The Cobweb Model Does it Apply to the

The Cobweb Model: Does it Apply to the Engineering Market? By Abigail Palmatier Cobweb Supply Table 3 a: Regression Estimates of Cobweb Supply Equations, 1948 -1972 Equation: ENT = GRAD RD DUR ASAL ENT 1 R-Squared =. 96 Coefficient Standard Error T-Statistic S. E. E. =. 05 Constant 18. 9 D. W. = 2. 09 GRAD -0. 41 0. 07 -5. 857142857 RD 0. 47 0. 11 4. 27273 DUR 0. 38 0. 13 2. 923076923 ASAL -1. 15 0. 49 -2. 346938776 ENT 1 0. 62 0. 09 6. 88889 Equation: Ent = GRAD RD DUR ASAL ENT 1 ENT 2 R-Squared =. 97 Coefficient Standard Error T-Statistic S. E. E. =. 50 Constant 18 D. W. =2. 21 GRAD -0. 34 0. 09 -3. 77778 RD 0. 47 0. 11 4. 27273 DUR 0. 35 0. 14 2. 5 ASAL -1. 87 0. 49 -3. 816326531 ENT 1 0. 77 0. 17 4. 529411765 ENT 2 -0. 17 0. 16 -1. 0625 Richard B. Freeman Equation: Ent = GRAD RD DUR ASAL ENT 1 ENT 2 R-Squared =. 7818 Coefficient Standard Error T-Statistic S. E. E. =. 004631382 Constant 2. 383079 1. 094019 2. 18 D. W. =1. 258304 GRAD 0. 3270326 0. 2147387 1. 52 RD 0. 9920839 0. 2656157 3. 74 DUR -0. 0658375 0. 1661319 -0. 4 ASAL -1. 515086 0. 5333412 -2. 84 ENT 1 -0. 1934356 0. 4246539 -0. 46 ENT 2 0. 2827926 0. 38745 0. 73 Equation: ENT = GRAD RD DUR ASAL ENT 1 ENT 2 SAL R-Squared =. 87 Equation: ENT = GRAD RD DUR ASAL ENT 1 ENT 2 SAL R-Squared =. 7834 Coefficient Standard Error T-Statistic S. E. E. =. 049 Coefficient Standard Error T-Statistic S. E. E. =. 004596749 Constant 18. 2 D. W. =2. 16 Constant 2. 436004 1. 143637 2. 13 D. W. =1. 290485 GRAD -0. 3 0. 09 -3. 33333 GRAD 0. 3492233 0. 233058 1. 5 RD 0. 35 0. 13 2. 692307692 RD 0. 8564673 0. 5130164 1. 67 DUR 0. 3 0. 14 2. 142857143 DUR 0. 0005377 0. 2729122 0 ASAL -2. 32 0. 59 -3. 93220339 ASAL -1. 691376 0. 7882521 -2. 15 ENT 1 0. 67 0. 18 3. 72222 ENT 1 -0. 1575744 0. 4537403 -0. 035 ENT 2 -0. 17 0. 15 -1. 13333 ENT 2 0. 29321 0. 4019503 0. 73 SAL 0. 89 0. 67 1. 328358209 Table 3 c: Regression Estimates of Cobweb Supply Equations, 1948 -1972 SAL 0. 3069077 0. 9806506 0. 31 Source Model Residual Total SS df MS 0. 0207467 0. 0004745 0. 0212212 6 14 20 ENT Coef. Std. Err. GRAD -0. 198045 RD 0. 6874522 ASAL -0. 338111 SAL -0. 855421 ENTRATIO 1 0. 1474876 ENGENROL 1. 169621 _cons -0. 779313 Durbin-Watson d-statistic( 7, 21) = 2. 086331 Source Model Residual Total SS t df Number of obs F( 6, 14) Prob > F R-squared Adj R-squared Root MSE 0. 003457785 0. 000033892 0. 00106106 P>t 0. 070983 0. 101193 0. 216471 0. 228723 0. 201337 0. 106015 0. 426326 -2. 79 6. 79 -1. 56 -3. 74 0. 73 11. 03 -1. 83 4 16 20 ENT Coef. Std. Err. RD 0. 7580844 ASAL -0. 456542 SAL -0. 821666 ENGENROL 0. 9925083 _cons -0. 89559 Durbin-Watson d-statistic( 5, 21) = 1. 636561 0. 014 0 0. 141 0. 002 0. 476 0 0. 089 P>t 0. 098131 0. 232843 0. 201014 0. 098755 0. 497067 Interval] -0. 3502882 0. 4704145 -0. 8023951 -1. 345982 -0. 2843366 0. 9422421 -1. 69369 -0. 0458025 0. 9044899 0. 126174 -0. 3648598 0. 5793119 1. 397 0. 1350643 Number of obs F( 4, 16) Prob > F R-squared Adj R-squared Root MSE 0. 005119259 0. 00004651 0. 00106106 t 21 102. 02 0 0. 9776 0. 9681 0. 00582 [95% Conf. MS 0. 020477 0. 0007442 0. 