arec econ 535 problem set 2 10:51 tuesday, september...

AREC ECON 535 Problem Set 2 10:51 Tuesday, September 5, 2017 1

Obs Year qb qp qc rpb rpp rpc rdpi

1 1960 63.4705 59.1006 23.5307 621.7 433.5 331.0 16157 2 1961 65.5438 56.6650 25.9554 602.3 448.9 295.8 16474 3 1962 66.3334 57.2803 25.9555 581.0 418.0 289.5 15925 4 1963 70.3508 58.3524 27.2374 528.3 380.9 269.7 15572 5 1964 74.8372 58.3944 27.8208 480.9 351.4 237.5 15599 6 1965 74.8082 51.7919 29.7791 472.5 375.7 224.6 15210 7 1966 78.3399 50.6572 32.0821 443.1 385.2 216.6 14800 8 1967 80.0734 55.4530 32.6266 435.0 342.2 195.6 15334 9 1968 82.2436 56.7023 32.8834 437.5 329.7 196.6 15824 10 1969 82.7676 54.9726 34.9105 456.4 340.9 195.5 15887 11 1970 84.7017 55.9371 36.8752 484.9 369.1 194.4 17711 12 1971 84.0101 60.6162 36.7437 507.1 327.6 192.6 18759 13 1972 85.8294 54.7022 38.4935 486.5 338.9 169.6 17577 14 1973 80.7634 48.9722 37.0195 548.5 421.7 230.2 18328 15 1974 85.6795 52.8234 36.9217 509.0 375.1 194.7 17864 16 1975 88.2354 43.0095 36.7014 493.8 429.3 201.8 18001 17 1976 94.5714 45.5452 39.8514 446.9 404.2 180.0 18333 18 1977 91.7108 47.0482 40.7288 420.2 355.0 170.1 18730 19 1978 87.4672 47.0280 43.1018 478.2 377.4 174.8 19250 20 1979 78.1852 53.7305 45.9882 534.5 360.2 159.9 18985 21 1980 76.6185 57.3234 45.8268 494.8 307.2 147.5 18451 22 1981 78.2770 54.7350 46.8592 450.2 304.1 138.0 18455 23 1982 77.0888 49.1439 47.0447 430.9 329.7 126.8 18556 24 1983 78.5643 51.7245 47.4250 411.7 310.6 125.3 19312 25 1984 78.4804 51.4722 49.2454 397.0 284.1 134.3 20359 26 1985 79.2534 51.8918 50.9795 372.2 273.4 122.1 20790 27 1986 78.8967 49.0099 52.0200 362.5 296.6 131.2 21464 28 1987 73.9062 49.1781 55.1052 367.6 302.2 119.0 21637 29 1988 72.7060 52.4795 55.3228 370.7 282.5 124.3 22396 30 1989 69.0286 51.9686 56.6261 374.8 268.7 128.7 22747 31 1990 67.7184 49.7084 59.4931 378.5 296.3 118.5 22707 32 1991 66.5795 50.1726 61.9175 364.5 283.4 111.3 22363 33 1992 66.1027 52.7407 65.5200 349.3 257.1 106.7 22932 34 1993 64.5631 51.9262 67.8988 349.7 249.2 106.1 22894 35 1994 66.2882 52.4803 68.7212 328.7 243.5 104.7 23130 36 1995 66.5683 51.7284 67.9139 321.3 232.9 103.6 23449 37 1996 67.1175 48.3294 69.1545 307.6 256.5 106.8 23723 38 1997 65.6796 47.8193 71.3737 299.9 262.8 107.5 24169 39 1998 66.6773 51.5366 72.0241 292.8 256.4 110.3 25100

