Trends in earned degrees in business and economics & US productivity growth: is there a feedback link?

ABSTRACT

This paper presents a simple model of education and growth to establish the link between human capital accumulation and productivity growth. To examine the dynamic relationship empirically, I used the unrestricted VAR approach to forecast systems of interrelated time series data. Based on the results of the two related feedback measures, shocks to undergraduate and advanced degrees awarded in both business and economics to working age population ratio could be a good predictor of productivity growth. These feedback effects to productivity growth are mainly concentrated in the medium-run (4-12 years) to long-run (over 12 years) for bachelor degrees in Business and Economics. The results also suggest a bi-directional feedback relationship between productivity growth and the ratio of earned bachelor degree in Business to working age population. For advanced degrees in Economics, the feedback effect to productivity growth is reflected as early as in the short-run (2-3 years) and remains strong across frequencies. In contrast, advanced degrees in Business exhibit strong feedback relationship to productivity growth in the long-run to permanent effect.

Keywords: Productivity, Earned degrees in economics & business, Feedback Link

1. INTRODUCTION

Undergraduate economics degree awarded in the United States (US) exhibited a decreasing trend during the early 1970s and 1990s. Siegfried (1998, 1999, 2003) however cautioned against alarm about this decline due to its subsequent mean-reversion phenomenon. In contrast, Becker (1997) postulated that the decline in the number of economics majors maybe attributed to the traditional "chalk and talk" pedagogy used by most academicians in economics. Consequently, economics tend to lose ground against other disciplines such as general Business, Business management and the like which, have already embraced more diversified teaching methods.

From a macro perspective, a more interesting question can be asked as to what are the implications of these trends in degrees awarded in Business and Economics to US productivity growth and vice versa. Undoubtedly, the type of activities or occupation university degree holders eventually end up doing can have significant effects on the country's economic welfare. Similarly, changes in the economy can have significant effects on one's decision as to what degree and the extent of academic training to pursue.

To help answer this question, this paper examines the dynamic relationship between productivity growth in the US and the ratio of earned undergraduate and advanced degrees in Economics and Business to working age population. A simple model of education and growth similar to Mankiw, Romer & Weil (1992) [MRW] is presented to establish the link between the role of human capital accumulation and productivity growth. Unlike in the MRW paper which uses cross-country data to estimate the relationship empirically, this paper presents a time series evidence on the timing and degree of feedback relationship between US productivity growth and the ratio of earned degrees in Business and Economics to working age population. The empirical investigation uses two feedback methods to measure the degree of dependence between data series and a related measure to distinguish between short-run and long-run effects of a given innovation or shock.

2. OVERVIEW OF ECONOMICS AND BUSINESS DEGREES AWARDED IN THE US, 1970-2000

As summarized in Table 1, the number of advanced degrees (MA and PhD) awarded in Economics posted negative average growth while the undergraduate degree showed a meager 0.50% average increase during the 1970s. In contrast, both undergraduate and advanced degrees in Business posted positive average growth with the biggest growth in the Masters level.

The 1980s showed a substantial turnaround in Economics with MA and Doctoral degrees posting an average increase of 0.28% and 1.28% respectively. The number of undergraduate Economics degree awarded continues to exhibit a positive average growth during the 1980s until a major contraction in the 1990s. In contrast, earned MA and PhD degrees continue to exhibit strong growth in the 1990s, which can be attributed to the earlier decades of growth in the undergraduate economics major.

In terms of business degrees, the trend continue to show positive, but smaller average growth during the 1980s than the previous decade, except for the PhD degree where the average growth almost doubled. Similar to economics, the 1990s exhibited a significant contraction in average growth in bachelor and PhD degrees awarded in Business.

3. A SIMPLE MODEL OF EDUCATION AND GROWTH

Many theories are put forth to explain US productivity. Explanations range from the role of physical capital investment (Caballe and Santos, 1993), human capital accumulation (Mincer, 1984; Glaeser, 1994) and improvement in technology (Jorgenson and Stiroh, 1999; Oliner and Sichel, 1994, 2000). This paper looks at the role of human capital accumulation due to schooling.

