111 for all workers in manufacturing, .067 for production workers, and .196 for non-production workers. The other variables in the regressions are: marital status, race, educational dummies, a dummy for SMSA, labor market experience (and its square), tenure with employer (and its square), union membership, a dummy for large firm (more than 1000 workers), industry unemployment rate, industry level of unionization, industry rate of job creation (mean over 1980-1988), industry rate of job destruction (mean over 1980-88), and year dummies.

Table 2 shows the effects of each of the five technological indicators on the incidence of training for all workers in the manufacturing sector (column 1) and for production and non-production workers separately (columns 2 and 3, respectively). We present the logit coefficient and the estimated probability that the coefficient is not different from zero (shown in parentheses beneath the coefficient). To the right of each coefficient, we show the derivative (dP/dX) multiplied by the standard deviation of the measure of technological change. This estimate enables us to compare the magnitudes of the effects of the various technological change measures. The results in column (1) show that all five proxies for technological change have a positive and significant effect on the incidence of training in the manufacturing sector, indicating that the negative effect of technological change due to the increase in the rate of depreciation or increased uncertainty is outweighed by the positive effects relating to reductions in the cost of training, and/or increases in the value of time in training relative to work. The largest impacts are observed for the Jorgenson TFP measure, the R&D/sales ratio and use of patents. Comparing the results in column (2) with those in column (3) shows that the impact of technological change on the incidence of training is larger for production workers than non-production workers, as anticipated. In fact, the estimated coefficients for non-production workers are not statistically significant.

B. Incidence of Non-Company Training

Although three-quarters of private sector training is provided by the firm, young workers do receive some training outside the firm. In Table 3, we consider whether technological change also has a positive impact on non-company training. In columns (1) through (3), the dependent variable is the likelihood of any type of private sector training (company or non-company), and in columns (4) through (6), we show results for the likelihood of non-company training. Since the vast majority of private-sector training is company-provided, the results in columns (1) through (3) are quite similar to those reported in Table 2. The analysis of non-company training alone shows that, with the exception of the Jorgenson TFP measure, technological change does not have a significant effect. Hence, the remainder of our analysis is confined to company training.

C. Education and Training

As we discussed in the Introduction, it is important from a policy perspective to estimate the effect of technological change on the post-schooling human capital investments of different education groups. Our theoretical discussion provided two reasons why the impact of technological change on the incidence of training may vary by education. One reason is that more educated individuals may require less training in response to technological change if their general skills enable them to learn the new technology and adapt to the changed environment, i.e. training and education are substitutes in production. Another reason is that technological change simplify the process of learning new skills, thereby increasing the value of time in investment relative to its value in work from the less educated. We test these hypotheses in Table 4 where the regressions include an interaction effect between education and the proxy for technological change.

The results in Table 4 show that for all workers, production and non-production workers alike, the more educated  are more likely  to receive company training. ₂₀ The interaction effects show, however, that technological change attenuates the impact of education on training.  This implies that, at higher rates of technological change, the training gap between the highly educated and the less educated narrows. The separate results for the production and non-production workers generally support this conclusion; with the exception of one measure, whenever the technological change indicator has a positive and significant effect on the incidence of training, the education-technological change interaction effect is negative and usually significant.

In order to more fully understand the relationship between technological change and the incidence of training for different education groups, we estimated the regressions in

Table 4 using a set of dummies for education groups (1-8, 9-11, 12, 13-15, 16, and 17+ years of schooling) in place of the continuous measure, and interacted the dummy variable with the technological change indicator. The coefficients from these regressions are shown in Table 5. We used these coefficients to create plots (see Figures 1-2) that depict the impact of technological change on the incidence of training for a worker of given characteristics in each education group. ₂₁ Whenever a slope is significantly different from zero, we indicate it with an "S" mark.

