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lab4 complete

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1 parent 8773fa9 commit a75e9a24c03c537d662cd61fd5fd23c7ff41ef32 @ashawnbandy committed Mar 12, 2013
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+--------------------------------------------------------------------------------------------------------------
+ name: <unnamed>
+ log: /Users/shawn/src/econ485/arclab2.log
+ log type: text
+ opened on: 11 Mar 2013, 19:02:10
+
+. use "arcdata1";
+file arcdata1.dta not found
+r(601);
+
+end of do-file
+
+r(601);
+
+. do "/var/folders/8r/6p_8585x5435jsc5wc_xdv5w0000gn/T//SD66697.000000"
+
+. /* A. Shawn Bandy
+> Lab #4
+> */
+. /* close previous run do-files */
+. cap log close
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208 lab4/arclab1.log
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+------------------------------------------------------------------------------------
+ name: <unnamed>
+ log: /Users/shawn/src/econ485/lab4/arclab1.log
+ log type: text
+ opened on: 11 Mar 2013, 20:26:34
+
+. use "arclab";
+
+. /*a. Create a dummy variable, arc that is equal to one if the arc_county variable
+> indicates it is an ARC county. Otherwise, non-ARC counties should have a
+> value of zero. This variable will be used to see if there is a difference
+> in employment growth between the ARC and non-ARC counties.*/
+>
+> gen arc=1 if arc_county=="ARC";
+(138 missing values generated)
+
+. replace arc=0 if arc==.;
+(138 real changes made)
+
+. /*b. Create a set of dummy variables for each of the 13 states in the ARC region.
+>
+> Use tabulate with the prefix state to create these variables. Hint: the state
+> variable has the unique names of the 13 states for each county in the dataset.*/
+>
+> tabulate state, gen(state);
+
+ state | Freq. Percent Cum.
+------------+-----------------------------------
+ AL | 47 8.44 8.44
+ GA | 50 8.98 17.41
+ KY | 74 13.29 30.70
+ MD | 4 0.72 31.42
+ MS | 36 6.46 37.88
+ NC | 36 6.46 44.34
+ NY | 33 5.92 50.27
+ OH | 45 8.08 58.35
+ PA | 59 10.59 68.94
+ SC | 11 1.97 70.92
+ TN | 69 12.39 83.30
+ VA | 38 6.82 90.13
+ WV | 55 9.87 100.00
+------------+-----------------------------------
+ Total | 557 100.00
+
+. /*c. Create a new variable empgrowth_9006 that is the percent change in employment
+> from 1990 to 2006. Use the label command to label this �Percent change in
+> employment from 1990 to 2006�. Make sure you save the data as arcdata1.dta so you
+> can use it for the next problem.*/
+>
+> gen empgrowth_9006 = (emp06 - emp90) / emp90;
+(4 missing values generated)
+
+. save arcdata_n.dta, replace;
+file arcdata_n.dta saved
+
+. /*d. Use the summarize command to look at the description of the variables in
+> this dataset. */
+> summarize;
+
+ Variable | Obs Mean Std. Dev. Min Max
+-------------+--------------------------------------------------------
+ fips | 558 33813.85 15810.15 1001 54109
+ state | 0
+ county | 0
+ manu90 | 554 6446.449 11222.06 13 118484
+ farm90 | 554 925.0144 653.6925 0 4762
+-------------+--------------------------------------------------------
+ percoll90 | 554 11.39375 5.642082 3.689338 41.72341
+ emp90 | 557 35498.5 79429.55 795 819868
+ emp06 | 554 44022.81 94828.9 897 963372
+ arc_county | 0
+ totpop90 | 554 67051.16 125637.7 2124 1336449
+-------------+--------------------------------------------------------
+ pop60 | 554 54965.85 114567.6 2443 1628587
+ popsqmi_60 | 554 112.2741 239.375 8 3735
+ rural | 554 .3122744 .4638399 0 1
+ permanu90 | 554 21.17014 10.98425 .7445443 53.52263
+ perfarm90 | 554 7.988959 7.926842 0 55.84906
+-------------+--------------------------------------------------------
+ pci90 | 554 14090.18 2814.397 7825 25984
+ perse90 | 557 16.13464 4.663423 4.079602 38.20309
+pci90_thou~s | 554 14.09018 2.814397 7.825 25.984
+ arc | 558 .7526882 .4318366 0 1
+ state1 | 557 .0843806 .2782076 0 1
+-------------+--------------------------------------------------------
+ state2 | 557 .0897666 .286104 0 1
+ state3 | 557 .1328546 .3397226 0 1
+ state4 | 557 .0071813 .0845138 0 1
+ state5 | 557 .064632 .2460963 0 1
+ state6 | 557 .064632 .2460963 0 1
+-------------+--------------------------------------------------------
+ state7 | 557 .059246 .2362967 0 1
+ state8 | 557 .0807899 .2727572 0 1
+ state9 | 557 .1059246 .3080177 0 1
+ state10 | 557 .0197487 .1392604 0 1
+ state11 | 557 .1238779 .3297384 0 1
+-------------+--------------------------------------------------------
+ state12 | 557 .0682226 .2523542 0 1
+ state13 | 557 .0987433 .2985852 0 1
+empgrow~9006 | 554 .3210966 .8151637 -.7296684 15.54692
+
+. /*e. Use the regression command to estimate the following linear
+> regression model, under the assumption that college educated people
+> contribute to employment growth: */
+> regress empgrowth_9006 percoll90;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 1, 552) = 3.42
+ Model | 2.26518362 1 2.26518362 Prob > F = 0.0648
+ Residual | 365.198846 552 .661592112 R-squared = 0.0062
+-------------+------------------------------ Adj R-squared = 0.0044
+ Total | 367.46403 553 .664491916 Root MSE = .81338
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0113436 .0061305 1.85 0.065 -.0006983 .0233855
+ _cons | .1918507 .07793 2.46 0.014 .0387751 .3449264
+------------------------------------------------------------------------------
+
+. /*f. What is the estimated slope coefficient for percoll90?