Consider a Cobb Douglas production function,

[Y.sub.t] = [K.sub.t.sup.[alpha]] [([H.sub.t]/[A.sub.t] [L.sub.t]).sup.[beta]][([A.sub.t][L.sub.t]).sup.1-[alpha]]

where [alpha]+[beta]<1, [K.sub.t] is the physical capital, [H.sub.t] is the human capital and, [A.sub.t][L.sub.t] is the effective labor. Human capital consists of abilities, skills and knowledge embodied in an individual. Therefore, like economic goods, human capital is rival and excludable. This view does not take into account the human capital externality recognized by Lucas (1988). Hence, I assume competitive markets, closed economy and no externalities.

To account for the different types of academic talent that are accumulated in the educational sector, one may suppose that

dH/dt = [S.sub.H] [K.sub.t,EDUC.sup.[alpha]] [([H.sub.t,EDUC]/[A.sub.t] [L.sub.t,EDUC]).sup.[beta]][([A.sub.t] [L.sub.t,EDUC).sup.1-[alpha]]

where [K.sub.t,EDUC], [H.sub.t,EDUC], [A.sub.t] [L.sub.t,EDUC] denote the quantities of physical capital, human capital and effective labor devoted to education respectively. Also, let [K.sub.t,EDUC] = [K.sub.undergrad] + [K.sub.grad] where, the quantity of physical capital devoted to education can be used to either support undergraduate or graduate degrees. The same reasoning applies to quantities of human capital and labor. The variable of interest in this paper is [S.sub.H] or the fraction of resources devoted to human capital accumulation as proxied by the ratio of undergraduate and advanced degrees in Business and Economics to working age population. In MRW paper, [S.sub.H] is proxied by the average fraction of working age population in secondary school.

The accumulation of physical capital is broadly assumed to be similar to the accumulation of human capital, i.e.,

dK/dt = [S.sub.K] [K.sub.t.SUP.[alpha]] [([H.sub.t]/[A.sub.t] [L.sub.t]).sup.[beta]][([A.sub.t] [L.sub.t]).sup.1-[alpha]]

where [S.sub.K] pertains to the fraction of resources devoted to physical capital accumulation. Note that I assume no depreciation for either capital for simplicity. Appendix A presents the detailed derivation of this model.

Solving the model yields the final reduced equation expressed as follows,

In [y.sup.*] = [[alpha]/l-[alpha]-[beta]] ln [S.sub.K] + [[beta]/1-[alpha]-[beta]] In [S.sub.H] - [[alpha]+[beta]]/1-[alpha]-[beta]] In (n+g).

This equation suggests that the long-run output growth ([y.sup.*]) is a function of the exogenous effect of population (n) and technological (g) growth as well as resources devoted to human ([S.sub.H]) and physical capital ([S.sub.K]) accumulation. In most cases, we take these variables as exogenous driving force of output growth. However, one cannot dismiss the possibility that changes in output growth may also determine or cause changes in the fraction of resources devoted to human capital accumulation. Hence, to explore this dynamic feedback relationship, this study uses two related measures of linear dependence to account for the endogeneity of variables.

4. DATA DESCRIPTION AND METHODOLOGY

Data on Economics and Business degrees awarded cover the period of 1969-2000 and were taken from the latest issue of Digest of Education Statistics (2003), US Dept. of Education. Productivity is the amount of output produced per hour worked in the non-farm business sector. Data on productivity and working age population were taken from the Bureau of Labor Statistics, US Dept. of Labor. Data on real private gross fixed investment were taken from the Bureau of Economic Analysis, US Dept. of Commerce.

Methodology:

Given that a number of models are consistent with observed correlation between human capital and productivity growth, I used the unrestricted vector autoregression (VAR) approach to model the dynamic relationship among pertinent variables in order to minimize specification error. The VAR approach avoids the need for tight structural modeling by treating variables in a system as a function of lagged values of all endogenous variables in the system. The VAR model uses only past regularities and historical patterns in the data as a basis for forecasting. In this study, a three-variable autoregression system is used. These variables include productivity growth as measured by taking the log difference of productivity data series, log transformed real private gross fixed investment as a fraction of real GDP and, the log transformed ratio of undergraduate and advanced degrees in Business and Economics to working age population. A lag length of four years is used for all variables as suggested by the likelihood ratio test done.

Details of the two related measures of linear dependence and feedback used in this study can be found in Appendix B. To measure the extent of feedback between productivity growth and the ratio of Economics and Business degrees to working age population, I used Geweke's (1982) bi-variate feedback method. The feedback measures are non-negative and zero only when feedback or causality of the relevant type is not present. A simple transformation of each feedback measure gives the reduction in the prediction error variance.