Although the education interactions are not monotonic and significant effects are observed for only one or two educational groups, ₂₂ Figures 1-2 generally support the conclusion that, at higher rates of technological change the gap between the training incidence of the highly educated and the less educated narrows. In the case of production workers, with the exception of the Jorgenson measure, we find that workers with some high school (9-11) and high school graduates train significantly more at higher rates of technological change, in some cases overtaking the training received by the 13-15 education group. For non-production workers, again with the exception of the Jorgenson measure, we find that the 13-15 group trains more at higher rates of technological change, over-taking those with at least 16 years of schooling.

Bartel and Lichtenberg (1987) have argued that highly-educated workers have a comparative advantage with respect to learning and implementing new technologies, and hence that the demand for these workers relative to the demand for less-educated workers is a declining function of experience with the technology. When a new technology is first introduced, there is a great deal of uncertainty about job tasks and highly educated workers are needed to help the firm through this difficult implementation stage. The general skills of the highly educated workforce serve as a substitute for company training. As experience with the new technology is gained, however, it is possible to train the less educated employees to perform the new tasks. In our empirical analysis, we measure "long term" differences across industries in the rate of technological change, and our finding that the training gap between the more and less educated narrows is consistent with the idea of the firm utilizing training to enable the less educated to work with the new technology. ₂₃ Thus it appears that technological change has acted to reduce the gap in the stocks of human capital accumulated by different education groups through formal company training.

We recognize that one reason for the observed narrowing of the formal training gap between education groups could be selectivity. At higher rates of technological change, firms are less likely to employ or retain the less able employees within each education group. This bias is likely to be more pronounced for the less educated workers, resulting in an overestimate of the impact of technological change on the training of the less educated. We attempted to correct for this bias by including a set of ability test scores (not reported here), and our results on the impact of technological change were virtually unchanged. We did find, however, a positive and significant correlation between ability (holding schooling constant) and the likelihood of training, and a smaller coefficient on education.

D. Occupations and Training

It is possible that our findings regarding the impact of technological change on education groups may reflect the fact that, within the categories of production and non-production workers, individuals with different amounts of education perform distinct job tasks, some of which are more sensitive to technological change. We, therefore, reestimated the regressions in Table 5, adding one-digit occupation dummies. The estimated coefficients of the interactions between the technological change measures and the education dummies were virtually unchanged.

The question of whether the impact of technological change varies across occupation groups can be considered directly. We estimated a regression which includes the one-digit occupation dummies and a set of technological change/occupation interaction terms. The results are shown in Table 6. In the case of production workers, we find that, at very low levels of technological change, there are no occupational differences in training incidence. But, at higher rates of technological change, craftsmen receive significantly more training than other production workers. ₂₄ For non-production workers, a very different pattern emerges. We find that, at low levels of technological change, clerical and unskilled workers receive the least amount of training among non-production workers. However, at high rates of technological change, they receive more training than the other non-production workers. ₂₅ It is interesting to note that this group includes occupations such as clerks, computer and peripheral equipment operators, secretaries, and office machine operators, occupations where the introduction of computers is likely to have had a strong impact on job tasks.

E. Initial Training versus Re-Training

We have interpreted all of our findings in this section as indicating that the observed differences in training are due to higher rates  of technological change. Alternatively, one could argue that our results are due to differences in the nature  of technology across industries. Perhaps industries that we rank higher on the dimension of technological change are simply industries that use more sophisticated technologies. These technologies may require more initial training in order for the worker to learn how to use them. If this hypothesis is correct, we would expect to see more training (especially formal training) when workers join the firm and virtually no impact of our "technological change" proxies on the training of more tenured workers.