+> What is the interpretation of this slope coefficient?
+>
+> INTERPRETATION
+>
+> */
+>
+> /*g. Use the regression command to estimate the following
+> linear regression model, where we now test whether college
+> educated people and having a higher percentage of self-employed
+> individuals are important to employment growth in this region:*/
+> regress empgrowth_9006 percoll90 perse90;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 2, 551) = 24.61
+ Model | 30.1386418 2 15.0693209 Prob > F = 0.0000
+ Residual | 337.325388 551 .612205785 R-squared = 0.0820
+-------------+------------------------------ Adj R-squared = 0.0787
+ Total | 367.46403 553 .664491916 Root MSE = .78244
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0180694 .0059809 3.02 0.003 .0063213 .0298175
+ perse90 | .0490121 .0072637 6.75 0.000 .0347442 .06328
+ _cons | -.6767699 .1489679 -4.54 0.000 -.9693844 -.3841554
+------------------------------------------------------------------------------
+
+. /*h. What is the estimated slope coefficient for percoll90 in
+> the model from part g? What is the interpretation of this slope coefficient?
+>
+> INTERPRETATION
+>
+> */
+>
+> /*i. Using your results from parts e and g, does the regression model in part
+> e suffer from omitted variable bias? Explain.
+>
+> INTERPRETATION
+>
+> */
+>
+>
+> /*j. Use the regression command to estimate the following linear
+> regression model:*/
+>
+> regress percoll90 perse90;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 1, 552) = 15.77
+ Model | 488.962959 1 488.962959 Prob > F = 0.0001
+ Residual | 17114.7368 552 31.0049579 R-squared = 0.0278
+-------------+------------------------------ Adj R-squared = 0.0260
+ Total | 17603.6997 553 31.8330917 Root MSE = 5.5682
+
+------------------------------------------------------------------------------
+ percoll90 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ perse90 | -.2024086 .0509691 -3.97 0.000 -.3025257 -.1022916
+ _cons | 14.66448 .8569131 17.11 0.000 12.98127 16.34769
+------------------------------------------------------------------------------
+
+. /*k. Use the predict command to capture the residuals from the regression in
+> part j in a new variable named res.*/
+>
+> predict residual, res;
+(4 missing values generated)
+
+. /*l. Use the covariance option of the correlate command to examine the
+> covariance between res and empgrowth_9006.*/
+> correlate res empgrowth_9006, covariance;
+(obs=554)
+
+ | residual emp~9006
+-------------+------------------
+ residual | 30.9489
+empgrow~9006 | .559228 .664492
+
+
+. save arcdata1.dta, replace;
+file arcdata1.dta saved
+
+. log close;
+ name: <unnamed>
+ log: /Users/shawn/src/econ485/lab4/arclab1.log
+ log type: text
+ closed on: 11 Mar 2013, 20:26:34
+------------------------------------------------------------------------------------
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208 lab4/arclab1x.log
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+------------------------------------------------------------------------------------
+ name: <unnamed>
+ log: /Users/shawn/src/econ485/lab4/arclab1x.log
+ log type: text
+ opened on: 11 Mar 2013, 22:19:04
+
+. use "arclab";
+
+. /*a. Create a dummy variable, arc that is equal to one if the arc_county variable
+> indicates it is an ARC county. Otherwise, non-ARC counties should have a
+> value of zero. This variable will be used to see if there is a difference
+> in employment growth between the ARC and non-ARC counties.*/
+>
+> gen arc=1 if arc_county=="ARC";
+(138 missing values generated)
+
+. replace arc=0 if arc==.;
+(138 real changes made)
+
+. /*b. Create a set of dummy variables for each of the 13 states in the ARC region.
+>
+> Use tabulate with the prefix state to create these variables. Hint: the state
+> variable has the unique names of the 13 states for each county in the dataset.*/
+>
+> tabulate state, gen(state);
+
+ state | Freq. Percent Cum.