�AREC ECON 535 Problem Set 2 10:51 Tuesday, September 5, 2017 2

Obs Year qb qp qc rpb rpp rpc rdpi

40 1999 67.5019 52.6033 76.2966 297.4 249.6 109.1 25444 41 2000 67.7650 51.2206 76.9627 306.4 258.2 107.1 26206 42 2001 66.3252 50.3085 76.7624 328.4 261.9 107.5 26427 43 2002 67.7669 51.5838 80.7225 317.4 254.4 102.8 26923 44 2003 65.0312 51.9134 81.7732 350.6 248.7 96.8 27326 45 2004 66.2375 51.4505 84.4879 370.6 254.5 97.5 27983 46 2005 65.6368 50.0525 85.9506 360.7 249.3 93.1 28003 47 2006 65.9120 49.4852 86.6746 339.1 239.8 89.6 28691 48 2007 65.2925 50.8349 85.3061 345.4 238.4 92.6 28929 49 2008 62.5039 49.5126 83.5446 346.0 234.9 96.5 28874 50 2009 61.1144 50.1850 79.7936 341.8 234.4 102.6 28592 51 2010 59.5816 47.7875 82.3642 346.1 245.8 99.7 28640 52 2011 57.2349 45.6892 82.8643 368.1 262.9 98.9 28951 53 2012 57.4894 45.9116 80.3548 373.9 260.0 106.7 29591 54 2013 56.2908 46.7935 81.8439 390.9 269.3 110.6 28939 55 2014 54.1462 45.7882 83.3118 434.3 292.4 111.5 29732 56 2015 53.9526 49.7169 88.9411 457.0 279.9 108.1 30801 57 2016 55.4430 50.0162 89.5776 427.9 268.8 105.0 30992

�Means of All Data Series 10:51 Tuesday, September 5, 2017 3

The MEANS Procedure

Variable Label N Mean Std Dev Minimum MaximumƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒYear Year 57 1988.00 16.5981927 1960.00 2016.00qb 57 71.4958382 9.9131131 53.9526284 94.5714229qp 57 51.4912988 3.7553145 43.0094907 60.6161579qc 57 57.6001850 21.0128804 23.5306925 89.5775909rpb 57 412.1929825 81.3338312 292.8000000 621.7000000rpp 57 306.4087719 60.6593718 232.9000000 448.9000000rpc 57 147.8754386 58.4900885 89.6000000 331.0000000rdpi 57 22210.49 4965.82 14800.00 30992.00lqb 57 4.2602407 0.1383212 3.9881064 4.5493553lrpb 57 6.0031029 0.1919559 5.6794898 6.4324577lrpp 57 5.7067717 0.1895348 5.4506092 6.1068001lrpc 57 4.9317851 0.3483641 4.4953553 5.8021184lrdpi 57 9.9834750 0.2257290 9.6023825 10.3414844d 57 0.6491228 0.4814868 0 1.0000000dlrpb 57 3.8257171 2.8395171 0 6.2041536dlrpp 57 3.6256742 2.6902921 0 5.7981832dlrpc 57 3.0528060 2.2663904 0 4.9938282dlrdpi 57 6.5664999 4.8722796 0 10.3414844t 57 29.0000000 16.5981927 1.0000000 57.0000000tsq 57 1111.67 993.1675757 1.0000000 3249.00tcb 57 47937.00 54402.04 1.0000000 185193.00ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ

�Correlations of All Data Series 10:51 Tuesday, September 5, 2017 4

The CORR Procedure

8 Variables: lqb lrpb lrpp lrpc lrdpi t tsq tcb

Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum

lqb 57 4.26024 0.13832 242.83372 3.98811 4.54936lrpb 57 6.00310 0.19196 342.17687 5.67949 6.43246lrpp 57 5.70677 0.18953 325.28599 5.45061 6.10680lrpc 57 4.93179 0.34836 281.11175 4.49536 5.80212lrdpi 57 9.98347 0.22573 569.05807 9.60238 10.34148t 57 29.00000 16.59819 1653 1.00000 57.00000tsq 57 1112 993.16758 63365 1.00000 3249tcb 57 47937 54402 2732409 1.00000 185193

Pearson Correlation Coefficients, N = 57 Prob > |r| under H0: Rho=0 lqb lrpb lrpp lrpc lrdpi t tsq tcb

lqb 1.00000 0.38753 0.59400 0.52851 -0.74246 -0.73492 -0.82228 -0.82883 0.0029 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

lrpb 0.38753 1.00000 0.88619 0.86017 -0.69939 -0.71741 -0.58755 -0.46589 0.0029 <.0001 <.0001 <.0001 <.0001 <.0001 0.0003

lrpp 0.59400 0.88619 1.00000 0.93675 -0.83818 -0.85318 -0.76441 -0.66913 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

lrpc 0.52851 0.86017 0.93675 1.00000 -0.88825 -0.91415 -0.80114 -0.70142 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

lrdpi -0.74246 -0.69939 -0.83818 -0.88825 1.00000 0.98618 0.95842 0.90479 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

t -0.73492 -0.71741 -0.85318 -0.91415 0.98618 1.00000 0.96932 0.91836 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

