1. The Cobweb Model: Does it Apply to the Engineering Market? By Abigail Palmatier Richard B. Freeman 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 Supply of First Year Students My Data 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 Salary Determinants The Model Supply of New Entrants ENT = a1 SAL* (0) – a2ASAL* (0) +u1 Supply of Graduates GRAD = b1 ENT (4) -b3 [ASAL(3) + ASAL(2)] +U2 Salary Determination SAL = c1 RD + c2 DUR - c3 GRAD + U3 Salary Expectations (a) SAL* = SAL; ASAL* ASAL 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 Table 1a: Regression Coefficients of the Supply of First-Year Engineering Enrollments 1948-1972 T-critical Value: 1.645 Equation: ENT = SAL ASAL R-Squared=.84 CoefficientStandard ErrorT-StatisticS.E.E. =.097 Constant20.46 D.W. =.87 SAL4.780.617.836065574 ASAL-4.550.71-6.408450704 Equation: ENT=SAL ASAL ENT1 R-Squared=.88 CoefficientStandard ErrorT-StatisticS.E.E.=.087 Constant14.11 D.W=.90 SAL3.210.843.821428571 ASAL-3.240.23-14.08695652 ENT10.430.172.529411765 Equation: ENT = SAL ASAL ENT1 ENT2 R-Squared =.93 CoefficientStandard ErrorT-StatisticS.E.E.=.066 Constant11.1 D.W.=2.10 SAL2.360.673.52238806 ASAL-2.20.68-3.235294118 ENT10.950.185.277777778 ENT2-0.560.17-3.294117647 Table 1B: Regression Coefficients of the Supply of First-Year Engineering Enrollments 1989-2007 T-critical Value: 1.645 Equation: ENT = SAL ASALR-Squared=.4456 CoefficientStandard ErrorT-StatisticS.E.E. =.011765514 Constant4.3201270.20159121.43D.W. =.6327376 SAL1.1593690.57775162.01 ASAL-1.0296430.6361716-1.62 Equation: ENT=SAL ASAL ENT1R-Squared=.5429 CoefficientStandard ErrorT-StatisticS.E.E.=.009700057 Constant4.4586240.201926922.08D.W=.4464336 SAL1.3698290.55101962.49 ASAL-1.3119110.6126206-2.14 ENT10.62817290.33016711.9 Equation: ENT = SAL ASAL ENT1 ENT2R-Squared =.5610 CoefficientStandard ErrorT-StatisticS.E.E.=.009317045 Constant4.4939150.208580521.55D.W.=.4778078 SAL1.3502890.55717282.42 ASAL-1.3032870.6189736-2.11 ENT10.29076180.53323270.55 ENT20.29548970.36434710.81 Table 1c: Regression Coefficients of the Supply of First-Year Engineering Enrollments T-critical Value: 1.645 SourceSSdfMS Number of obs =21 Model0.01062930.003543004 F( 3, 17) =5.69 Residual0.0105922170.00062307 Prob > F =0.0069 Total0.0212212200.00106106 R-squared =0.5009 Adj R-squared =0.4128 Root MSE =0.02496 ENTCoef.Std. Err.tP>t[95% Conf.Interval] SAL1.7227540.6976642.470.0240.25081273.194695 ASAL-1.652540.769301-2.150.046-3.275625-0.0294563 ENTRATIO10.94189420.6863731.370.188-0.50622552.390014 _cons4.3312950.19698921.9903.9156854.746905 Durbin-Watson d-statistic( 4, 21) =.5688132 SourceSSdfMS Number of obs21 Model0.010800440.0027001 F( 4, 16)4.15 Residual0.0104208160.0006513 Prob > F0.0171 Total0.0212212200.00106106 R-squared0.5089 Adj R-squared0.3862 Root MSE0.02552 ENTCoef.Std. Err.tP>t[95% Conf.Interval] SAL1.7772310.7211562.460.0250.248453.306013 ASAL-1.7099730.794465-2.150.047-3.394163-0.0257837 ENTRATIO10.5617541.0205860.550.59-1.6017922.7253 ENTRATIO20.32325660.6301540.510.615-1.012611.659124 _cons4.3248340.20179521.4303.8970474.752621 Durbin-Watson d-statistic( 5, 21) =.6376554 Table 2a: Regression Estimates of Salary Determination Equations 1948-1972 Equation: SAL = RD DUR GRAD1 R-Squared =.99 CoefficientStandard ErrorT-StatisticS.E.E. =.021 Constant4.14 D.W.