Hello,
My objective is to estimate the effect that a 1% change in the volume of ride-share trips completed has on the volume of trips completed by taxis. In other words, I am trying to estimate the elasticity of demand for taxi trips with respect to ride-share trips. The setting for my research is NYC.
The data I am using includes daily observations from January 1, 2015 - December 31, 2017 on the number of trips completed by taxis and the ride-share platform. I have these data point for the entire market, as well as for each of the five boroughs in NYC. Therefore, my panel variable is: location (1-5, for 5 Boroughs), and my time variable is: date, 20089 to 21184. The panel is strongly balanced.
My hope is that I can come up with an elasticity estimate for the entire NYC market, as well individual estimates for each of the five boroughs. I have struggle with choosing the correct model, so I am really hoping you guys can help me out. Below are the results of the various models I have run. From these I have the following concerns:
1. The OLS coef. is positive, despite me knowing the relationship between the variables is negatively correlated
2. None of my coefficients should be > 1 or < -1 since I am estimating elasticity; however, locations 4 and 5 in the RE model both have a coef. < -1.
3. The RE model obtains a suspiciously large overall and between R-sq.
4. When I include "i.location" and "i.year" in the random effects model, my results change - namely R-sq.
I am also hoping for some advice on whether I should be using the log values of the daily number of trips or the log-differenced values in order to capture elasticity. When I log-difference the values, I seem to get a positive correlation between the variables, which, again, is not what I want.
I am new to Stata, so please forgive my ignorance if I have made a very obvious mistake. In addition, my apologies in advance if the results presented below are formatted poorly.
Thanks for your help!
OLS
. regress logyg logx
Source | SS df MS Number of obs = 5,480
-------------+---------------------------------- F(1, 5478) = 1116.82
Model | 700.994682 1 700.994682 Prob > F = 0.0000
Residual | 3438.36686 5,478 .627668285 R-squared = 0.1693
-------------+---------------------------------- Adj R-squared = 0.1692
Total | 4139.36155 5,479 .755495811 Root MSE = .79226
------------------------------------------------------------------------------
logyg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | .4331075 .01296 33.42 0.000 .4077009 .4585142
_cons | 7.147051 .1455509 49.10 0.000 6.861713 7.432388
------------------------------------------------------------------------------
FE
. xtreg logyg logx, re
Random-effects GLS regression Number of obs = 5,480
Group variable: location Number of groups = 5
R-sq: Obs per group:
within = 0.1377 min = 1,096
between = 0.4138 avg = 1,096.0
overall. = 0.1693 max = 1,096
Wald chi2(1) = 872.93
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
logyg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | -.1557063 .0052701 -29.55 0.000 -.1660354 -.1453772
_cons | 13.74201 .3758786 36.56 0.000 13.0053 14.47872
-------------+----------------------------------------------------------------
sigma_u | .82988976
sigma_e | .20857212
rho | .94058839 (fraction of variance due to u_i)
------------------------------------------------------------------------------
RE: 1
. xtreg logyg logx i.location i.year, re
Random-effects GLS regression Number of obs = 5,480
Group variable: location Number of groups = 5
R-sq: Obs per group:
within = 0.3471 min = 1,096
between = 1.0000 avg = 1,096.0
overall. = 0.9564 max = 1,096
Wald chi2(7) = 120146.95
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
logyg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | .1074844 .0080007 13.43 0.000 .0918033 .1231656
|
location |
2 | -.0621415 .0086306 -7.20 0.000 -.079057 -.0452259
3 | -.4222705 .0098275 -42.97 0.000 -.4415321 -.4030089
4 | -1.04315 .016972 -61.46 0.000 -1.076414 -1.009885
5 | -2.148028 .0113356 -189.49 0.000 -2.170246 -2.125811
|
year |
2016 | -.1949114 .0079084 -24.65 0.000 -.2104116 -.1794112
2017 | -.4265239 .0104341 -40.88 0.000 -.4469744 -.4060735
|
_cons | 11.73642 .0919199 127.68 0.000 11.55626 11.91658
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .18152611
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------
RE: 2
. xtreg logyg logx, re
Random-effects GLS regression Number of obs = 5,480
Group variable: location Number of groups = 5
R-sq: Obs per group:
within = 0.1377 min = 1,096
between = 0.4138 avg = 1,096.0
overall = 0.1693 max = 1,096
Wald chi2(1) = 872.93
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
logyg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | -.1557063 .0052701 -29.55 0.000 -.1660354 -.1453772
_cons | 13.74201 .3758786 36.56 0.000 13.0053 14.47872
-------------+----------------------------------------------------------------
sigma_u | .82988976
sigma_e | .20857212
rho | .94058839 (fraction of variance due to u_i)
------------------------------------------------------------------------------
My objective is to estimate the effect that a 1% change in the volume of ride-share trips completed has on the volume of trips completed by taxis. In other words, I am trying to estimate the elasticity of demand for taxi trips with respect to ride-share trips. The setting for my research is NYC.