�Correlations of All Data Series 10:51 Tuesday, September 5, 2017 5

The CORR Procedure

Pearson Correlation Coefficients, N = 57 Prob > |r| under H0: Rho=0 lqb lrpb lrpp lrpc lrdpi t tsq tcb

tsq -0.82228 -0.58755 -0.76441 -0.80114 0.95842 0.96932 1.00000 0.98615 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

tcb -0.82883 -0.46589 -0.66913 -0.70142 0.90479 0.91836 0.98615 1.00000 <.0001 0.0003 <.0001 <.0001 <.0001 <.0001 <.0001

�Means of Data in Levels 10:51 Tuesday, September 5, 2017 6

The MEANS Procedure

Variable N Mean Std Dev Minimum Maximumƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒqb 57 71.4958382 9.9131131 53.9526284 94.5714229rpb 57 412.1929825 81.3338312 292.8000000 621.7000000rpp 57 306.4087719 60.6593718 232.9000000 448.9000000rpc 57 147.8754386 58.4900885 89.6000000 331.0000000rdpi 57 22210.49 4965.82 14800.00 30992.00ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ

�Correlations of Data in Models 10:51 Tuesday, September 5, 2017 7

The CORR Procedure

5 Variables: lqb lrpb lrpp lrpc lrdpi

Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum

lqb 57 4.26024 0.13832 242.83372 3.98811 4.54936lrpb 57 6.00310 0.19196 342.17687 5.67949 6.43246lrpp 57 5.70677 0.18953 325.28599 5.45061 6.10680lrpc 57 4.93179 0.34836 281.11175 4.49536 5.80212lrdpi 57 9.98347 0.22573 569.05807 9.60238 10.34148

Pearson Correlation Coefficients, N = 57 Prob > |r| under H0: Rho=0 lqb lrpb lrpp lrpc lrdpi

lqb 1.00000 0.38753 0.59400 0.52851 -0.74246 0.0029 <.0001 <.0001 <.0001

lrpb 0.38753 1.00000 0.88619 0.86017 -0.69939 0.0029 <.0001 <.0001 <.0001

lrpp 0.59400 0.88619 1.00000 0.93675 -0.83818 <.0001 <.0001 <.0001 <.0001

lrpc 0.52851 0.86017 0.93675 1.00000 -0.88825 <.0001 <.0001 <.0001 <.0001

lrdpi -0.74246 -0.69939 -0.83818 -0.88825 1.00000 <.0001 <.0001 <.0001 <.0001

�Double Log Model of Beef Demand 10:51 Tuesday, September 5, 2017 8

The REG ProcedureModel: MODEL1Dependent Variable: lqb

Number of Observations Read 57Number of Observations Used 57

Analysis of Variance Sum of MeanSource DF Squares Square F Value Pr > F

Model 4 0.76187 0.19047 31.99 <.0001Error 52 0.30956 0.00595 Corrected Total 56 1.07143

Root MSE 0.07716 R-Square 0.7111Dependent Mean 4.26024 Adj R-Sq 0.6889Coeff Var 1.81108

Parameter Estimates Parameter StandardVariable DF Estimate Error t Value Pr > |t|

Intercept 1 11.12886 1.41794 7.85 <.0001lrpb 1 -0.17398 0.12490 -1.39 0.1696lrpp 1 0.66159 0.17730 3.73 0.0005lrpc 1 -0.46586 0.10665 -4.37 <.0001lrdpi 1 -0.73143 0.10536 -6.94 <.0001


The REG ProcedureModel: MODEL1

Test equal Results for Dependent Variable lqb MeanSource DF Square F Value Pr > F

Numerator 1 0.12466 20.94 <.0001Denominator 52 0.00595



Test shift Results for Dependent Variable lqb MeanSource DF Square F Value Pr > F




Test homog Results for Dependent Variable lqb MeanSource DF Square F Value Pr > F

Numerator 1 0.09054 15.21 0.0003Denominator 52 0.00595

�Restricted Double Log Model of Beef Demand 10:51 Tuesday, September 5, 2017 12


NOTE: Restrictions have been applied to parameter estimates.






