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Question: Metro Transit seeks to understand the cross price elasticity of demand for bus transit. This data...

Metro Transit seeks to understand the cross price elasticity of demand for bus transit. This dataset includes deseasonalized ridership data for one of the Metro Transit commuter markets from January 2009 to May of 2016 along with gas price and unemployment data in the twin cities region. The data are all in natural log form and we will assume constant elasticity/log-linear functional form for this analysis. Metro Transit has not changed the price during this period, so we will not consider this in the analysis. Please perform a regression to identify the cross price elasticity of demand for gas prices.

1. Run a regression using OLS

2. Provide the regression output

3. Discuss the effect of gas prices and unemployment on ridership

4. Are these effects elastic? Inelastic?

5. What variables might we be excluding?

6. Are there any policy implications for your findings?

Month LN_Deseasonalized_Ridership LN_Gas Unemployment Jan-09 13.37310641 0.60976557 1.90822905 Feb-09 13.32106787 0.63127178 1.94090292 Mar-09 13.4810664 0.66782937 1.97254304 Apr-09 13.46502645 0.69813472 1.99616889 May-09 13.26538987 0.81977983 2.0192493 Jun-09 13.37107386 0.96698385 2.03232635 Jul-09 13.31737585 0.89199804 2.04523473 Aug-09 13.29812228 0.9282193 2.04904754 Sep-09 13.40551694 0.88376754 2.05284587 Oct-09 13.48313729 0.90421815 2.04997282 Nov-09 13.22331027 0.94000726 2.04709163 Dec-09 13.2114525 0.91629073 2.0399689 Jan-10 13.29923244 0.96698385 2.03279493 Feb-10 13.30863827 0.9282193 2.02433493 Mar-10 13.50917425 0.98581679 2.01580275 Apr-10 13.42724516 1.01884732 2.00796192 May-10 13.24494832 1.00063188 2.00005913 Jun-10 13.36003719 0.97077892 1.99195164 Jul-10 13.22552564 0.97455964 1.98377789 Aug-10 13.34415553 0.96698385 1.97365218 Sep-10 13.39940096 0.97832612 1.9634229 Oct-10 13.45701554 1.00063188 1.95311315 Nov-10 13.30133828 1.01523068 1.94269585 Dec-10 13.21605909 1.05431203 1.93389381 Jan-11 13.38636673 1.0919233 1.92501362 Feb-11 13.30487091 1.11841492 1.91436936 Mar-11 13.55652222 1.21491274 1.90361058 Apr-11 13.45702078 1.28647403 1.88962759 May-11 13.39155446 1.30833282 1.8754463 Jun-11 13.43485923 1.24415459 1.86031211 Jul-11 13.22750392 1.24126859 1.84494551 Aug-11 13.49816051 1.23547147 1.83016944 Sep-11 13.44749317 1.22082992 1.81517191 Oct-11 13.51930471 1.15373159 1.79949266 Nov-11 13.38385594 1.13140211 1.78356347 Dec-11 13.23804989 1.10525683 1.76837773 Jan-12 13.43538754 1.137833 1.75295765 Feb-12 13.408108 1.1817272 1.74092747 Mar-12 13.51266369 1.26412673 1.7287508 Apr-12 13.47070802 1.26412673 1.72037231 May-12 13.45759496 1.22082992 1.71192284 Jun-12 13.36429221 1.18478998 1.70470555 Jul-12 13.31210014 1.16627094 1.69743597 Aug-12 13.48748903 1.24990174 1.68871885 Sep-12 13.38541267 1.26976054 1.67992527 Oct-12 13.6355304 1.20896035 1.66897507 Nov-12 13.36439471 1.13140211 1.65790364 Dec-12 13.12661336 1.09527339 1.6450336 Jan-13 13.4380618 1.08518927 1.63199596 Feb-13 13.3397626 1.20597081 1.61841906 Mar-13 13.42558241 1.21194097 1.60465549 Apr-13 13.52591974 1.17557333 1.59127618 May-13 13.39815126 1.22964055 1.57771564 Jun-13 13.2768924 1.23256026 1.56521661 Jul-13 13.37759076 1.17248214 1.55255937 Aug-13 13.36846794 1.17248214 1.54134385 Sep-13 13.45266352 1.16627094 1.53000112 Oct-13 13.64705169 1.09861229 1.51727745 Nov-13 13.30320038 1.0612565 1.50438957 Dec-13 13.18893326 1.05779029 1.48812076 Jan-14 13.34526174 1.07840958 1.47158267 Feb-14 13.31717668 1.10856262 1.45346925 Mar-14 13.45446108 1.16938136 1.43502167 Apr-14 13.51276241 1.18478998 1.41652842 May-14 13.36842706 1.1817272 1.39768647 Jun-14 13.34653835 1.2029723 1.37977868 Jul-14 13.38627655 1.15373159 1.36154434 Aug-14 13.32658434 1.12817109 1.34477916 Sep-14 13.41585552 1.10856262 1.3277281 Oct-14 13.55875286 1.0260416 1.3144981 Nov-14 13.13673318 0.95935022 1.30109071 Dec-14 13.13530136 0.78845736 1.29054446 Jan-15 13.27057192 0.58778666 1.27988607 Feb-15 13.2181603 0.69314718 1.26989059 Mar-15 13.37712701 0.76546784 1.25979391 Apr-15 13.3900275 0.76546784 1.25140576 May-15 13.11402112 0.84156719 1.24294666 Jun-15 13.25916856 0.90016135 1.23700489 Jul-15 13.27298664 0.88376754 1.23102731 Aug-15 13.25256961 0.85015093 1.22921619 Sep-15 13.35563596 0.74193734 1.22740208 Oct-15 13.47766232 0.75141609 1.22745219 Nov-15 13.13445939 0.64710324 1.2275023 Dec-15 13.12019576 0.54812141 1.22782692 Jan-16 13.21435484 0.48242615 1.22815114 Feb-16 13.24498229 0.39877612 1.22894265 Mar-16 13.37820262 0.56531381 1.22973324 Apr-16 13.32100748 0.61518564 1.23095431 May-16 13.20547256 0.70309751 1.23217418

Explanation / Answer

Answer

As per the given data from - Jan09 to May16 then solution is;

Part 1:

We ran the regression using R.

code used :-

> reg<- lm(ln_ridership ~ ln_GAS + ln_unemployment , data = datafile name)
> summary(reg)

The result is as follows:

Residuals:

Min 1Q Median 3Q Max

-0.249822 -0.059711 -0.005834 0.066461 0.275685

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 13.07126 0.07388 176.937 <2e-16 ***

ln_GAS 0.21077 0.05424 3.885 0.0002 ***

ln_unemployment 0.04518 0.04048 1.116 0.2674   

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Part 2

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.106 on 86 degrees of freedom

Multiple R-squared: 0.1926, Adjusted R-squared: 0.1739

F-statistic: 10.26 on 2 and 86 DF, p-value: 0.0001009

Part 3:

effect of gas price = If gas prices changes by 1 % then on an average ridership changes by 0.21 % keeping all other variables constant.

effect of unemployment = If unemployment changes by 1% then on an average ridership changes by 0.04% keeping all other variables constant.

Part 4 :-

both of these effects are inelastic as elasticity is less than 1. The regression coefficients are elasticities.

Part 5:

we might exclude unemployment as it is statistically insignificant since the p value is less than 2( also p value is less than alpha which we assume to be 5%)

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