=1.74 RD0.260.0213 DUR0.140.034.666666667 GRAD1-0.090.02-4.5 Table 2B: Regression Estimates of Salary Determination Equations 1989-2007 Equation: SAL = RD DUR GRAD1R-Squared =.9958 CoefficientStandard ErrorT-StatisticS.E.E. =.000624437 Constant-0.12976410.1306148-0.99D.W.=3.086887 RD0.63561750.039805115.97 DUR-0.13816290.0479292-2.88 GRAD10.82014950.16669464.92 Cobweb Supply Table 3a: Regression Estimates of Cobweb Supply Equations, 1948-1972 Equation: ENT = GRAD RD DUR ASAL ENT1R-Squared =.96 CoefficientStandard ErrorT-StatisticS.E.E. =.05 Constant18.9 D.W.= 2.09 GRAD-0.410.07-5.857142857 RD0.470.114.272727273 DUR0.380.132.923076923 ASAL-1.150.49-2.346938776 ENT10.620.096.888888889 Equation: Ent = GRAD RD DUR ASAL ENT1 ENT2R-Squared =.97 CoefficientStandard ErrorT-StatisticS.E.E. =.50 Constant18 D.W.=2.21 GRAD-0.340.09-3.777777778 RD0.470.114.272727273 DUR0.350.142.5 ASAL-1.870.49-3.816326531 ENT10.770.174.529411765 ENT2-0.170.16-1.0625 Equation: ENT = GRAD RD DUR ASAL ENT1 ENT2 SALR-Squared =.87 CoefficientStandard ErrorT-StatisticS.E.E.=.049 Constant18.2 D.W.=2.16 GRAD-0.30.09-3.333333333 RD0.350.132.692307692 DUR0.30.142.142857143 ASAL-2.320.59-3.93220339 ENT10.670.183.722222222 ENT2-0.170.15-1.133333333 SAL0.890.671.328358209 Table 3B: Regression Estimates of Cobweb Supply Equations, 1989-2007 Equation: ENT = GRAD RD DUR ASAL ENT1R-Squared =.7735 CoefficientStandard ErrorT-StatisticS.E.E. =.004507615 Constant2.8612460.862423.32D.W.= 1.194158 GRAD0.23394150.17004661.38 RD1.0763450.23546014.57 DUR-0.01940340.1510589-0.013 ASAL-1.7228850.4439157-3.88 ENT10.03081250.28854480.11 Equation: Ent = GRAD RD DUR ASAL ENT1 ENT2R-Squared =.7818 CoefficientStandard ErrorT-StatisticS.E.E. =.004631382 Constant2.3830791.0940192.18D.W.=1.258304 GRAD0.32703260.21473871.52 RD0.99208390.26561573.74 DUR-0.06583750.1661319-0.4 ASAL-1.5150860.5333412-2.84 ENT1-0.19343560.4246539-0.46 ENT20.28279260.387450.73 Equation: ENT = GRAD RD DUR ASAL ENT1 ENT2 SALR-Squared =.7834 CoefficientStandard ErrorT-StatisticS.E.E.=.004596749 Constant2.4360041.1436372.13D.W.=1.290485 GRAD0.34922330.2330581.5 RD0.85646730.51301641.67 DUR0.00053770.27291220 ASAL-1.6913760.7882521-2.15 ENT1-0.15757440.4537403-0.035 ENT20.293210.40195030.73 SAL0.30690770.98065060.31 Table3c: Regression Estimates of Cobweb Supply Equations, 1948-1972 SourceSSdfMS Number of obs21 Model0.020746760.003457785 F( 6, 14)102.02 Residual0.0004745140.000033892 Prob > F0 Total0.0212212200.00106106 R-squared0.9776 Adj R-squared0.9681 Root MSE0.00582 ENTCoef.Std. Err.tP>t[95% Conf.Interval] GRAD-0.1980450.070983-2.790.014-0.3502882-0.0458025 RD0.68745220.1011936.7900.47041450.9044899 ASAL-0.3381110.216471-1.560.141-0.80239510.126174 SAL-0.8554210.228723-3.740.002-1.345982-0.3648598 ENTRATIO10.14748760.2013370.730.476-0.28433660.5793119 ENGENROL1.1696210.10601511.0300.94224211.397 _cons-0.7793130.426326-1.830.089-1.693690.1350643 Durbin-Watson d-statistic( 7, 21) = 2.086331 SourceSSdfMS Number of obs21 Model0.02047740.005119259 F( 4, 16)110.07 Residual0.0007442160.00004651 Prob > F0 Total0.0212212200.00106106 R-squared0.9649 Adj R-squared0.9562 Root MSE0.00682 ENTCoef.Std. Err.tP>t[95% Conf.Interval] RD0.75808440.0981317.7300.55005520.9661136 ASAL-0.4565420.232843-1.960.068-0.95014650.0370632 SAL-0.8216660.201014-4.090.001-1.247798-0.3955348 ENGENROL0.99250830.09875510.0500.78315721.201859 _cons-0.895590.497067-1.80.09-1.9493250.1581456 Durbin-Watson d-statistic( 5, 21) = 1.636561 Conclusion 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 Cobweb Supply