The data I am using includes daily observations from January 1, 2015 - December 31, 2017 on the number of trips completed by taxis and the ride-share platform. I have these data point for the entire market, as well as for each of the five boroughs in NYC. Therefore, my panel variable is: location (1-5, for 5 Boroughs), and my time variable is: date, 20089 to 21184. The panel is strongly balanced.
My hope is that I can come up with an elasticity estimate for the entire NYC market, as well individual estimates for each of the five boroughs. I have struggle with choosing the correct model, so I am really hoping you guys can help me out. Below are the results of the various models I have run. From these I have the following concerns:
1. The OLS coef. is positive, despite me knowing the relationship between the variables is negatively correlated
2. None of my coefficients should be > 1 or < -1 since I am estimating elasticity; however, locations 4 and 5 in the RE model both have a coef. < -1.
3. The RE model obtains a suspiciously large overall and between R-sq.
4. When I include "i.location" and "i.year" in the random effects model, my results change - namely R-sq.
I am also hoping for some advice on whether I should be using the log values of the daily number of trips or the log-differenced values in order to capture elasticity. When I log-difference the values, I seem to get a positive correlation between the variables, which, again, is not what I want.
I am new to Stata, so please forgive my ignorance if I have made a very obvious mistake. In addition, my apologies in advance if the results presented below are formatted poorly.
Thanks for your help!
OLS
. regress logyg logx
Source | SS df MS Number of obs = 5,480
-------------+---------------------------------- F(1, 5478) = 1116.82
Model | 700.994682 1 700.994682 Prob > F = 0.0000
Residual | 3438.36686 5,478 .627668285 R-squared = 0.1693
-------------+---------------------------------- Adj R-squared = 0.1692
Total | 4139.36155 5,479 .755495811 Root MSE = .79226
------------------------------------------------------------------------------
logyg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | .4331075 .01296 33.42 0.000 .4077009 .4585142
_cons | 7.147051 .1455509 49.10 0.000 6.861713 7.432388
------------------------------------------------------------------------------
FE
. xtreg logyg logx, re
Random-effects GLS regression Number of obs = 5,480
Group variable: location Number of groups = 5
R-sq: Obs per group:
within = 0.1377 min = 1,096
between = 0.4138 avg = 1,096.0
overall. = 0.1693 max = 1,096
Wald chi2(1) = 872.93
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
logyg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | -.1557063 .0052701 -29.55 0.000 -.1660354 -.1453772
_cons | 13.74201 .3758786 36.56 0.000 13.0053 14.47872
-------------+----------------------------------------------------------------
sigma_u | .82988976
sigma_e | .20857212
rho | .94058839 (fraction of variance due to u_i)
------------------------------------------------------------------------------
RE: 1
. xtreg logyg logx i.location i.year, re
Random-effects GLS regression Number of obs = 5,480
Group variable: location Number of groups = 5
R-sq: Obs per group:
within = 0.3471 min = 1,096
between = 1.0000 avg = 1,096.0
overall. = 0.9564 max = 1,096
Wald chi2(7) = 120146.95
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
logyg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | .1074844 .0080007 13.43 0.000 .0918033 .1231656
|
location |
2 | -.0621415 .0086306 -7.20 0.000 -.079057 -.0452259
3 | -.4222705 .0098275 -42.97 0.000 -.4415321 -.4030089
4 | -1.04315 .016972 -61.46 0.000 -1.076414 -1.009885
5 | -2.148028 .0113356 -189.49 0.000 -2.170246 -2.125811
|
year |
2016 | -.1949114 .0079084 -24.65 0.000 -.2104116 -.1794112
2017 | -.4265239 .0104341 -40.88 0.000 -.4469744 -.4060735
|
_cons | 11.73642 .0919199 127.68 0.000 11.55626 11.91658
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .18152611
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------
RE: 2
. xtreg logyg logx, re
Random-effects GLS regression Number of obs = 5,480
Group variable: location Number of groups = 5
R-sq: Obs per group:
within = 0.1377 min = 1,096
between = 0.4138 avg = 1,096.0
overall = 0.1693 max = 1,096
Wald chi2(1) = 872.93
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
logyg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
logx | -.1557063 .0052701 -29.55 0.000 -.1660354 -.1453772
_cons | 13.74201 .3758786 36.56 0.000 13.0053 14.47872
-------------+----------------------------------------------------------------
sigma_u | .82988976
sigma_e | .20857212
rho | .94058839 (fraction of variance due to u_i)
------------------------------------------------------------------------------
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