In order to distinguish these two possible effects, we interact the measures of technological change with two dummies, one indicating that the worker has tenure of one year or less with the employer and the other indicating tenure of more than one year. Our assumption is that the effect of the technological change measure on longer tenured workers is more likely to reflect the response to technological change. ₂₆

Table 7 reports the estimated coefficients on the technological change variables on the likelihood of training, separated for tenure levels below and above one year. If our earlier results were due simply to the cross-sectional differences in the nature of technology, we would not expect to observe significant coefficients for workers beyond their first year of tenure. The results in Table 7 show that, although the measured effects of the technological change variables are larger for individuals with less than one year of tenure, all of the technological change proxies have positive and significant effects on longer-tenured production workers. A test of equality of coefficients between the low tenure and high tenure groups rejects the hypothesis that they are equal. Hence these results provide support for our claim that what we are indeed measuring is the effect of technological change,  not only the nature of technology, and ongoing technological change results in training of workers beyond their first year of tenure.

F. Duration of Company Training

In Table 8 we report the Tobit estimates of the effects of the various technological change measures on hours of company training received since the last survey. Complete Tobit regressions (for one specification) are shown in Appendix D where it can be observed that more educated workers have more hours of training. Table 8 reports the partial derivatives and elasticities on the technological change measures and then decomposes them into the change that is due to the increase in the incidence of training and that which is due to the increase in hours of training, given positive hours. The main finding of the Tobit analysis is that the change in hours of training is due largely to the increase in participation; the ratio of the derivative due to the change in participation divided by the total derivative is approximately .85.

Table 8 The Effects of Technological Change on Hours of Company Training Tobit "Decomposition" Analysis Using Different Measures of Technological Change; Males Workers; Manufacturing (standard errors in parentheses)
Measure of Tec. Change & Group of Workers	Tobit Marginal Effect		Due to Change Participation		Due to increased hours
	Der.	Elast.	Der.	Elast.	Der.	Elast.
Jorgenson TFP
All workers	206 (88)	.234 (.101)	177 (76)	.201 (.086)	29 (12.5)	.033 (.14)
Production	258 (98)	.384 (.0146)	226 (86)	.336 (.128)	31 (12)	.047 (.18)
Non-Production	-74.85 (229)	.060 (.184)	-61 (189)	-.050 (.152)	-13 (40)	-.010 (.032)
NBER TFP
All workers	14.8 (16.8)	.022 (.024)	12.71 (14.43)	.019 (.021)	2.09 (2.38)	.003 (.003)
Production	38.10 (25.35)	.057 (.038)	33.37 (22.18)	.050 (.033)	4.73 (3.17)	.007 (.005)
Non-Production	-9.02 (33.37)	-.013 (.047)	-7.44 (27.55)	-.011 (.039)	-1.57 (5.82)	-.002 (.008)
Share of Investment in Computers
All workers	18.44 (14.08)	.119 (.092)	15.84 (12.09)	.103 (.078)	2.60 (1.99)	.017 (.012)
Production	14.02 (18.69)	.107 (.142)	12.28 (16.37)	.093 (.125)	1.74 (2.32)	.013 (.017)
Non-Production	17.10 (30.24)	.093 (.165)	14.11 (24.96)	.077 (.136)	2.98 (5.28)	.016 (.029)
R&D/Sales Ratio
All workers	.699 (.285)	.161 (.066)	.600 (.245)	.138 (.565)	.098 (.041)	.022 (.009)
Production	1.034 (.38)	.259 (.095)	.906 (.333)	.227 (.083)	.127 (.048)	.032 (.012)
Non-Production	.477 (.602)	.101 (.128)	.394 (.497)	.083 (.105)	.017 (.022)	.083 (.105)
Use of Patents
All workers	47.88 (24.95)	1.64 (.86)	41.11 (21.42)	1.41 (.73)	6.75 (3.54)	.23 (.12)
Production	63.43 (33.09)	2.92 (1.53)	55.58 (28.97)	2.56 (1.33)	7.85 (4.14)	.36 (.19)
Non-Production	16.90 (52.86)	.39 (1.23)	13.94 (43.63)	.32 (1.01)	2.95 (9.23)	.07 (.21)
The number of observations are 3812 for "all workers", 2524 for "production workers", and 1286 for "non-production workers".