Building on Geweke's feedback measure, McGarvey(1985) developed a useful alternative summary measure by decomposing the feedback by frequency in order to distinguish between short-run and long-run effects of a given innovation or shock.

5. EMPIRICAL RESULTS

The results using Geweke's linear feedback measure are summarized in Table 2.

The results suggest that the magnitude of feedback to productivity growth given shocks from earned advanced degrees in Economics (PhD) and in Business (MA) to working age population ratio to be bigger than the reverse feedback from shocks in growth to degrees earned. In particular, about 13% and 28% of the variance in productivity are explained by shocks in the ratio of PhD in Economics and MA in Business degrees to working age population, respectively. Conversely, only 0.33% and 1.30% of the variance in PhD in Economics and MA in Business degrees respectively can be explained by shocks in growth. This finding may suggest uni-directional feedback effect to productivity growth due to shocks in the ratio of advanced degrees in business and economics to working age population.

In terms of the undergraduate degree in Economics, the results suggest that there exist a bi-directional feedback between productivity growth and the bachelor degree to working age population ratio. The proportion of variance explained by either shocks, i.e., in the degree or productivity growth are comparable (i.e. about 10%). Also, the total feedback figure suggests that the two data series are not linearly independent given that about 23% of the variance in each series is associated with movements in the other but only about 5% of this total feedback is due to their contemporaneous feedback.

In terms of advanced (PhD) degrees in Business and Economics, the results suggest that shocks in productivity growth explain about 34% of the variance in Business PhD degree compared to only a meager 0.3% of the variance in Economics PhD degree. This finding may suggest the greater sensitivity of obtaining advanced academic training in Business than in Economics to changes or shocks in productivity growth.

In order to have a better idea of short-run versus long-run effects to productivity growth given shocks in the undergraduate and advanced degrees in Business and Economics to working age population ratio, I decomposed the feedback measure by frequency using McGarvey's (1985) methodology. I used this method on an expanded three-variable system and specified the ordering of 'growth prior to degree prior to investment' in the Choleski decomposition. This ordering constrains the system such that a shock in growth has contemporaneous effect on degree and investment while the contemporaneous value of degree does not have a contemporaneous effect on growth. Also, the contemporaneous value of investment does not have a contemporaneous effect on degree and growth. Given the dynamics of these variables, this system identification restriction is deemed reasonable. Table 3 summarizes the feedback results from earned degrees in Business and Economics to productivity growth by frequency.

In terms of degrees in Economics, the results suggest bigger overall effect on US productivity growth given shocks to the proportion of the working age population with PhD degrees compared to those with only Bachelors and MA degrees. This finding confirms the previous result found in the bi-variate feedback method. Moreover, these feedback effects to productivity growth are concentrated mainly in the medium-run (4-12 years) to long-run (over 12 years) for bachelor degree while for PhD degree, the feedback effect is reflected even as early as in the short-run (2-3 years). Also, shocks in MA degree in economics suggest a substantial long-run to permanent effect on productivity growth. Perhaps, these results can be taken as a compelling reason to promote advance training in economics education given its substantial and significant effect on the productivity of the economy.

In terms of degrees in Business, the results suggest that overall, a bigger proportion of the variance in productivity growth is explained by shocks in the fraction of working age population with bachelor and MA degrees than shocks from the highest terminal degree or PhD in business. These feedback effects to productivity growth are concentrated mainly in the medium-run to long-run for shocks in bachelor degree. Conversely, advanced degrees in business exhibit long-run to permanent effect in explaining the variance in productivity growth.

Shocks or innovations in the undergraduate degree for both Business and Economics show comparable overall effect on productivity growth. These results should perhaps send a message to educators not to undermine the importance of the undergraduate training they provide in Business and Economics programs given their significant impact on the country's productivity growth. However, the stark difference appear in terms of advanced degrees, i.e., innovations in PhD Economics surpassed PhD in Business Management in terms of its overall effect on productivity growth while shocks in MA degrees in Business exhibited bigger overall effect on productivity growth than shocks in MA degrees in Economics. These results perhaps suggest a diminishing return-like impact of advanced degrees in Business on productivity growth as compared to a sustained impact of advanced training in Economics. A plausible explanation to this finding is that most advanced degree holders in Economics usually find their contribution to the economy by taking teaching or research positions in the academia or serve as policy makers in the government, if not consultants in the private sector. Conversely, Business degree holders usually need no further academic training to run a business, become managers or entrepreneurs.