+------------+-----------------------------------
+ AL | 47 8.44 8.44
+ GA | 50 8.98 17.41
+ KY | 74 13.29 30.70
+ MD | 4 0.72 31.42
+ MS | 36 6.46 37.88
+ NC | 36 6.46 44.34
+ NY | 33 5.92 50.27
+ OH | 45 8.08 58.35
+ PA | 59 10.59 68.94
+ SC | 11 1.97 70.92
+ TN | 69 12.39 83.30
+ VA | 38 6.82 90.13
+ WV | 55 9.87 100.00
+------------+-----------------------------------
+ Total | 557 100.00
+
+. /*c. Create a new variable empgrowth_9006 that is the percent change in employment
+> from 1990 to 2006. Use the label command to label this �Percent change in
+> employment from 1990 to 2006�. Make sure you save the data as arcdata1.dta so you
+> can use it for the next problem.*/
+>
+> gen empgrowth_9006 = (emp06 - emp90) / emp90;
+(4 missing values generated)
+
+. save arcdata_n.dta, replace;
+file arcdata_n.dta saved
+
+. /*d. Use the summarize command to look at the description of the variables in
+> this dataset. */
+> summarize;
+
+ Variable | Obs Mean Std. Dev. Min Max
+-------------+--------------------------------------------------------
+ fips | 558 33813.85 15810.15 1001 54109
+ state | 0
+ county | 0
+ manu90 | 554 6446.449 11222.06 13 118484
+ farm90 | 554 925.0144 653.6925 0 4762
+-------------+--------------------------------------------------------
+ percoll90 | 554 11.39375 5.642082 3.689338 41.72341
+ emp90 | 557 35498.5 79429.55 795 819868
+ emp06 | 554 44022.81 94828.9 897 963372
+ arc_county | 0
+ totpop90 | 554 67051.16 125637.7 2124 1336449
+-------------+--------------------------------------------------------
+ pop60 | 554 54965.85 114567.6 2443 1628587
+ popsqmi_60 | 554 112.2741 239.375 8 3735
+ rural | 554 .3122744 .4638399 0 1
+ permanu90 | 554 21.17014 10.98425 .7445443 53.52263
+ perfarm90 | 554 7.988959 7.926842 0 55.84906
+-------------+--------------------------------------------------------
+ pci90 | 554 14090.18 2814.397 7825 25984
+ perse90 | 557 16.13464 4.663423 4.079602 38.20309
+pci90_thou~s | 554 14.09018 2.814397 7.825 25.984
+ arc | 558 .7526882 .4318366 0 1
+ state1 | 557 .0843806 .2782076 0 1
+-------------+--------------------------------------------------------
+ state2 | 557 .0897666 .286104 0 1
+ state3 | 557 .1328546 .3397226 0 1
+ state4 | 557 .0071813 .0845138 0 1
+ state5 | 557 .064632 .2460963 0 1
+ state6 | 557 .064632 .2460963 0 1
+-------------+--------------------------------------------------------
+ state7 | 557 .059246 .2362967 0 1
+ state8 | 557 .0807899 .2727572 0 1
+ state9 | 557 .1059246 .3080177 0 1
+ state10 | 557 .0197487 .1392604 0 1
+ state11 | 557 .1238779 .3297384 0 1
+-------------+--------------------------------------------------------
+ state12 | 557 .0682226 .2523542 0 1
+ state13 | 557 .0987433 .2985852 0 1
+empgrow~9006 | 554 .3210966 .8151637 -.7296684 15.54692
+
+. /*e. Use the regression command to estimate the following linear
+> regression model, under the assumption that college educated people
+> contribute to employment growth: */
+> regress empgrowth_9006 percoll90;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 1, 552) = 3.42
+ Model | 2.26518362 1 2.26518362 Prob > F = 0.0648
+ Residual | 365.198846 552 .661592112 R-squared = 0.0062
+-------------+------------------------------ Adj R-squared = 0.0044
+ Total | 367.46403 553 .664491916 Root MSE = .81338
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0113436 .0061305 1.85 0.065 -.0006983 .0233855
+ _cons | .1918507 .07793 2.46 0.014 .0387751 .3449264
+------------------------------------------------------------------------------
+
+. /*f. What is the estimated slope coefficient for percoll90?
+> What is the interpretation of this slope coefficient?
+>
+> INTERPRETATION
+>
+> */
+>
+> /*g. Use the regression command to estimate the following
+> linear regression model, where we now test whether college
+> educated people and having a higher percentage of self-employed
+> individuals are important to employment growth in this region:*/
+> regress empgrowth_9006 percoll90 perse90;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 2, 551) = 24.61
+ Model | 30.1386418 2 15.0693209 Prob > F = 0.0000
+ Residual | 337.325388 551 .612205785 R-squared = 0.0820
+-------------+------------------------------ Adj R-squared = 0.0787
+ Total | 367.46403 553 .664491916 Root MSE = .78244
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0180694 .0059809 3.02 0.003 .0063213 .0298175
+ perse90 | .0490121 .0072637 6.75 0.000 .0347442 .06328
+ _cons | -.6767699 .1489679 -4.54 0.000 -.9693844 -.3841554
+------------------------------------------------------------------------------
+
+. /*h. What is the estimated slope coefficient for percoll90 in
+> the model from part g? What is the interpretation of this slope coefficient?
+>
+> INTERPRETATION
+>
+> */
+>
+> /*i. Using your results from parts e and g, does the regression model in part
+> e suffer from omitted variable bias? Explain.
+>
+> INTERPRETATION
+>
+> */
+>
+>
+> /*j. Use the regression command to estimate the following linear
+> regression model:*/
+>
+> regress percoll90 perse90;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 1, 552) = 15.77
+ Model | 488.962959 1 488.962959 Prob > F = 0.0001
+ Residual | 17114.7368 552 31.0049579 R-squared = 0.0278
+-------------+------------------------------ Adj R-squared = 0.0260
+ Total | 17603.6997 553 31.8330917 Root MSE = 5.5682
+
+------------------------------------------------------------------------------
+ percoll90 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ perse90 | -.2024086 .0509691 -3.97 0.000 -.3025257 -.1022916
+ _cons | 14.66448 .8569131 17.11 0.000 12.98127 16.34769
+------------------------------------------------------------------------------
+
+. /*k. Use the predict command to capture the residuals from the regression in
+> part j in a new variable named res.*/
+>
+> predict residual, res;
+(4 missing values generated)
+
+. /*l. Use the covariance option of the correlate command to examine the
+> covariance between res and empgrowth_9006.*/
+> correlate res empgrowth_9006, covariance;
+(obs=554)
+
+ | residual emp~9006
+-------------+------------------
+ residual | 30.9489
+empgrow~9006 | .559228 .664492
+
+
+. save arcdata1.dta, replace;
+file arcdata1.dta saved
+
+. log close;
+ name: <unnamed>
+ log: /Users/shawn/src/econ485/lab4/arclab1x.log
+ log type: text
+ closed on: 11 Mar 2013, 22:19:04
+------------------------------------------------------------------------------------
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222 lab4/arclab2.log
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+------------------------------------------------------------------------------------
+ name: <unnamed>
+ log: /Users/shawn/src/econ485/lab4/arclab2.log
+ log type: text
+ opened on: 11 Mar 2013, 20:28:01
+
+. use "arcdata1";
+
+. /* a. Now, we want to test if additional variables would add to the explanatory
+> value of employment growth in the region. Add the following additional variables
+> to the model from L1 part g: pci90_thousands and pci90. */
+>
+> regress empgrowth_9006 percoll90 perse90 pci90_thousands pci90;
+note: pci90_thousands omitted because of collinearity
+
+ Source | SS df MS Number of obs = 551
+-------------+------------------------------ F( 3, 547) = 16.76
+ Model | 30.917101 3 10.3057003 Prob > F = 0.0000
+ Residual | 336.41239 547 .61501351 R-squared = 0.0842
+-------------+------------------------------ Adj R-squared = 0.0791
+ Total | 367.329491 550 .667871801 Root MSE = .78423
+
+---------------------------------------------------------------------------------
+ empgrowth_9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+----------------+----------------------------------------------------------------
+ percoll90 | .0123651 .007772 1.59 0.112 -.0029015 .0276317
+ perse90 | .0500949 .0073594 6.81 0.000 .0356387 .0645511
+pci90_thousands | 0 (omitted)
+ pci90 | .0000186 .0000156 1.19 0.233 -.000012 .0000492
+ _cons | -.8912981 .233067 -3.82 0.000 -1.349114 -.4334821
+---------------------------------------------------------------------------------
+
+. /* b. Does the STATA output from part a) include both the new variables?