Intercept 1 5.62622 0.15795 35.62 <.0001 lrpb 1 -0.25579 0.13866 -1.84 0.0707 lrpp 1 0.99140 0.17547 5.65 <.0001 lrpc 1 -0.36736 0.11668 -3.15 0.0027 lrdpi 1 -0.36825 0.05548 -6.64 <.0001 RESTRICT -1 -0.12758 0.03684 -3.46 0.0003*

* Probability computed using beta distribution.

�Variance-Covariance Matrix 10:51 Tuesday, September 5, 2017 13

Obs _MODEL_ _TYPE_ _NAME_ _DEPVAR_ _RMSE_ Intercept lrpb lrpp lrpc lrdpi lqb

1 MODEL1 PARMS lqb 0.086886 5.62622 -0.25579 0.99140 -0.36736 -0.36825 -1 2 MODEL1 COV Intercept lqb 0.086886 0.02495 0.00329 0.01598 -0.01121 -0.00806 . 3 MODEL1 COV lrpb lqb 0.086886 0.00329 0.01923 -0.01123 -0.00499 -0.00301 . 4 MODEL1 COV lrpp lqb 0.086886 0.01598 -0.01123 0.03079 -0.01406 -0.00551 . 5 MODEL1 COV lrpc lqb 0.086886 -0.01121 -0.00499 -0.01406 0.01361 0.00543 . 6 MODEL1 COV lrdpi lqb 0.086886 -0.00806 -0.00301 -0.00551 0.00543 0.00308 .

�Model of Structural Change with Dummy Variables 10:51 Tuesday, September 5, 2017 14







Intercept 1 2.10067 1.94428 1.08 0.2855lrpb 1 -0.71852 0.19956 -3.60 0.0008lrpp 1 0.16126 0.16968 0.95 0.3468lrpc 1 -0.10583 0.15434 -0.69 0.4963lrdpi 1 0.65151 0.24384 2.67 0.0103d 1 9.95302 2.41349 4.12 0.0002dlrpb 1 0.57861 0.21928 2.64 0.0113dlrpp 1 -0.16105 0.24378 -0.66 0.5121dlrpc 1 0.05727 0.21527 0.27 0.7914dlrdpi 1 -1.32414 0.26034 -5.09 <.0001

�Model of Structural Change with Dummy Variables 10:51 Tuesday, September 5, 2017 15


Test chow Results for Dependent Variable lqb MeanSource DF Square F Value Pr > F


�Model of First Portion of Sample 10:51 Tuesday, September 5, 2017 16







Intercept 1 2.10067 1.41032 1.49 0.1571lrpb 1 -0.71852 0.14476 -4.96 0.0002lrpp 1 0.16126 0.12308 1.31 0.2098lrpc 1 -0.10583 0.11196 -0.95 0.3595lrdpi 1 0.65151 0.17688 3.68 0.0022

�Model of Second Portion of Sample 10:51 Tuesday, September 5, 2017 17







Intercept 1 12.05369 1.58077 7.63 <.0001lrpb 1 -0.13991 0.10045 -1.39 0.1733lrpp 1 0.00020794 0.19349 0.00 0.9991lrpc 1 -0.04857 0.16590 -0.29 0.7716lrdpi 1 -0.67263 0.10082 -6.67 <.0001

�F-Test of Difference Variances 10:51 Tuesday, September 5, 2017 18

Obs sse1 df1 sse2 df2 fstat12 pvalue12 fstat21 pvalue21

1 0.016776 15 0.083126 32 0.43053 0.95724 2.32271 0.042763

�Heteroskedastic Model where Variance is Linear 10:51 Tuesday, September 5, 2017 19

The AUTOREG Procedure

Dependent Variable lqb

Ordinary Least Squares Estimates

SSE 0.09990129 DFE 47MSE 0.00213 Root MSE 0.04610SBC -159.56806 AIC -179.99857MAE 0.03460996 AICC -175.21596MAPE 0.81545303 HQC -172.05858Durbin-Watson 0.3890 Regress R-Square 0.9068 Total R-Square 0.9068

Parameter Estimates Standard ApproxVariable DF Estimate Error t Value Pr > |t|

Intercept 1 2.1007 1.9443 1.08 0.2855lrpb 1 -0.7185 0.1996 -3.60 0.0008lrpp 1 0.1613 0.1697 0.95 0.3468lrpc 1 -0.1058 0.1543 -0.69 0.4963lrdpi 1 0.6515 0.2438 2.67 0.0103d 1 9.9530 2.4135 4.12 0.0002dlrpb 1 0.5786 0.2193 2.64 0.0113dlrpp 1 -0.1611 0.2438 -0.66 0.5121dlrpc 1 0.0573 0.2153 0.27 0.7914dlrdpi 1 -1.3241 0.2603 -5.09 <.0001

Test CHANGE MeanSource DF Square F Value Pr > F




Algorithm converged.