6. CONCLUDING REMARKS, LIMITATIONS OF THE STUDY AND SUGGESTIONS FOR FUTURE RESEARCH

This paper presents a simple model of education and growth to establish the link between human capital accumulation and productivity growth. To examine the dynamic relationship empirically, I used the unrestricted VAR approach to forecast systems of interrelated time series data. Based on the results of the two related measures of feedback, shocks to earned undergraduate and advanced degrees in both business and economics to working age population ratio could be a good predictor of productivity growth. These feedback effects to productivity growth are mainly concentrated in the medium-run (4-12 years) to long-run (over 12 years) for bachelor degrees in Business and Economics. The results also suggest a bi-directional feedback relationship between productivity growth and the ratio of earned bachelor degree in Business to working age population. For advanced degrees in Economics, the feedback effect to productivity growth is reflected as early as in the short-run (2-3 years) and remains strong across frequencies. In contrast, advanced degrees in Business exhibit strong feedback relationship to productivity growth in the long-run to permanent effect.

It is crucial to note that like most forecasts, the results presented in this study are only suggestive. Nonetheless, it provided us with insights as to the magnitude, timing and, direction of feedback relationship between productivity growth and earned degrees in Business and Economics to working age population ratio. Moreover, data on degrees awarded as tabulated by the U.S. Department of Education, National Center for Education Statistics were taken from several survey instruments such as the Higher Education General Information Survey (HEGIS), Degrees and Other Formal Awards Conferred surveys, and Integrated Postsecondary Education Data System (IPEDS) and "Completions" surveys. Hence, the data used may suffer from sampling and non-sampling error inherent in most surveys. Given the limitation of the data such as no distinction made between domestic and international students/graduates, the results of the study cannot account for cases where some of the graduates may end up not working in the US but rather work in their country of origin. Also, this study does not account as to how much of the variation in US productivity is attributable to business and economics education relative to other education in other disciplines (e.g. engineering, computer science, chemistry, etc.) For future study, it would perhaps be more instructive to use longitudinal data or disaggregated data in a given industry or different occupation categories, in order to better explain the different responses of employed workers with degrees in business and economics to productivity growth changes and vice versa.

APPENDIX A: DERIVATION OF THE MODEL

To solve the model easily, let the transition equation for human capital in the educational sector to be simply,

dH/dt = [S.sub.H] [K.sub.t.sup.[alpha]] [([H.sub.t]/[A.sub.t] [L.sub.t]).sup.[beta]][([A.sub.t][L.sub.t]).sup.1- [alpha]]

Also, it is assumed that raw labor and technology grows at a constant and exogenous rate, n and g respectively. This assumption is reasonable given that the intent of the model is not to explain worldwide growth.

Alternatively, in per capita terms, define k = K/AL, h = H/AL and y = Y/AL. So, the production function is simply, [Y.sub.t] = [k.sub.t.sup.[alpha]] [h.sub.t.sup.[beta]]. Correspondingly, the transition equations become

dk/dt = [S.sub.K] [k.sub.t.sup.[alpha]] [h.sub.t.sup.[beta]] - (n + g) [k.sub.t]

dh/dt = [S.sub.H] [k.sub.t.sup.[alpha]] [h.sub.t.sup.[beta]] - (n + g) [h.sub.t]

Define [k.sup.*] and [h.sup.*] as steady-state values of per capita physical and human capital respectively and where dk/dt=dh/dt=0 at the steady-state.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Taking logs of the above equations and solving for In [k.sup.*], In [h.sup.*] and substituting the expressions derived to the linearized production function In [y.sup.*] = [alpha] In [k.sup.*] + [beta] In [h.sup.*] yields,

In [y.sup.*] = [[alpha]/1-[alpha]-[beta]] In [S.sub.K] + [[beta]/1-[alpha]-[beta]] In [S.sub.H] - [[alpha]+[beta]/1- alpha]-[beta]] In (n+g)

APPENDIX B: TWO RELATED FEEDBACK MEASURES

I. Geweke's Linear Feedback Measure:

He defined the measures of linear dependence between say X and Y wide-sense stationary series in terms of the following linear projections.

