Question

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

Answer 1

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   

---

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%)