Linear Heteroscedasticity Estimates

SSE 0.09990129 Observations 57MSE 0.00175 Root MSE 0.04186Log Likelihood 102.774997 Total R-Square 0.9068SBC -157.03338 AIC -181.54999MAE 0.03460997 AICC -174.45909MAPE 0.81545311 HQC -172.022 Normality Test 1.9938 Pr > ChiSq 0.3690

Parameter Estimates Standard ApproxVariable DF Estimate Error t Value Pr > |t|

Intercept 1 2.1007 1.7822 1.18 0.2385lrpb 1 -0.7185 0.0769 -9.34 <.0001lrpp 1 0.1613 0.1517 1.06 0.2879lrpc 1 -0.1058 0.1043 -1.01 0.3104lrdpi 1 0.6515 0.1946 3.35 0.0008d 1 9.9530 2.3378 4.26 <.0001dlrpb 1 0.5786 0.1484 3.90 <.0001dlrpp 1 -0.1611 0.2812 -0.57 0.5668dlrpc 1 0.0573 0.2312 0.25 0.8044dlrdpi 1 -1.3241 0.2308 -5.74 <.0001HET0 1 0.0290 0.007335 3.95 <.0001HET1 1 1.6784 1.6833 1.00 0.3187



Test CHANGE Source DF F Value Pr > F

Numerator 5 25.57 <.0001Denominator 45

�Structural Change with Time Trend Variables 10:51 Tuesday, September 5, 2017 22







Intercept 1 -1.17123 2.00678 -0.58 0.5621lrpb 1 -0.40079 0.10089 -3.97 0.0002lrpp 1 0.31811 0.13530 2.35 0.0228lrpc 1 -0.23995 0.13860 -1.73 0.0897lrdpi 1 0.75804 0.23618 3.21 0.0023t 1 0.02480 0.00719 3.45 0.0012tsq 1 -0.00186 0.00025173 -7.40 <.0001tcb 1 0.00002065 0.00000306 6.76 <.0001

�Structural Change with Time Trend Variables 10:51 Tuesday, September 5, 2017 23


Test trend Results for Dependent Variable lqb MeanSource DF Square F Value Pr > F


�Collinearity Results from Double Log Model of Beef Demand 10:51 Tuesday, September 5, 2017 24






Parameter Estimates Parameter Standard VarianceVariable DF Estimate Error t Value Pr > |t| Inflation

Intercept 1 11.12886 1.41794 7.85 <.0001 0lrpb 1 -0.17398 0.12490 -1.39 0.1696 5.40751lrpp 1 0.66159 0.17730 3.73 0.0005 10.62232lrpc 1 -0.46586 0.10665 -4.37 <.0001 12.98373lrdpi 1 -0.73143 0.10536 -6.94 <.0001 5.32032

�Collinearity Results from Double Log Model of Beef Demand 10:51 Tuesday, September 5, 2017 25


Collinearity Diagnostics Condition ------------------------Proportion of Variation------------------------ Number Eigenvalue Index Intercept lrpb lrpp lrpc lrdpi

1 4.99501 1.00000 0.00000208 0.00000744 0.00000408 0.00001502 0.00000377 2 0.00468 32.67586 0.00109 0.00028338 0.00043562 0.03977 0.00765 3 0.00018184 165.73744 0.02815 0.69686 0.00470 0.36358 0.01778 4 0.00009356 231.05545 0.00533 0.17389 0.76017 0.47815 0.08648 5 0.00003194 395.46782 0.96542 0.12896 0.23469 0.11849 0.88808

�Collinearity Results from Double Log Model with Trends 10:51 Tuesday, September 5, 2017 26







Intercept 1 4.09896 2.60070 1.58 0.1212 0lrpb 1 -0.11345 0.11712 -0.97 0.3373 5.55905lrpp 1 0.69593 0.16433 4.23 <.0001 10.66990lrpc 1 -0.63179 0.11197 -5.64 <.0001 16.73483lrdpi 1 0.03611 0.26386 0.14 0.8917 39.01704t 1 -0.01289 0.00412 -3.13 0.0029 51.39831