One limitation of the standard Tobit model is that it does not allow for different signs on the effect of technological change on the selection into training and its effect on hours of training, given selection. In order to allow for such a possibility, we reestimated the models presented in Table 8 using a general Tobit specification, where separate coefficients are estimated for the effect of technological change on selection and its effect on hours. Our results (not reported here) reject&nsp; the hypothesis that technological change increases the incidence of training and  reduces the number of hours per spell. We found that, in virtually all models, the effect of technological change on hours per spell was positive and insignificant. This confirms the findings of the standard Tobit model that the effects of technological change on training are incidence-, not duration-related.

G. The Effects of Prior Training

The results of the Tobit analysis indicate that technological change increases training at the extensive margin, i.e. the incidence of training, not hours conditional on participation, increases. In order to be more confident in this conclusion, we exploit the panel nature of the NLSY data. We examine whether higher rates of technological change induce firms to provide training to individuals who have already received training or to those who did not receive training in the prior period. If the latter is true, then technological change serves an important function; it acts to increase the proportion of workers who receive training. We test this hypothesis in Table 9 by interacting the various measures of technological change with two dummy variables, one indicating the individual received training in the prior year (i.e. between t-2 and t-1, since the dependent variable is training between t-1 and t), and the other indicating no training in the prior year. In columns (1) and (2) the sample is restricted to individuals who did not change industries between time periods t-2 and t, and in columns (3) and (4) we restrict the analysis to individuals who did not change employers between the two time periods. The results show insignificant effects of technological change for previously trained workers and significant effects for most of the technological change indicators for individuals who did not receive training in the prior year. A test of equality of coefficients for the two groups rejects the hypothesis that they are equal. The increase in incidence of training due to technological change occurs because different individuals are now receiving training.

V. Summary and Implications

In this paper we have analyzed the impact of technological change on young workers' investments in on-the-job training. Economic theory does not provide a clear prediction on the sign of this relationship. While higher rates of obsolescence and increased uncertainty will decrease the amount of investment, on-the-job training will increase if technological change reduces the cost of training or increases the value of time in training relative to work. The impact of technological change on the post-schooling investments of different education groups is also theoretically ambiguous; although, in general, more educated workers train more, we show that, in the presence of technological change, a weaker relationship between education and training may exist.

We linked a sample of male workers in manufacturing industries from the 1987-92 waves of the NLSY to five different measures of industry rates of technological change in order to empirically resolve the ambiguous theoretical predictions and found essentially similar results for all five measures. In particular, we found that: (1) Production workers in industries with higher rates of technological change are more likely to receive formal company  training than those working in industries with lower rates of technological change, controlling for a set of worker, job and industry characteristics. (2) While more educated workers are more likely to receive training, the training gap between the highly educated and the less educated narrows,  on average, as the rate of technological increases. (3) The relationship between training and technological change is insignificant for the aggregate group of non-production workers. Disaggregating the group, we find that, at higher rates of technological change, the lower-skilled non-production workers, i.e. clerical and unskilled workers receive significantly more training compared to the more highly skilled non-production workers, such as professionals, technical employees, managers, and sales workers. (4) The observed increase in hours of training due to technological change is due to an increase in the frequency of training, not an increase in hours of training, given participation. Technological change therefore acts to increase the extensive margin of training, increasing the pool of trainees. (5) Consistent with the latter result, we find that at higher rates of technological change, firms are more likely to train individuals who have not received training in the prior period rather than those who were previously trained.

Our findings have clarified the relationship between investment in human capital and technological change. We have confirmed that, at higher rates of technological change, firms employ more educated workers and provide more training to their workforces. At the same time, however, higher rates of technological change have been shown to induce employers to provide more training to their less  educated employees since the general skills of the more educated facilitate their adaptation to the new technologies. It is not clear apriori how these effects will impact the wage structure, a topic that we reserve for future research.