+> Explain what happened.*/
+>
+> /*INTERPRETATION */
+>
+> /* c. Now, use the regression command to estimate a linear regression where
+> y=empgrowth_9006 and x includes percoll90, perse90, and the dummy variable arc.*/
+>
+> regress empgrowth_9006 percoll90 perse90 arc;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 3, 550) = 16.49
+ Model | 30.3162271 3 10.105409 Prob > F = 0.0000
+ Residual | 337.147802 550 .612996004 R-squared = 0.0825
+-------------+------------------------------ Adj R-squared = 0.0775
+ Total | 367.46403 553 .664491916 Root MSE = .78294
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0171481 .0062247 2.75 0.006 .004921 .0293752
+ perse90 | .0495403 .0073343 6.75 0.000 .0351336 .0639471
+ arc | -.0441713 .0820664 -0.54 0.591 -.2053732 .1170306
+ _cons | -.6413213 .1629652 -3.94 0.000 -.9614317 -.3212109
+------------------------------------------------------------------------------
+
+. /* d. What is the coefficient on arc? What is the interpretation of this
+> coefficient in our model? (Hint: Look at the t-statistic!) */
+>
+> /* INTERPRETATION */
+>
+> /* e. Now, use the regression command to estimate a linear regression where
+> y=empgrowth_9006 and x includes percoll90, perse90, and dummy variables for
+> each of the states in the model (state1,� state13). Exclude the dummy
+> variable for state2 (Georgia) from the model.*/
+>
+> regress empgrowth_9006 percoll90 perse90 state1 state3-state13;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 14, 539) = 7.87
+ Model | 62.3617058 14 4.45440755 Prob > F = 0.0000
+ Residual | 305.102324 539 .566052549 R-squared = 0.1697
+-------------+------------------------------ Adj R-squared = 0.1481
+ Total | 367.46403 553 .664491916 Root MSE = .75236
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0194194 .0062607 3.10 0.002 .0071211 .0317178
+ perse90 | .0504565 .0073927 6.83 0.000 .0359344 .0649785
+ state1 | -.337751 .156141 -2.16 0.031 -.6444705 -.0310316
+ state3 | -.4122454 .1414116 -2.92 0.004 -.6900307 -.1344601
+ state4 | -.3204748 .391161 -0.82 0.413 -1.088862 .4479122
+ state5 | -.2342322 .1698213 -1.38 0.168 -.5678249 .0993604
+ state6 | -.4584991 .1645499 -2.79 0.006 -.7817368 -.1352615
+ state7 | -.696958 .1727595 -4.03 0.000 -1.036322 -.3575936
+ state8 | -.4095359 .1557558 -2.63 0.009 -.7154986 -.1035731
+ state9 | -.5738907 .1446458 -3.97 0.000 -.8580292 -.2897521
+ state10 | -.303029 .2549405 -1.19 0.235 -.8038276 .1977697
+ state11 | -.3601028 .1420734 -2.53 0.012 -.6391883 -.0810173
+ state12 | .2990636 .1622676 1.84 0.066 -.0196908 .6178179
+ state13 | -.5381868 .1482697 -3.63 0.000 -.8294441 -.2469296
+ _cons | -.3670907 .197466 -1.86 0.064 -.754988 .0208067
+------------------------------------------------------------------------------
+
+. /* f. Why did we exclude Georgia from the model in part e? What is
+> the interpretation of the coefficient on state1 (Alabama)?*/
+>
+> /* INTERPRETATION */
+>
+> /* g. Now, add the following additional variables to the model from part e:
+> popsqmi_60 and rural. */
+>
+> regress empgrowth_9006 percoll90 perse90 state1 state3-state13 popsqmi_60 rural;
+
+ Source | SS df MS Number of obs = 554
+-------------+------------------------------ F( 16, 537) = 6.89
+ Model | 62.5846817 16 3.9115426 Prob > F = 0.0000
+ Residual | 304.879348 537 .567745527 R-squared = 0.1703
+-------------+------------------------------ Adj R-squared = 0.1456
+ Total | 367.46403 553 .664491916 Root MSE = .75349
+
+------------------------------------------------------------------------------
+empgrow~9006 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
+-------------+----------------------------------------------------------------
+ percoll90 | .0195789 .0065059 3.01 0.003 .0067988 .032359
+ perse90 | .0496949 .0077024 6.45 0.000 .0345643 .0648255
+ state1 | -.3446213 .1569492 -2.20 0.029 -.652931 -.0363117
+ state3 | -.3966821 .1444483 -2.75 0.006 -.680435 -.1129291
+ state4 | -.331701 .3922187 -0.85 0.398 -1.102172 .4387699
+ state5 | -.2158291 .1750308 -1.23 0.218 -.5596581 .1279998
+ state6 | -.4553793 .1649681 -2.76 0.006 -.7794412 -.1313174
+ state7 | -.7026335 .1733895 -4.05 0.000 -1.043238 -.3620286
+ state8 | -.4128032 .1567536 -2.63 0.009 -.7207286 -.1048778
+ state9 | -.574764 .1455941 -3.95 0.000 -.8607678 -.2887602
+ state10 | -.3148877 .2561012 -1.23 0.219 -.8179707 .1881953