Collinearity Diagnostics Condition --------------------------------Proportion of Variation------------------------------- Number Eigenvalue Index Intercept lrpb lrpp lrpc lrdpi t

1 5.77027 1.00000 3.951404E-7 0.00000538 0.00000302 0.00000862 3.857949E-7 0.00011477 2 0.22897 5.02002 9.241528E-7 0.00002415 0.00001531 0.00008670 3.642101E-7 0.01747 3 0.00050600 106.78787 0.00749 0.02509 0.00041138 0.22016 0.00621 0.13065 4 0.00016688 185.95255 0.00136 0.60524 0.02081 0.61675 0.00273 0.01557 5 0.00008213 265.06151 0.00251 0.36801 0.93166 0.08644 0.00596 0.02113 6 0.00000656 937.53684 0.98863 0.00163 0.04710 0.07655 0.98510 0.81506








Intercept 1 -1.17123 2.00678 -0.58 0.5621 0lrpb 1 -0.40079 0.10089 -3.97 0.0002 8.62374lrpp 1 0.31811 0.13530 2.35 0.0228 15.12126lrpc 1 -0.23995 0.13860 -1.73 0.0897 53.60426lrdpi 1 0.75804 0.23618 3.21 0.0023 65.35263t 1 0.02480 0.00719 3.45 0.0012 327.43620tsq 1 -0.00186 0.00025173 -7.40 <.0001 1437.17942tcb 1 0.00002065 0.00000306 6.76 <.0001 635.58371



Collinearity Diagnostics Condition Number Eigenvalue Index

1 7.05227 1.00000 2 0.91655 2.77388 3 0.03038 15.23513 4 0.00052845 115.52100 5 0.00012705 235.59784 6 0.00009322 275.05614 7 0.00004777 384.24093 8 0.00000450 1252.02526

Collinearity Diagnostics -----------------------------------------------Proportion of Variation---------------------------------------------- Number Intercept lrpb lrpp lrpc lrdpi t tsq tcb

1 2.028571E-7 0.00000221 0.00000135 0.00000169 1.482163E-7 0.00001359 0.00000473 0.00001165 2 6.193028E-7 0.00000791 0.00000514 0.00000818 3.679345E-7 0.00006532 0.00008401 0.00034499 3 1.005012E-7 0.00004230 0.00001520 0.00013965 6.43104E-7 0.01402 0.00008694 0.01017 4 0.00024548 0.01826 0.00307 0.00934 0.00036615 0.21429 0.29126 0.24467 5 0.01804 0.07444 0.11380 0.23246 0.00886 0.15580 0.00031899 0.01988 6 0.01934 0.75469 0.00015466 0.01165 0.00558 0.06971 0.31741 0.37926 7 0.00124 0.04938 0.85084 0.65714 0.00019450 0.46273 0.17421 0.06176 8 0.96112 0.10317 0.03211 0.08926 0.98500 0.08337 0.21663 0.28391

�Influence Results from Double Log Model of Beef Demand 10:51 Tuesday, September 5, 2017 30







Intercept 1 11.12886 1.41794 7.85 <.0001lrpb 1 -0.17398 0.12490 -1.39 0.1696lrpp 1 0.66159 0.17730 3.73 0.0005lrpc 1 -0.46586 0.10665 -4.37 <.0001lrdpi 1 -0.73143 0.10536 -6.94 <.0001



Output Statistics Hat Diag Cov -----------------------DFBETAS----------------------- Obs Residual RStudent H Ratio DFFITS Intercept lrpb lrpp lrpc lrdpi