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Appendix A

Data

1. General
   The data are from 1979-1992 National Longitudinal Surveys of Labor Market Experience of youth age 14-21 in 1979 (NLSY). Additional data are obtained from the NLSY work history file. The NLSY work history file contains primarily employment related spell data constructed from the main NLSY file. Both files are available in cd-rom format. Many questions are asked with regards to the time since the last survey. For the first survey (1979), the questions, in most cases, are with regards to the time period since January 1, 1978.

   In addition to the NLSY, we use information from variety of sources. These are industry measures of technological change and other industry level variables. They are described in the text.

2. The Sample
   The number of men interviewed in 1979 is 6403. Not all individuals are interviewed each year. The first observation for an individual (to be included in our sample) is the first survey in which the main activity reported for the week prior to the survey is working (1), with a job, but not working (2), or looking for a job (3). Following that, an individual is included in the sample as long as he is interviewed (even if leaving the labor market). Other restrictions apply only for specific analyses. The panel is unbalanced, and the number of observations per individual varies.

3. CPS Job
   For each respondent, employment information on up to a maximum of 5 jobs is recorded in each survey year. One of these jobs is designated as a CPS job and it is the most recent/current job at the time of interview. Typically it is also the main job. Each job is identified by a number (1 to 5) and job #1 in most cases is also the CPS job. For only this so called CPS job there are a host of additional employer/employee related questions that are asked in the NLSY surveys. Our analysis is restricted to CPS jobs.

4. The Work History File
   We use the work history file to construct the tenure, separation and reason for separation variables.

   (a) Tracing jobs and Tenure with Employer:  The tenure variable is already constructed in the work history file. The major difficulty is tracing CPS jobs over the interview years. A variable called PREV allows matching of employers between consecutive interview years. For each job in a particular survey year it gives the job number that was assigned to that job in the previous year (assuming of course that the current job existed in the previous year). Our programming strategy was to pick CPS jobs in which the respondents are actually employed at the time of interview, and to trace these jobs to the next survey year via the PREV variable in the succeeding survey year. There are, however, a few cases where we cannot trace the current CPS job in the succeeding interview year with PREV. The current tenure value is the total number of weeks worked up to the interview date. A shortcoming of PREV is that it allows for matching employers between consecutive interview years only. If, therefore, a respondent worked for a particular employer say in 1980 but not in 1981 and started working for the same employer in survey year 1982 then there is no way of knowing the total years of tenure with that employer since employer numbers are followed only in contiguous interviews. This may not be a problem for turnover analysis since re-employment with the same employer after an absence of that length (i.e., a period longer than that between two successive interview years) maybe considered a new job.

5. Weeks between surveys
   The number of weeks between surveys ranges between 26 and 552 weeks. The large numbers are the results of individuals not being surveyed for several years. In all our analyses we included (when it made sense) the variable WKSSINCE (weeks since last survey). The variable was excluded if it made no difference.

6. Training:
   A variety of formal training questions were asked in all survey years, except 1987. Individuals were asked to report up to two government programs in which they were enrolled since the previous interview, and up to four vocational/technical programs. Until 1986 the maximum was two programs, and in 1988 it was increased to four.

   Up until 1986, only if the program lasted more than 4 weeks, further questions were asked, in particular the type of program and the dates it started and ended. Starting in 1988 these questions were asked about all programs, regardless of length. The four weeks condition up to 1986 is a major shortcoming of the data set. Any analysis that focus on a specific type of training (e.g. company training) has to be limited to post 1986. The following example illustrates the problem: The percentage of workers in our sample that reported enrollment in company training is 4.7% over the period 1976-1990. Limiting the sample to 1988-1990, the rate increases to 11%.

   In certain years (80-86, 89-90) a distinction was made between programs in which the individual was enrolled at the time of the previous interview, and programs that started after the previous interview. ₂₇ When such a distinction is made, up to two programs at the time  of last interview can be reported. A person was asked about training that took place at the time of last interview, only if the interviewer had a record indicating so. Therefore, fur 1980-86, such a record did not exist if training took less than a month!

   For all programs the starting and ending month and year are reported. Also reported are the average number of hours per week spent in training.