+ state11 | -.3582187 .1423211 -2.52 0.012 -.637793 -.0786444
+ state12 | .2898573 .1638023 1.77 0.077 -.0319146 .6116291
+ state13 | -.5252413 .1500485 -3.50 0.001 -.8199954 -.2304872
+ popsqmi_60 | -.000048 .00015 -0.32 0.749 -.0003427 .0002467
+ rural | -.045763 .0802845 -0.57 0.569 -.2034732 .1119472
+ _cons | -.3396657 .2030335 -1.67 0.095 -.738503 .0591716
+------------------------------------------------------------------------------
+
+. /* h. Test for multicollinearity in your data by running the vif command.*/
+>
+> vif;
+
+ Variable | VIF 1/VIF
+-------------+----------------------
+ state3 | 2.36 0.424391
+ state11 | 2.13 0.469872
+ state9 | 1.97 0.508064
+ state13 | 1.96 0.509022
+ state1 | 1.87 0.535845
+ state8 | 1.79 0.558854
+ state5 | 1.77 0.565196
+ state12 | 1.67 0.597847
+ state6 | 1.61 0.619771
+ state7 | 1.60 0.626321
+ rural | 1.35 0.740336
+ percoll90 | 1.31 0.761969
+ popsqmi_60 | 1.26 0.795968
+ perse90 | 1.25 0.801824
+ state10 | 1.25 0.802875
+ state4 | 1.08 0.929361
+-------------+----------------------
+ Mean VIF | 1.64
+
+. /* i. Are there any problems with multicollinearity in your model? Explain.*/
+>
+> /* INTERPRETATION */
+>
+> /* j. Compare the final model in part g to the model in L1, part g in terms of
+> how much they explain the variance in employment growth. Explain.*/
+>
+> /*INTERPRETATION */
+
+end of do-file
+
+. correlate empgrowth_9006 percoll90 perse90 state1 state3-state13 popsqmi_60 rural
+(obs=554)
+
+ | emp~9006 perco~90 perse90 state1 state3 state4 state5
+-------------+---------------------------------------------------------------
+empgrow~9006 | 1.0000
+ percoll90 | 0.0785 1.0000
+ perse90 | 0.2585 -0.1667 1.0000
+ state1 | -0.0424 0.0055 -0.1638 1.0000
+ state3 | -0.0634 -0.1902 -0.0244 -0.1195 1.0000
+ state4 | 0.0052 0.0344 -0.0081 -0.0260 -0.0335 1.0000
+ state5 | -0.0126 -0.0423 -0.1507 -0.0791 -0.1020 -0.0221 1.0000
+ state6 | -0.0160 0.0637 0.0384 -0.0803 -0.1035 -0.0225 -0.0685
+ state7 | -0.0668 0.2771 0.0067 -0.0754 -0.0972 -0.0211 -0.0643
+ state8 | -0.0284 -0.0262 -0.0091 -0.0905 -0.1167 -0.0254 -0.0772
+ state9 | -0.0581 0.0751 0.0953 -0.1051 -0.1356 -0.0294 -0.0897
+ state10 | -0.0310 0.0361 -0.1523 -0.0433 -0.0559 -0.0121 -0.0370
+ state11 | -0.0048 -0.1238 0.0597 -0.1139 -0.1469 -0.0319 -0.0971
+ state12 | 0.2256 0.0314 0.0196 -0.0826 -0.1066 -0.0231 -0.0705
+ state13 | -0.0656 -0.0809 0.0786 -0.1011 -0.1304 -0.0283 -0.0862
+ popsqmi_60 | -0.0507 0.3227 -0.2656 -0.0575 -0.0742 0.0076 -0.0780
+ rural | -0.0794 -0.2025 -0.0268 -0.0794 0.2735 -0.0575 0.2573
+
+ | state6 state7 state8 state9 state10 state11 state12
+-------------+---------------------------------------------------------------
+ state6 | 1.0000
+ state7 | -0.0653 1.0000
+ state8 | -0.0784 -0.0736 1.0000
+ state9 | -0.0910 -0.0855 -0.1027 1.0000
+ state10 | -0.0375 -0.0352 -0.0423 -0.0491 1.0000
+ state11 | -0.0986 -0.0926 -0.1112 -0.1291 -0.0532 1.0000
+ state12 | -0.0715 -0.0672 -0.0807 -0.0937 -0.0386 -0.1015 1.0000
+ state13 | -0.0875 -0.0822 -0.0987 -0.1146 -0.0473 -0.1242 -0.0901
+ popsqmi_60 | -0.0203 0.0846 0.0835 0.1109 -0.0057 -0.0509 0.0518
+ rural | 0.0120 -0.1334 -0.1291 -0.1316 -0.0680 -0.0028 -0.1829
+
+ | state13 popsq~60 rural
+-------------+---------------------------
+ state13 | 1.0000
+ popsqmi_60 | -0.0200 1.0000
+ rural | 0.1540 -0.1821 1.0000
+
+
+. do "/var/folders/8r/6p_8585x5435jsc5wc_xdv5w0000gn/T//SD66697.000000"
+
+. /* A. Shawn Bandy
+> Lab #4 - L1
+> */
+. /* close previous run do-files */
+. cap log close
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3 lab4/homework4_201200307-1.aux
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+\@writefile{toc}{\contentsline {section}{\numberline {2}Questions}{14}}
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+\documentclass{article}
+\usepackage{mathtools}
+\usepackage[top=2in, bottom=1.5in, left=1in, right=1in]{geometry}
+\usepackage{graphicx}
+\usepackage[normalem]{ulem}
+\usepackage{fancyhdr}
+\pagestyle{fancyplain}
+\usepackage{enumerate}
+\usepackage{verbatim}
+
+\rhead{A. Shawn Bandy
+(003635396)}
+\lhead{Economics 485}
+\begin{document}
+\title{Homework \#4}
+\author{A. Shawn Bandy}
+\date{March 7th, 2013}
+\maketitle
+
+ \section{Lab Problems}
+ \begin{enumerate}[L1]
+ \item
+ \begin{description}
+ \item{STATA code:}
+ {\small {
+ \verbatiminput{lab4.do}
+ }}
+ \item{Log output:}