1 -0.0857 -1.2666 0.2229 1.2146 -0.6783 0.3064 -0.0297 0.2008 -0.4831 -0.3454 2 -0.1203 -1.7202 0.1477 0.9752 -0.7162 0.4387 0.0480 -0.0814 -0.3275 -0.3860 3 -0.1022 -1.4328 0.1279 1.0372 -0.5486 0.1918 -0.0304 0.1333 -0.3310 -0.2016 4 -0.0479 -0.6614 0.1299 1.2135 -0.2555 0.0038 -0.0080 0.1319 -0.1790 -0.0377 5 -0.007028 -0.0961 0.1190 1.2497 -0.0353 -0.0097 -0.0006 0.0220 -0.0222 0.0034 6 -0.0992 -1.3418 0.0676 0.9936 -0.3612 -0.1101 0.0819 0.0240 -0.0779 0.1042 7 -0.1177 -1.6326 0.0997 0.9487 -0.5432 -0.1465 0.2777 -0.1836 0.0144 0.1667 8 -0.0423 -0.5679 0.0823 1.1635 -0.1701 -0.1138 0.0174 0.0445 -0.0107 0.1028 9 0.0355 0.4784 0.0893 1.1832 0.1498 0.0944 0.0022 -0.0803 0.0440 -0.0729 10 0.0274 0.3648 0.0687 1.1680 0.0991 0.0625 0.0139 -0.0422 0.0090 -0.0577 11 0.0853 1.1306 0.0386 1.0127 0.2264 -0.0332 0.0013 0.0642 -0.0179 -0.0075 12 0.2015 2.9454 0.0976 0.5567 0.9685 0.0996 0.5696 -0.7201 0.3827 -0.0349 13 0.0865 1.1638 0.0667 1.0357 0.3111 0.1451 0.2015 -0.0671 -0.1436 -0.2014 14 0.0748 1.0281 0.1102 1.1176 0.3617 -0.2554 -0.0436 0.1791 0.0370 0.1860 15 0.1016 1.3594 0.0469 0.9677 0.3017 -0.0581 0.0798 0.0783 -0.0700 -0.0171 16 0.0587 0.8353 0.1760 1.2495 0.3860 -0.1900 -0.1478 0.3391 -0.1150 0.0940 17 0.1106 1.6060 0.1787 1.0484 0.7491 -0.2722 -0.3739 0.6860 -0.2632 0.1076 18 0.1444 1.9867 0.0626 0.8098 0.5134 -0.1008 -0.3097 0.3678 -0.0716 0.0413 19 0.1117 1.5250 0.0750 0.9533 0.4344 -0.1844 -0.0540 0.3308 -0.1773 0.0596 20 -0.001860 -0.0256 0.1303 1.2670 -0.0099 -0.0004 -0.0067 -0.0019 0.0070 0.0037 21 0.0113 0.1587 0.1645 1.3156 0.0704 0.0377 0.0600 -0.0331 -0.0305 -0.0463 22 -0.007867 -0.1075 0.1172 1.2468 -0.0392 -0.0258 -0.0269 0.0111 0.0234 0.0314 23 -0.1197 -1.7382 0.1725 0.9986 -0.7935 -0.3088 -0.2133 -0.3432 0.7294 0.5312 24 -0.0455 -0.6191 0.1026 1.1828 -0.2093 -0.1052 -0.0596 -0.0627 0.1806 0.1535 25 0.0770 1.0200 0.0417 1.0394 0.2127 0.1485 0.0781 -0.1171 -0.0220 -0.1309 26 0.0719 0.9552 0.0486 1.0599 0.2158 0.1698 0.0466 -0.0811 -0.0579 -0.1539 27 0.0658 0.8676 0.0390 1.0657 0.1749 0.0148 -0.1174 0.0762 -0.0073 -0.0048 28 -0.0491 -0.6556 0.0681 1.1339 -0.1772 -0.0219 0.0604 -0.1250 0.1118 0.0499 29 0.0261 0.3392 0.0224 1.1145 0.0513 0.0135 -0.0126 0.0011 -0.0027 -0.0084 30 0.0368 0.4839 0.0415 1.1237 0.1008 0.0285 0.0065 -0.0688 0.0501 -0.0013 31 -0.0851 -1.1296 0.0422 1.0168 -0.2372 -0.0011 0.0458 -0.1516 0.1453 0.0405 32 -0.1195 -1.6132 0.0498 0.9042 -0.3693 -0.1291 0.0260 -0.1579 0.2582 0.1761



Output Statistics Hat Diag Cov -----------------------DFBETAS----------------------- Obs Residual RStudent H Ratio DFFITS Intercept lrpb lrpp lrpc lrdpi