(1) [Y.sub.t] = [[summation].sup.[infinity].sub.s=1] [[alpha].sub.1s] [Y.sub.t-s] + [[summation].sup.[infinity].sub.s=1] [[alpha].sub.2s] [X.sub.t-s] + [u.sub.1t]

(2) [Y.sub.t] = [[summation].sup.[infinity]].sub.s=1] [[beta].sub.1s] [[beta].sub.1s] + [[summation].sup.[infinity].sub.s=0] [[beta].sub.2s] [X.sub.t-s] + [u.sub.2t]

(3) [Y.sub.t] = [[summation].sup.[infinity]].sub.s=1] [[gamma].sub.1s] + [Y.sub.t-s] + [u.sub.3t]

where the linear feedback measure from X to Y is defined as [F.sub.X [right arrow] Y] = log [var ([u.sub.3t])/var([u.sub.1t])] while the measure of contemporaneous feedback between X and Y is defined as [F.sub.X [??] Y] = log [var ([u.sub.1t])/var([u.sub.2t])].

So, the measure of linear dependence between X and Y or [F.sub.X,Y] is the sum of linear feedback from X to Y, [F.sub.X [right arrow] Y], linear feedback from Y to X, [F.sub.Y [right arrow] X] and instantaneous linear feedback [F.sub.X [??] Y] Y. where [F.sub.Y [right arrow] X] is found by switching X and Y in equations (1) and (3) and in the definition of directional feedback.

II. McGarvey's(1985) Decomposition of Feedback Measure by Frequency: In the context of this study, the MA representation of the 3-variable orthogonalized autoregressive system is as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where for example, [C.sub.21](L) gives the response of [Y.sub.t] to innovations in [X.sub.t] and, the overall feedback from X to Y is defined as

[F.sub.X [right arrow] Y] = log [var ([Y.sub.t]) / var([Y.sub.t]) - [[summation].sup.[infinity].sub.s=0] [C.sub.21] [(s).sup.2]var([[upsilon].sub.t])t)]

The transformation (1-exp[-[F.sub.X [right arrow] Y] Y]) gives the proportion of Y's variance explained by shocks to X. To distinguish between short-run from long-run effects, the overall feedback is decomposed frequency bands. Feedback from X to Y over the interval ([[lambda].sub.1], [[lambda].sub.2]) is defined as [f.sub.X [right arrow] Y] ([[lambda].sub.1], [[lambda].sub.2]) = log [([[integral].sub.[lambda]1].sup.[lambda]2][S.sub.Y] ([lambda])[d.sub.[lambda]])/([[integral].sub.[lambda]1].sup.[lambda]1], [S.sub.Y]([lambda]) - [C.sub.21] [([lambda]).sup.2] [[sigma].sub.[upsilon].sup.2]) d[lambda])] since var(Y)= (1/2 [pi]) [[integral].sub.[pi].sup.-[pi]] [S.sub.Y]([lambda])d[lambda] and [S.sub.Y] ([lambda])=[C.sub.21][([lambda]).sup.2][[sigma].sub.[upsilon].sup.2] + [C.sub.22][([lambda]).sup.2] [[sigma].sup.[omega].sup.2] + [C.sub.22][([lambda]).sup.2] [[sigma].sup.[eta].sup.2]. So, if [[upslilon].sub.t] contributes nothing to the variance of Y at frequency [lambda], the ratio will be one and the feedback measure will be zero. Note that a period of a cycle is defined as the ratio of 2[pi] to the frequency.

REFERENCES:

Becker, W.E., "Teaching Economics to Undergraduates", Journal of Economic Literature, vol. 35 September 1997,1347-73.

Bureau of Labor Statistics. Department of Labor.

Bureau of Economic Analysis. US Department of Commerce.

Caballe, J. and M. Santos, "On Endogenous Growth with Physical and Human Capital", Journal of Political Economy, vol 101, 1993,1042-67.

Geweke, John, "Measurement of Linear Dependence and Feedback between Multiple Time Series",. Journal of the American Statistical Association, vol 77, 1982, 304-313.

Glaeser, Edward L.,." Why Does Schooling Generate Economic Growth?", Economics Letter, vol 44, 1994, 333-37.

Hamilton, James, Time Series Analysis, Princeton University Press, 1994.

Jorgenson, D. and K. Stiroh, "Information Technology and Growth", mimeo. Dept. of Economics. Harvard University, MA., 1999.

Lucas, Robert, "On the Mechanics of Economic Development", Journal of Monetary Economics, vol 22 July, 1988, 3-42.

Mankiw, G., Romer, D. and Weil, D., "A Contribution to the Empirics of Economic Growth", Quarterly Journal of Economics, vol 107, May 1992, 407-437.