+ {\small {
+ \verbatiminput{arclab.log}
+ }}
+ \item{Answers:}
+ \begin{description}
+ \item{f. What is the estimated slope coefficient for percoll90? What is the interpretation of this slope coefficient?} \\
+
+ The estimated slope is .0113436. For each unit change in percoll90, there is a 0.113436 unit change in employment growth between 1990 and 2006. It should be noted that in this regression the value for percoll90 is not within the 95\% confidence interval and so there may be no realistic interpretation for the coefficient.\\
+
+ \item{h. What is the estimated slope coefficient for percoll90 in the model from part g? What is the interpretation of this slope coefficient?}\\
+
+ The estimate slope is .0180694. For each unit change in percoll90, there is a .0180694 unit change in employment growth between 1990 and 2006, holding perse90 constant. In this case the coefficient is in the 95\% confidence interval although it has very little impact on the dependent variable.\\
+
+ \item{i. Using your results from parts e and g, does the regression model in part e suffer from omitted variable bias? Explain.}\\
+
+ The model in part e suffers from omitted bias only if the additional variable, perse90, has a zero coefficient in the model in part g \emph{and} the omitted variable is correlated with percoll90. The coefficient for perse90 in model g is \emph{not} zero within the 95\% confidence interval and there is a negative correlation between the variables. We can conclude that there is omitted variable bias in model e.
+
+ \end{description}
+ \end{description}
+ \item
+ \begin{description}
+ \item{STATA code:}
+ {\small {
+ \verbatiminput{lab42.do}
+ }}
+ \item{Log output:}
+ {\small {
+ \verbatiminput{arclab2.log}
+ }}
+ \item{Answers:}
+ \begin{description}
+
+ \item{b. Does the STATA output from part a) include both the new variables? Explain what happened.}\\
+
+ STATA omits an independent variable when there is a dependency between it and one or more other variables. Running \emph{regress pci90\_thousands percoll90 perse90 pci90} shows that there is a dependency between pci90\_thousands and pci90.\\
+
+ \item{d. What is the coefficient on arc? What is the interpretation of this coefficient in our model?}\\
+
+ The coefficient for arc is -.0441713, so for each unit change in the variable arc there is about a 4\% drop in employment growth between 1990 and 2006. Because the t-stat is -0.54 and compounded by having a coefficient fairly close to zero, we should interpret this as almost certainly having no meaning in our model.\\
+
+ \item{f. Why did we exclude Georgia from the model in part e? What is the interpretation of the coefficient on state1 (Alabama)?}\\
+
+ We excluded Georgia because not doing so for at least one categorical dummy variable leads to perfect multicollinearity. In other words, if we included all the dummy variables then the sum of all dummy variables for each observation. In another sense, the Georgia variable becomes the basis by which all other dummy variables are measured. \\
+
+ \item{i. Are there any problems with multicollinearity in your model? Explain.}\\
+
+ The VIF($\hat{\beta}_i$) for all variables in the regression is less than 5 (or less than 10) so I would say that our model is reasonably free of multicollinearity. As a rule-of-thumb, multicollinearity is not considered high when VIF($\hat{\beta}_i$) is less than 5 (or less than 10, depending on the particular thumb). \\
+
+ \item{j. Compare the final model in part g to the model in L1, part g in terms of how much they explain the variance in employment growth. Explain.}\\
+
+ $R^2$ is the measure of how much variation in the dependent variable is explained by the regression model. In the L2.g model, adjusted $R^2$ is 0.1456. In the L1.g model, adjusted $R^2$ is 0.0787 which is about half of the L2.g model. The F-stat for both would lead us to reject the null hypothesis for the model at the 95\% confidence level. In the L2.g model, the t-stat is low enough for popsqmi\_60 and rural that we cannot reject the null hypothesis, but these variables are correlated with others in the model and so should be left in. \\
+
+ \end{description}
+ \end{description}
+ \end{enumerate}
+
+ \section{Questions}
+
+ \begin{enumerate}[Q1]
+ \item
+Suppose you are interested in whether there is a gender bias in setting wages.
+ \begin{enumerate}[a.]