0212212 • Wrote “A Cobweb Model of the Supply and Starting Salary of New Engineers” • Analyzed the engineering market during the 1940’s to 1970’s • Used a recursive cobweb model • Found that cobweb model could explain the supply of new engineers Table 3 B: Regression Estimates of Cobweb Supply Equations, 1989 -2007 Equation: ENT = GRAD RD DUR ASAL ENT 1 R-Squared =. 7735 Coefficient Standard Error T-Statistic S. E. E. =. 004507615 Constant 2. 861246 0. 86242 3. 32 D. W. = 1. 194158 GRAD 0. 2339415 0. 1700466 1. 38 RD 1. 076345 0. 2354601 4. 57 DUR -0. 0194034 0. 1510589 -0. 013 ASAL -1. 722885 0. 4439157 -3. 88 ENT 1 0. 0308125 0. 2885448 0. 11 7. 73 -1. 96 -4. 09 10. 05 -1. 8 21 110. 07 0 0. 9649 0. 9562 0. 00682 [95% Conf. 0 0. 068 0. 001 0 0. 09 The Model 0. 9661136 0. 0370632 -0. 3955348 1. 201859 0. 1581456 Cobweb Supply • • • • • 0, 27 • 0, 25 0, 24 0, 23 19 79 19 80 19 81 19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 Ratio of Freshman Studnets Freshmen Ratio 0, 26 Engineer Enrollment 550 000 500 000 450 000 Freshmen Enrollment 400 000 Total Enrollment Used data from years 1983 -2007 Federal Reserve Bank of St. Louis Bureau of Labor Statistics Current Population Survey U. S. Research and Development Expenditures Science and Engineering Indicators Freemans models don’t apply well to the engineering labor market during the years 1989 to 2007 The equation for the Supply of First-Year Engineering Enrollments doesn’t do a good job at explaining enrollment behavior from 1989 to 2007 (Table 1) The equation for the salary determination still held, though not in the same way (Table 2) • Sign of some variables opposite of what Freeman found The equation for the cobweb supply did not apply well for the period from 1989 to 2007 (Table 3) • Many variables were statistically insignificant Main Points that held: • Salary for engineers can still be explained through the variables research and development, durable goods output, and the number of graduates the year prior • Research and Development is still an important explanatory variable for both salaries and enrollment in engineering • Every regression ran found that research and development was statistically significant and positive Year Table 1 B: Regression Coefficients of the Supply of First-Year Engineering Enrollments 1989 -2007 T-critical Value: 1. 645 Equation: ENT = SAL ASAL R-Squared=. 84 Constant SAL ASAL Coefficient Standard Error T-Statistic S. E. E. =. 097 20. 46 D. W. =. 87 4. 78 0. 61 7. 836065574 -4. 55 0. 71 -6. 408450704 Equation: ENT=SAL ASAL ENT 1 Constant SAL Coefficient -3. 24 0. 43 0. 23 -14. 08695652 0. 17 2. 529411765 T-Statistic 4. 320127 0. 201591 SAL 1. 159369 0. 5777516 2. 01 -1. 029643 0. 6361716 -1. 62 ASAL Coefficient R-Squared=. 5429 Standard Error T-Statistic Constant 4. 458624 0. 2019269 SAL 1. 369829 0. 5510196 2. 49 ASAL -1. 311911 0. 6126206 -2. 14 ENT 1 0. 6281729 0. 3301671 1. 9 Standard Error S. E. E. =. 009700057 22. 08 D. W=. 4464336 Equation: ENT = SAL ASAL ENT 1 ENT 2 Coefficient S. E. E. =. 011765514 21. 43 D. W. =. 6327376 Equation: ENT=SAL ASAL ENT 1 R-Squared =. 93 Coefficient Standard Error T-Statistic S. E. E. =. 066 11. 1 D. W. =2. 10 2. 36 0. 67 3. 52238806 Standard Error Constant R-Squared=. 88 Coefficient Standard Error T-Statistic S. E. E. =. 