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 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 T-critical Value: Equation: ENT = SAL ASAL R-Squared=.84 CoefficientStandard ErrorT-StatisticS.E.E. =.097 Constant20.46 D.W. =.87 SAL ASAL Equation: ENT=SAL ASAL ENT1 R-Squared=.88 CoefficientStandard ErrorT-StatisticS.E.E.=.087 Constant14.11 D.W=.90 SAL ASAL ENT Equation: ENT = SAL ASAL ENT1 ENT2 R-Squared =.93 CoefficientStandard ErrorT-StatisticS.E.E.=.066 Constant11.1 D.W.=2.10 SAL ASAL ENT ENT Table 1B: Regression Coefficients of the Supply of First-Year Engineering Enrollments T-critical Value: Equation: ENT = SAL ASALR-Squared=.4456 CoefficientStandard ErrorT-StatisticS.E.E. = Constant D.W. = SAL ASAL Equation: ENT=SAL ASAL ENT1R-Squared=.5429 CoefficientStandard ErrorT-StatisticS.E.E.= Constant D.W= SAL ASAL ENT Equation: ENT = SAL ASAL ENT1 ENT2R-Squared =.5610 CoefficientStandard ErrorT-StatisticS.E.E.= Constant D.W.= SAL ASAL ENT ENT Table 1c: Regression Coefficients of the Supply of First-Year Engineering Enrollments T-critical Value: SourceSSdfMS Number of obs =21 Model F( 3, 17) =5.69 Residual Prob > F = Total R-squared = Adj R-squared = Root MSE = ENTCoef.Std. Err.tP>t[95% Conf.Interval] SAL ASAL ENTRATIO _cons Durbin-Watson d-statistic( 4, 21) = SourceSSdfMS Number of obs21 Model F( 4, 16)4.15 Residual Prob > F Total R-squared Adj R-squared Root MSE ENTCoef.Std. Err.tP>t[95% Conf.Interval] SAL ASAL ENTRATIO ENTRATIO _cons Durbin-Watson d-statistic( 5, 21) = Table 2a: Regression Estimates of Salary Determination Equations Equation: SAL = RD DUR GRAD1 R-Squared =.99 CoefficientStandard ErrorT-StatisticS.E.E. =.021 Constant4.14 D.W.=1.74 RD DUR GRAD Table 2B: Regression Estimates of Salary Determination Equations Equation: SAL = RD DUR GRAD1R-Squared =.9958 CoefficientStandard ErrorT-StatisticS.E.E. = Constant D.W.= RD DUR GRAD Cobweb Supply Table 3a: Regression Estimates of Cobweb Supply Equations, Equation: ENT = GRAD RD DUR ASAL ENT1R-Squared =.96 CoefficientStandard ErrorT-StatisticS.E.E. =.05 Constant18.9 D.W.= 2.09 GRAD RD DUR ASAL ENT Equation: Ent = GRAD RD DUR ASAL ENT1 ENT2R-Squared =.97 CoefficientStandard ErrorT-StatisticS.E.E. =.50 Constant18 D.W.=2.21 GRAD RD DUR ASAL ENT ENT Equation: ENT = GRAD RD DUR ASAL ENT1 ENT2 SALR-Squared =.87 CoefficientStandard ErrorT-StatisticS.E.E.=.049 Constant18.2 D.W.=2.16 GRAD RD DUR ASAL ENT ENT SAL Table 3B: Regression Estimates of Cobweb Supply Equations, Equation: ENT = GRAD RD DUR ASAL ENT1R-Squared =.7735 CoefficientStandard ErrorT-StatisticS.E.E. = Constant D.W.= GRAD RD DUR ASAL ENT Equation: Ent = GRAD RD DUR ASAL ENT1 ENT2R-Squared =.7818 CoefficientStandard ErrorT-StatisticS.E.E. = Constant D.W.= GRAD RD DUR ASAL ENT ENT Equation: ENT = GRAD RD DUR ASAL ENT1 ENT2 SALR-Squared =.7834 CoefficientStandard ErrorT-StatisticS.E.E.= Constant D.W.= GRAD RD DUR ASAL ENT ENT SAL Table3c: Regression Estimates of Cobweb Supply Equations, SourceSSdfMS Number of obs21 Model F( 6, 14) Residual Prob > F0 Total R-squared Adj R-squared Root MSE ENTCoef.Std. Err.tP>t[95% Conf.Interval] GRAD RD ASAL SAL ENTRATIO ENGENROL _cons Durbin-Watson d-statistic( 7, 21) = SourceSSdfMS Number of obs21 Model F( 4, 16) Residual Prob > F0 Total R-squared Adj R-squared Root MSE ENTCoef.Std. Err.tP>t[95% Conf.Interval] RD ASAL SAL ENGENROL _cons Durbin-Watson d-statistic( 5, 21) = 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