33 -0.0710 -0.9405 0.0460 1.0599 -0.2065 -0.1406 -0.0299 0.0589 0.0626 0.1216 34 -0.0775 -1.0377 0.0614 1.0576 -0.2654 -0.1940 -0.0757 0.1398 0.0438 0.1578 35 -0.0453 -0.6034 0.0649 1.1373 -0.1590 -0.1111 0.0016 0.0775 -0.0049 0.0757 36 -0.0105 -0.1414 0.0922 1.2115 -0.0451 -0.0299 -0.0013 0.0294 -0.0097 0.0176 37 -0.0510 -0.6833 0.0719 1.1345 -0.1902 -0.0481 0.1332 -0.0286 -0.0249 0.0089 38 -0.0765 -1.0466 0.1008 1.1020 -0.3504 -0.0116 0.2947 -0.1284 -0.0514 -0.0466 39 -0.009659 -0.1328 0.1277 1.2612 -0.0508 0.0043 0.0437 -0.0101 -0.0217 -0.0166 40 0.0280 0.3809 0.1080 1.2179 0.1325 -0.0050 -0.1023 0.0032 0.0682 0.0430 41 0.0276 0.3728 0.0931 1.1987 0.1195 -0.0260 -0.0968 0.0323 0.0447 0.0511 42 0.0167 0.2204 0.0563 1.1622 0.0538 -0.0163 -0.0355 0.0138 0.0166 0.0260 43 0.0442 0.5886 0.0628 1.1367 0.1524 -0.0358 -0.1016 0.0333 0.0464 0.0661 44 0.0182 0.2383 0.0394 1.1408 0.0483 -0.0004 0.0098 -0.0076 -0.0059 0.0042 45 0.0517 0.6838 0.0494 1.1075 0.1559 -0.0285 0.0635 -0.0141 -0.0352 0.0253 46 0.0306 0.4032 0.0513 1.1432 0.0938 -0.0044 0.0375 -0.0067 -0.0316 0.0020 47 0.0496 0.6554 0.0487 1.1108 0.1483 -0.0040 0.0271 -0.0175 -0.0228 0.0152 48 0.0686 0.9123 0.0529 1.0730 0.2156 -0.0174 0.0540 -0.0687 0.0137 0.0454 49 0.0529 0.7056 0.0657 1.1236 0.1872 -0.0131 0.0427 -0.0993 0.0623 0.0527 50 0.0511 0.6883 0.0850 1.1499 0.2097 -0.0231 0.0123 -0.1253 0.1231 0.0823 51 -0.0157 -0.2071 0.0510 1.1563 -0.0480 0.0139 0.0005 0.0118 -0.0158 -0.0228 52 -0.0855 -1.1444 0.0563 1.0286 -0.2795 0.1449 -0.0258 -0.0697 0.0409 -0.1318 53 -0.0197 -0.2622 0.0712 1.1785 -0.0726 0.0451 -0.0039 0.0061 -0.0249 -0.0518 54 -0.0558 -0.7468 0.0692 1.1213 -0.2037 0.1345 -0.0318 0.0042 -0.0470 -0.1402 55 -0.1073 -1.5058 0.1270 1.0155 -0.5742 0.4195 -0.1690 -0.1668 0.0852 -0.3293 56 -0.0617 -0.8742 0.1681 1.2297 -0.3930 0.2249 -0.2243 0.0068 0.0454 -0.1737 57 -0.0281 -0.3880 0.1321 1.2511 -0.1514 0.0876 -0.0761 0.0118 0.0012 -0.0763

Sum of Residuals 0Sum of Squared Residuals 0.30956Predicted Residual SS (PRESS) 0.37984

�Non-Nested Test of Linear versus Double Log Model 10:51 Tuesday, September 5, 2017 33

The REG ProcedureModel: MODEL1Dependent Variable: qb






Intercept 1 104.86407 9.31724 11.25 <.0001rpb 1 -0.02954 0.01866 -1.58 0.1196rpp 1 0.11097 0.03263 3.40 0.0013rpc 1 -0.11207 0.03730 -3.00 0.0041rdpi 1 -0.00175 0.00023876 -7.32 <.0001infolog 1 103.03082 33.90585 3.04 0.0037

�Non-Nested Test of Linear versus Double Log Model 10:51 Tuesday, September 5, 2017 34







Intercept 1 11.29487 1.11432 10.14 <.0001lrpb 1 -0.21282 0.09836 -2.16 0.0352lrpp 1 0.36581 0.14843 2.46 0.0171lrpc 1 -0.25042 0.09173 -2.73 0.0087lrdpi 1 -0.66265 0.08362 -7.92 <.0001infolin 1 -0.02998 0.00520 -5.77 <.0001

arec econ 535 problem set 2 10:51 tuesday, september...

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