+ \item
+
+You get data from the Current Population Survey. You then use STATA to estimate a regression function as follows:
+
+\begin{center}
+$wage_i = \beta_0 + \beta_1 Female_i + \beta_2 Nonwhite_i + \beta_3 Union Member_i + \beta_4 Education_i + \beta_5 Experience_i + u_i $
+\end{center}
+\begin{samepage}
+Some of the Stata output is as follows:
+
+\nopagebreak
+\includegraphics[width=400px]{q1_a_1}
+\end{samepage}
+
+What is the coefficient on female? What is the interpretation of this coefficient? Calculate the t-statistic and test whether it is statistically significant at the 5\% level. Based on the regression, do you think that women earn less than men?\\
+
+The coefficient for female is -3.0749. Holding all other variables in the model constant, being female reduces one's wages by -3.0749 dollars.\footnote{I am assuming the unit here is dollars.} The t-statistic is calculated as $|\frac{\hat{\beta_1}}{SE}| = |\frac{-3.0749}{0.36462}| = |-8.43| >1.96$ so this variable is statistically significant at the 5\% level. Yes, I would say based on this regression, women earn less than men.
+
+ \item
+What are the R2 and Adjusted R2 of this regression model?\\
+
+$R^2$ equals 0.3233 and $\bar{R^2}$ equals 0.3207.
+
+ $R^2 \equiv 1 - \frac{SS_{residuals}}{SS_{total}} = 1 - \frac{54342.5}{80309.8} = 0.3233$
+
+ $\bar{R^2} = 1 - \frac{SS_{residuals}}{SS_{total}} * \frac{df_t}{df_e} = 1 - \frac{54342.5}{80309.8} * \frac{1288}{1283} = 0.3207$\\
+
+ \item
+As an alternative to the regression in part a, you collect data about gender and salaries from people who stop by a table at the local mall. You then use a â"difference in means" test to see if the average salary for women is less than the average salary for men. You find that there is a statistical difference in the means with women's average salary statistically lower than men's.\\
+
+I see.\\
+
+ \item
+Even though both approaches give you the same answer, explain which method is a better way to test if women earn less than men.\\
+
+Using the Current Population Survey is a much better method. Sampling from a population is, at best, a means of estimating population parameters. In this case, the sample size may be insufficient and the sample may in some way be self-selecting but more importantly a table at a local mall almost certainly does not adequately represent the population. \\
+
+ \item
+\begin{samepage}
+What if you also want to know whether women and men get the same additional wages for each additional year of school? To test this, you generate a new variable (female*education) which interacts the female dummy variable and education. The results of the regression are below:
+
+\nopagebreak
+\includegraphics[width=400px]{q1_e_1}
+
+What is the coefficient on women\_educ? Interpret the meaning of this coefficient in this regression model. \\
+
+The coefficient on women\_educ is -0.2734 and it is statistically significant at the 5\% confidence level. All other variables held constant, women receive -0.2734 fewer dollars per unit of education. \footnote{I would have thought doing this would lead to a dependency issue if women\_educ is calculated directly from two other independent variables, but this does not appear to be an issue.}
+
+\end{samepage}
+
+ \end{enumerate}
+ \item
+Use the results from L1 to do the following. Follow the directions carefully in terms of what to calculate. Even if other parts of L1 include the answer, show how these elements are calculated, assuming you only had certain results. Please show the formula you use and the steps you take to get to the final answer. You can always use the output to see if you did it right!
+
+ \begin{enumerate}[a.]
+ \item
+Use the results from L1 parts j and l to calculate the coefficient of percoll90 in the following regression model:
+
+\begin{center}
+$empgrowth\_9006_i = \beta_0 + \beta_1 percoll90_i + \beta_2 perse90_i + u_i$
+\end{center}
+
+I used the following formula to estimate $\beta_1$ : $\hat{\beta_1} = \frac{COV(empgrowth\_9006,residual)}{VAR(residual)} = \frac{.559228}{ 5.5682^2} = 0.01804$, where VAR(residual) = $Root MSE^2$\\
+ \item
+
+Calculate the t-statistic to test whether the coefficient on percoll90 is different than zero. Note: In this part it is OK to use the standard error calculated by the regression output rather than having to calculate it.\\
+
+The t-statistic for $\hat{\beta_1}$ is 3.0157 which is greater than 1.96, making this statistically significant at the 95\% confidence interval and we can reject $H_0$.\\
+
+I used the following formula to estimate the t-stat value: $t-stat = \frac{\hat{\beta_1}}{SE} = \frac{0.01804}{.0059809} = 3.0157$.\\
+ \end{enumerate}
+ \end{enumerate}
+\end{document}
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88 lab4/lab4 (Autosaved)
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+/* A. Shawn Bandy
+ Lab #4 - L1
+*/
+/* close previous run do-files */
+cap log close
+set more 1
+clear
+#delimit ;
+
+cd "/Users/Shawn/src/econ485/lab4";
+log using arclab1x.log , replace;
+use "arclab";
+
+/*a. Create a dummy variable, arc that is equal to one if the arc_county variable
+ indicates it is an ARC county. Otherwise, non-ARC counties should have a
+ value of zero. This variable will be used to see if there is a difference
+ in employment growth between the ARC and non-ARC counties.*/
+
+ gen arc=1 if arc_county=="ARC";
+ replace arc=0 if arc==.;
+
+ /*b. Create a set of dummy variables for each of the 13 states in the ARC region.
+Use tabulate with the prefix state to create these variables. Hint: the state
+variable has the unique names of the 13 states for each county in the dataset.*/
+
+tabulate state, gen(state);
+
+/*c. Create a new variable empgrowth_9006 that is the percent change in employment
+ from 1990 to 2006. Use the label command to label this �Percent change in
+ employment from 1990 to 2006�. Make sure you save the data as arcdata1.dta so you
+ can use it for the next problem.*/
+
+ gen empgrowth_9006 = (emp06 - emp90) / emp90;
+save arcdata_n.dta, replace;
+
+/*d. Use the summarize command to look at the description of the variables in
+ this dataset. */
+summarize;
+
+/*e. Use the regression command to estimate the following linear
+ regression model, under the assumption that college educated people
+ contribute to employment growth: */
+regress empgrowth_9006 percoll90;
+
+/*f. What is the estimated slope coefficient for percoll90?