   In our programming we number all programs in the following order: the four vocational/technical programs are numbered 1-4, the two programs at time of last interview are numbered 5-6, and the government programs are numbered 7-8. Type of Training: Up to 1986, the following categories are reported:

   
   1=Business College,
   2=Nurses Program,
   3=apprenticeship,
   4=vocationaltechnical Institution,
   5=Barber Beauty,
   6=Flight School,
   7=correspondence,
   8=company/military,
   9=other.

   We aggregate them into company training (8), apprenticeship (3), and "other" (1,2,4,5,6,7,9). Starting in 1988, the breakdown is more detailed:

   
   1-7 are unchanged.
   8=A formal company training run by employer or military training (excluding basic training).
   9=Seminars or training programs at work run by someone other than employer,
   10=Seminars or training programs outside of work,
   11=vocational rehabilitation center,
   12=other.

   We now aggregate 8-10 as company training, and 11-12 as "other".

Below are additional descriptions of some of the variables used:

Any Tech/Voc Training Dummy: Whether the worker received any technical or vocational training since (or at the time of) last interview.

Any Training Dummy (TANYD): Like the above, but also includes government training .

Company Training Dummy (TCOMD): If any of the training programs was #8 up to 85, or #8, #9, or #10 after 86. Notice that only after 86 the type of program was asked of all workers who reported training. Prior to 88, only for those who spent more than 4 weeks on training the program type question was asked (see above for more discussion of this problem).

Length of Training: Starting in 1988, in addition to asking when (month and year) did different training program start and end, individuals were also asked "altogether, for how many weeks did you attend this training?". The question was not asked of government training. If the answer was 0 (less than a week), we re-coded it to half a week.

For each of the eight programs, individuals were asked for the average hours per week spent training. Multiplying the hours per week in each program with the weeks in each program, we get the total hours in each program.

Imputing training data for 1987: In 1987 no training questions were asked. We utilize the answers to the 1988 survey to construct training information for the 1987 survey. We do so by using information on the starting and ending dates of training programs. If reporting in 88 that still in training (end month=0 and endyr=0 or 1) we set the end date to the interview date. For some individuals the answer for the beginning date indicates "still in training". This is an error.

Appendix B

Appendix C

Appendix D

Appendix E
The Tobit Model and the McDonald & Moffitt Decomposition

Consider the following relationship:

where y_i is the dependent variable, X_i is a vector of independent variables, is a vector of unknown coefficients, and u_i  is an independently distributed error term assumed to be normal with zero mean and constant variance ². Therefore, the assumption is that there is an underlying, stochastic index equal to which is observed only when it is positive, and hence is an unobserved, latent variable. The expected value of y in the model is

where is the unit normal density, and F (z ) is the cumulative normal distribution function. The expected value of y for observations above the limit, denoted by y*, is plus the expected value of the truncated normal error term

Consequently, the basic relationship between the expected value of all observations (Ey ), the expected value conditional upon being above the limit (Ey *), and the probability of being above the limit (F (z )), is:

The decomposition suggested by McDonald and Moffitt is obtained by considering the effect of a change in the j variable of X on y:

Therefore, the total change in y can be decomposed into two parts: The change in y of those above the limit, weighted by the probability of being above the limit, and the change in the probability of being above the limit, weighted by the expected value of y if above.

Each of the above terms can be evaluated at some value of . The value of Ey * can be calculated from equation (3). The two partial derivatives that we focus on are:

Note 1: Lillard and Tan (1986) used the CPS and the NLS Samples of Young Men and Young Women, while Mincer (1989) analyzed the young workers in the PSID. Back.

Note 2: Although Lynch (1991 and 1992) used the NLSY data to study the determinants of private sector training, her work did not analyze the role played by technological change. Back.