Mincer, Jacob, "Human Capital and Economic Growth", Economics of Education Review, 3:3, 1984, 195-205.

Oliner, Stephen and D. Sichel, "Computers and Output Growth Revisited: How Big is the Puzzle?", Brookings on Economic Activity, vol2, 1994,273-334.

--. "The Resurgence of Growth in the Late 1990s: Is Information Technology the Story?", Mimeo, Federal Reserve Bank, 2000, 1-48.

Siegfried, J.J., "Trends in Undergraduate Economics Degrees: A 1996-97 update", Journal of Economic Education, vol. 29 Summer, 1998, 285-88.

--, "Trends in Undergraduate Economics Degrees, 1997-98", Journal of Economic Education, Summer, 1999, 325-28.

"Trends in Undergraduate Economics Degrees, 1991 to 2003", Journal of Economic Education, vol. 35 Summer, 2003, 340

US Department of Education. Digest of Education Statistics; www.nces.ed.gov//programs/digest/d03/tables/dt296.asp

Antonina Espiritu, Hawaii Pacific University, Honolulu, Hawaii, USA

Dr. Antonina Espiritu earned her Ph.D. in Economics at the University of Nebraska-Lincoln in 1998 under the NSF Economic Education Graduate Scholarship* She is currently an Associate Professor of Economics at the Hawaii Pacific University in Honolulu, Hawaii.

TABLE 1: AVERAGE GROWTH RATE OF ECONOMICS AND BUSINESS
DEGREES AWARDED

             1970-79   1980-89   1990-2000
Economics
Bachelor     0.50      2.76      -1.71
Masters      -0.74     0.28      1.10
PhD          -1.39     1.28      0.76
Business
Bachelor     5.78      2.53      0.70
Masters      9.87      3.30      4.08
PhD          2.33      3.99      0.04

Source: Digest of Education Statistics, 2003; US Dept of
Education, NCES

TABLE 2: FEEDBACK BETWEEN PRODUCTIVITY GROWTH AND THE PROPORTION
OF WORKING AGE POPULATION WITH ECONOMICS AND BUSINESS DEGREES

            Degree                 Growth
            [right arrow] Growth   [right arrow] Degree

Economics
BA          .104                   .106
            (9.88%)                (10.02%)
MA          .036                   .241
            (3.58)                 (21.42)
PhD         .139                   .003
            (12.96)                (0.33)
Business
BA          .183                   .139
            (16.70%)               (13.02%)
MA          .333                   .013
            (28.32)                (1.30)
PhD         .118                   .409
            (11.10)                (33.55)

            Contemporaneous        Total
            Feedback               Feedback

Economics
BA          .055                   .265
            (5.34%)                (23.24%)
MA          .022                   .299
            (2.14)                 (25.86)
PhD         .019                   .162
            (1.96)                 (14.94)
Business
BA          .004                   .327
            (0.44%)                (27.86%)
MA          .013                   .359
            (1.32)                 (30.18)
PhD         .106                   .632
            (10.05)                (46.86)

Note: The proportion of variance explained by shocks to a given
data series are expressed in percentages and in parentheses.

TABLE 3: FEEDBACK FROM PROPORTION OF WORKING AGE POPULATION WITH
EARNED DEGREES TO PRODUCTIVITY GROWTH, BY FREQUENCY LEVELS

Economics
             Bachelor        MA               PhD

Permanent    .236 (21.03%)   .591 (44.60%)    0.284 (24.76%)
Long-run     .231 (20.63)    .325 (27.74)     0.232 (20.74)
Medium-run   .173 (15.89)    .111 (10.48)     0.205 (18.55)
Short-run    .070 (6.73)     .123 (11.57)     0.232 (20.69)
Overall      .125 (11.77%)   .138 (12.86%)    0.222 (19.94%)
Business

             Bachelor        MA               PhD

Permanent    .110 (10.40%)   3.092 (95.46%)   .171 (15.73%)
Long-run     .148 (13.74)    .621 (46.27)     .173 (15.87)
Medium-run   .133 (12.49)    .343 (29.05)     .016 (1.63)
Short-run    .084 (8.01)     .123 (11.62)     .098 (9.36)
Overall      .111 (10.50%)   .242 (21.46%)    .077 (7.45%)

Note: The proportion of variance in growth explained by shocks
to degrees is expressed in percentages and in parentheses.