+ What is the interpretation of this slope coefficient?
+
+ INTERPRETATION
+
+ */
+
+ /*g. Use the regression command to estimate the following
+linear regression model, where we now test whether college
+educated people and having a higher percentage of self-employed
+individuals are important to employment growth in this region:*/
+regress empgrowth_9006 percoll90 perse90;
+
+/*h. What is the estimated slope coefficient for percoll90 in
+ the model from part g? What is the interpretation of this slope coefficient?
+
+ INTERPRETATION
+
+ */
+
+/*i. Using your results from parts e and g, does the regression model in part
+e suffer from omitted variable bias? Explain.
+
+INTERPRETATION
+
+*/
+
+
+/*j. Use the regression command to estimate the following linear
+ regression model:*/
+
+ regress percoll90 perse90;
+
+/*k. Use the predict command to capture the residuals from the regression in
+ part j in a new variable named res.*/
+
+ predict residual, res;
+
+/*l. Use the covariance option of the correlate command to examine the
+ covariance between res and empgrowth_9006.*/
+ correlate res empgrowth_9006, covariance;
+
+save arcdata1.dta, replace;
+log close;
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63 lab4/lab42 (Autosaved)
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+/* A. Shawn Bandy
+ Lab #4
+*/
+/* close previous run do-files */
+cap log close
+set more 1
+clear
+#delimit ;
+
+cd "/Users/shawn/src/econ485/lab4";
+log using arclab2x.log , replace;
+use "arcdata1";
+
+/* a. Now, we want to test if additional variables would add to the explanatory
+value of employment growth in the region. Add the following additional variables
+ to the model from L1 part g: pci90_thousands and pci90. */
+
+ regress empgrowth_9006 percoll90 perse90 pci90_thousands pci90;
+
+/* b. Does the STATA output from part a) include both the new variables?
+Explain what happened.*/
+
+/*INTERPRETATION */
+
+/* c. Now, use the regression command to estimate a linear regression where
+ y=empgrowth_9006 and x includes percoll90, perse90, and the dummy variable arc.*/
+
+ regress empgrowth_9006 percoll90 perse90 arc;
+
+/* d. What is the coefficient on arc? What is the interpretation of this
+coefficient in our model? (Hint: Look at the t-statistic!) */
+
+/* INTERPRETATION */
+
+/* e. Now, use the regression command to estimate a linear regression where
+ y=empgrowth_9006 and x includes percoll90, perse90, and dummy variables for
+ each of the states in the model (state1,� state13). Exclude the dummy
+ variable for state2 (Georgia) from the model.*/
+
+ regress empgrowth_9006 percoll90 perse90 state1 state3-state13;
+
+/* f. Why did we exclude Georgia from the model in part e? What is
+the interpretation of the coefficient on state1 (Alabama)?*/
+
+/* INTERPRETATION */
+
+/* g. Now, add the following additional variables to the model from part e:
+ popsqmi_60 and rural. */
+
+ regress empgrowth_9006 percoll90 perse90 state1 state3-state13 popsqmi_60 rural;
+
+/* h. Test for multicollinearity in your data by running the vif command.*/
+
+vif;
+
+/* i. Are there any problems with multicollinearity in your model? Explain.*/
+
+/* INTERPRETATION */
+
+/* j. Compare the final model in part g to the model in L1, part g in terms of
+ how much they explain the variance in employment growth. Explain.*/
+
+ /*INTERPRETATION */
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63 lab4/lab42.do
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+/* A. Shawn Bandy
+ Lab #4
+*/
+/* close previous run do-files */
+cap log close
+set more 1
+clear
+#delimit ;
+
+cd "C:\Users\cla-spa206.CAMPUS-DOMAIN\Desktop\econ485-lab4\lab4";
+log using arclab2.log , replace;
+use "arcdata1";
+
+/* a. Now, we want to test if additional variables would add to the explanatory
+value of employment growth in the region. Add the following additional variables
+ to the model from L1 part g: pci90_thousands and pci90. */
+
+ regress percoll90 perse90 pci90_thousands pci90;
+
+/* b. Does the STATA output from part a) include both the new variables?
+Explain what happened.*/
+
+/*INTERPRETATION */
+
+/* c. Now, use the regression command to estimate a linear regression where
+ y=empgrowth_9006 and x includes percoll90, perse90, and the dummy variable arc.*/
+
+ regress empgrowth_9006 percoll90 perse90 arc;
+
+/* d. What is the coefficient on arc? What is the interpretation of this
+coefficient in our model? (Hint: Look at the t-statistic!) */
+
+/* INTERPRETATION */
+
+/* e. Now, use the regression command to estimate a linear regression where
+ y=empgrowth_9006 and x includes percoll90, perse90, and dummy variables for
+ each of the states in the model (state1,… state13). Exclude the dummy
+ variable for state2 (Georgia) from the model.*/
+
+ regress empgrowth_9006 percoll90 perse90 state1 state3-state13;
+
+/* f. Why did we exclude Georgia from the model in part e? What is
+the interpretation of the coefficient on state1 (Alabama)?*/
+
+/* INTERPRETATION */
+
+/* g. Now, add the following additional variables to the model from part e:
+ popsqmi_60 and rural. */
+
+ regress empgrowth_9006 percoll90 perse90 state1 state3-state13 popsqmi_60 rural;
+
+/* h. Test for multicollinearity in your data by running the vif command.*/
+
+vif;
+
+/* i. Are there any problems with multicollinearity in your model? Explain.*/
+
+/* INTERPRETATION */
+
+/* j. Compare the final model in part g to the model in L1, part g in terms of
+ how much they explain the variance in employment growth. Explain.*/
+
+ /*INTERPRETATION */
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