087 14. 11 D. W=. 90 3. 21 0. 84 3. 821428571 R-Squared=. 4456 R-Squared =. 5610 T-Statistic Constant 4. 493915 0. 2085805 1. 350289 0. 5571728 2. 42 S. E. E. =. 009317045 21. 55 D. W. =. 4778078 ASAL ENT 1 -2. 2 0. 95 0. 68 -3. 235294118 0. 18 5. 277777778 SAL ASAL -1. 303287 0. 6189736 -2. 11 ENT 2 -0. 56 0. 17 -3. 294117647 ENT 1 0. 2907618 0. 5332327 0. 55 ENT 2 0. 2954897 0. 3643471 0. 81 Table 1 c: Regression Coefficients of the Supply of First-Year Engineering Enrollments T-critical Value: 1. 645 Source Model Residual Total SS df 0. 010629 0. 0105922 0. 0212212 MS 3 17 20 Source Model Residual Total SS df 0. 0108004 0. 0104208 0. 0212212 Number of obs = F( 3, 17) = Prob > F = R-squared = Adj R-squared = Root MSE = 0. 003543004 0. 00062307 0. 00106106 ENT Coef. Std. Err. t SAL 1. 722754 0. 697664 ASAL -1. 65254 0. 769301 ENTRATIO 1 0. 9418942 0. 686373 _cons 4. 331295 0. 196989 Durbin-Watson d-statistic( 4, 21) =. 5688132 P>t 2. 47 -2. 15 1. 37 21. 99 4 16 20 Interval] 0. 024 0. 046 0. 188 0 0. 2508127 -3. 275625 -0. 5062255 3. 915685 P>t 21 4. 15 0. 0171 0. 5089 0. 3862 0. 02552 [95% Conf. Interval] 0. 025 0. 047 0. 59 0. 615 0 0. 24845 -3. 394163 -1. 601792 -1. 01261 3. 897047 Salary Determinants Table 2 a: Regression Estimates of Salary Determination Equations 1948 -1972 Equation: SAL = RD DUR GRAD 1 R-Squared =. 99 Coefficient Standard Error T-Statistic S. E. E. =. 021 Constant 4. 14 RD 0. 26 0. 02 13 DUR 0. 14 0. 03 4. 66667 -0. 09 0. 02 -4. 5 GRAD 1 D. W. =1. 74 Table 2 B: Regression Estimates of Salary Determination Equations 1989 -2007 Equation: SAL = RD DUR GRAD 1 Coefficient Constant RD DUR R-Squared =. 9958 Standard Error 3. 194695 -0. 0294563 2. 390014 4. 746905 Number of obs F( 4, 16) Prob > F R-squared Adj R-squared Root MSE 0. 0027001 0. 0006513 0. 00106106 2. 46 -2. 15 0. 51 21. 43 21 5. 69 0. 0069 0. 5009 0. 4128 0. 02496 [95% Conf. MS ENT Coef. Std. Err. t SAL 1. 777231 0. 721156 ASAL -1. 709973 0. 794465 ENTRATIO 1 0. 561754 1. 020586 ENTRATIO 2 0. 3232566 0. 630154 _cons 4. 324834 0. 201795 Durbin-Watson d-statistic( 5, 21) =. 6376554 GRAD 1 350 000 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Engineering Students Enrolled Year All variables are in log form (#) indicates the year lag ENT=first year enrollment SAL=engineering salary ASAL=alternative salary GRAD=number of engineering graduates RD=research and development spending DUR=durable goods output Conclusion • 0, 28 Supply of New Entrants ENT = a 1 SAL* (0) – a 2 ASAL* (0) +u 1 Supply of Graduates GRAD = b 1 ENT (4) -b 3 [ASAL(3) + ASAL(2)] +U 2 Salary Determination SAL = c 1 RD + c 2 DUR - c 3 GRAD + U 3 Salary Expectations • (a) SAL* = SAL; ASAL* ASAL My Data • 0, 29 Table 1 a: Regression Coefficients of the Supply of First-Year Engineering Enrollments 1948 -1972 T-critical Value: 1. 645 Equation: ENT = SAL ASAL ENT 1 ENT 2 Interval] 0. 5500552 -0. 9501465 -1. 247798 0. 7831572 -1. 949325 Supply of First Year Students T-Statistic S. E. E. =. 000624437 -0. 1297641 0. 1306148 -0. 99 D. W. =3. 086887 0. 6356175 0. 0398051 15. 97 -0. 1381629 0. 0479292 -2. 88 0. 8201495 0. 1666946 4. 92 3. 306013 -0. 0257837 2. 7253 1. 659124 4. 752621