Note 3: Technological change is implicitly treated as an exogenous variable in this section. Our ultimate goal is to understand how labor markets operate in a world of high rates of technological change, relative to a world where the rates of technological change are much lower. While the adoption of new technologies in each of those worlds, at any given time, is endogenous, the overall differences between the two worlds, as measured by their average rates of technological change, are exogenous from the point of view of firms and workers. Back.

Note 4: The "neutrality hypothesis" in the Ben-Porath (1967) model does not allow for such a possibility, but Ben-Porath does discuss the effects of relaxing this assumption. Heckman (1976) also provides a model where the rate of investment can increase over time. Back.

Note 5: Our findings for this time period do not necessarily apply to earlier time periods when the sign on the relationship between technological change and training may have differed. Back.

Note 6: Sicherman (1990) provides evidence that education and training are substitutes in the production of human capital. Back.

Note 7: Like most other datasets, the NLSY provides information only on formal training. Ignoring informal training, a major portion of on-the-job training, is a drawback (see Sicherman, 1990). Back.

Note 8: Not available for government programs. Back.

Note 9: For example, if an individual reported starting a training program in January of the survey year and finishing it in December of that year, training duration would be recorded as 52 weeks even if the individual had only received one day of training per month. Back.

Note 10: Fifty-six weeks is the average length of time between survey dates. Back.

Note 11: An alternative approach would be to collect data from a small sample of firms that are undergoing technological change and analyze the impact on their employees. The disadvantage of this approach is that the findings may not hold for individuals who work in other firms. See Siegel (1994) for a study restricted to high-tech firms on Long Island. Back.

Note 12: Another approach is to create a composite index of technological change similar to the one used by Lichtenberg and Griliches (1989). Due to the different levels of aggregation in our measures of technological change, we do not employ this method here. Back.

Note 13: Krueger (1993) used data from the October 1984 and 1989 Current Population Surveys to show that workers who use computers on their job earn 10 to 15 percent higher wages. Back.

Note 14: Berman, Bound and Griliches (1994) show that both the level and the change in the share of computer investments are good proxies for technological change in an industry. Back.

Note 15: One factor that affects the correlations is the different levels of aggregation used to construct the different measures. See Appendix B for information on the construction of the correlation table. Back.

Note 16: If the rate of technological change faced by workers in industry _i and occupation _j, T_ij, is given by T_ij=T_i+V_ij, where T_i is the industry rate of technological change, and V_ij is the difference between the industry and occupation means, then by regressing training on T_i rather than the "true" measure, T_ij, the estimated effect of technological change on training will be biased towards zero. Back.

Note 17: In order to test whether the effect of technological change varies by education or occupation group, in some of our specifications we interact the proxies for technological change with education or occupation group. Back.

Note 18: This is not a strong assumption. In practice, our results were very similar using probit, and even OLS. For more details, see Amemiya, 1981. Back.

Note 19: In Appendix C, the full specification using the R&D/sales ratio is presented. The coefficients on the non-technological change variables are very similar to those shown in Appendix C when the other proxies for technological change are used. Back.

Note 20: See Appendix C for separate coefficients on education groups. The results show a monotonic relationship between years of education and training. Back.

Note 21: For these plots, we assumed that the individual had the following characteristics: married, lives in an SMSA, works in a large firm, has 10 years of market experience, and 4 years of tenure with his employer. All other variables are the mean values, and the year is 1992. Back.

Note 22: They do, however, train more than other schooling groups, even at high rates of technological change. Back.

Note 23: If job training is more likely to be informal at higher levels of education, it could bias our results. Notice, however, that we do find a monotonic increase of training with the level of schooling. See the complete regression results in the Appendix. Back.

Note 24: When the technological change/occupation interaction terms are deleted, we find that craftsmen on average receive more training than other production workers. This result is not reported in the table. Back.

Note 25: These two findings do not hold for the Jorgenson measure. Back.

Note 26: A more accurate distinction would be based on tenure in job assignment, which we do not observe. Back.

Note 27: This distinction is not obvious and could be a major source of error. We thank Lisa Lynch for pointing it to us. Back.