Help with the Error Message in R "Error in 1:nchid : result would be too long a vector"
Hello,
I tried to reduce the size of my dataframe. Now I have 57 columns of which
29 are already dummy coded. If I run *mldata1<- mlogit.data(mydata1,
shape = "long", alt.var = "Alt_name", choice = "Choice_binary", id.var =
"IND") *it still gives me the same error message-* Error in 1:nchid :
result would be too long a vector. *
I will not use all of those variables in one regression model, but I need
those for different model specifications. The Excel file I created from my
survey looks like the attached file. The main data is a panel of 516
individuals each answering 9 questions over 3 alternatives.
Following is the output of the summary of the dataframe.
summary(mydata1)
IND QES STR ALT_name
Choice_binary
Min. : 1.0 Min. :1 Min. : 101 Length:13932 Min.
:0.0000
1st Qu.:129.8 1st Qu.:3 1st Qu.:12978 Class :character 1st
Qu.:0.0000
Median :258.5 Median :5 Median :25855 Mode :character Median
:0.0000
Mean :258.5 Mean :5 Mean :25855 Mean
:0.3333
3rd Qu.:387.2 3rd Qu.:7 3rd Qu.:38732 3rd
Qu.:1.0000
Max. :516.0 Max. :9 Max. :51609 Max.
:1.0000
Price Refuel_availability Registration_charges Running_cost
Min. : 9.00 Min. :0.25 Min. :0.00000 Min. :115.0
1st Qu.:10.00 1st Qu.:0.75 1st Qu.:0.04000 1st Qu.:192.0
Median :10.00 Median :0.90 Median :0.06000 Median :268.0
Mean :10.33 Mean :0.80 Mean :0.05333 Mean :268.2
3rd Qu.:11.00 3rd Qu.:1.00 3rd Qu.:0.08000 3rd Qu.:383.0
Max. :12.00 Max. :1.00 Max. :0.08000 Max. :383.0
Market_share Friends_share Refuel_time Emission
Min. :0.0500 Min. :0.0000 Min. : 5.00 Min. :0.0000
1st Qu.:0.1500 1st Qu.:0.1500 1st Qu.: 5.00 1st Qu.:0.0000
Median :0.2500 Median :0.3000 Median : 5.00 Median :0.7500
Mean :0.3333 Mean :0.3333 Mean :13.33 Mean :0.5833
3rd Qu.:0.6000 3rd Qu.:0.5500 3rd Qu.:30.00 3rd Qu.:1.0000
Max. :0.9000 Max. :1.0000 Max. :30.00 Max. :1.0000
Sex Age2 Age3 Age4
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :1.0000 Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.7791 Mean :0.4574 Mean :0.2326 Mean :0.1531
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
Edu_PG Edu_Oth Occu_Pvt Occu_Pub
Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
Mean :0.4147 Mean :0.1841 Mean :0.376 Mean :0.2733
3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
Occu_SE Location_metro Location_majorcity Ahm
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.00000
Median :0.0000 Median :1.0000 Median :0.0000 Median :0.00000
Mean :0.2655 Mean :0.7655 Mean :0.1453 Mean :0.04457
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
Ben Chen NCR Hyd
Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.00000
1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
Median :0.00000 Median :0.00000 Median :0.0000 Median :0.00000
Mean :0.06977 Mean :0.04651 Mean :0.2558 Mean :0.03682
3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:0.00000
Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.00000
Kol Mum MajCity HH_size
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. : 1.000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.: 3.000
Median :0.0000 Median :0.0000 Median :0.0000 Median : 5.000
Mean :0.2016 Mean :0.1105 Mean :0.1453 Mean : 4.463
3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.: 6.000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :10.000
Children IG2 IG3 IG4
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :1.0000 Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.8721 Mean :0.3818 Mean :0.4109 Mean :0.1841
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
Max. :4.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
HH_cars PPC_morethan10 Daily_travel_medium Daily_travel_long
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
Median :0.0000 Median :0.0000 Median :0.0000 Median :0.00000
Mean :0.4864 Mean :0.4516 Mean :0.3702 Mean :0.02713
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.00000
Max. :3.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
Garage_y DL_y Own_accom Freerider_tot
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :2.000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:2.000
Median :1.0000 Median :1.0000 Median :1.0000 Median :2.000
Mean :0.7267 Mean :0.6357 Mean :0.6647 Mean :2.244
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:2.000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :8.000
Satisfaction_tot Political_view WTP_env_tot Warmglow_tot
Standout
Min. : 2.000 Min. :1.000 Min. : 2.000 Min. : 2.00 Min.
:1.000
1st Qu.: 3.000 1st Qu.:3.000 1st Qu.: 7.000 1st Qu.: 6.00 1st
Qu.:2.000
Median : 4.000 Median :3.000 Median : 8.000 Median : 8.00 Median
:3.000
Mean : 4.264 Mean :3.258 Mean : 8.124 Mean : 7.61 Mean
:2.657
3rd Qu.: 5.000 3rd Qu.:4.000 3rd Qu.: 9.000 3rd Qu.: 9.00 3rd
Qu.:3.000
Max. :10.000 Max. :5.000 Max. :10.000 Max. :10.00 Max.
:5.000
Acceptance_new Climate_perception Env_pref Tech_leader
Min. :1.0 Min. :1.000 Min. :1.000 Min. :1.0
1st Qu.:2.0 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:2.0
Median :3.0 Median :5.000 Median :3.000 Median :2.0
Mean :2.8 Mean :4.483 Mean :3.093 Mean :2.5
3rd Qu.:4.0 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:3.0
Max. :5.0 Max. :5.000 Max. :5.000 Max. :5.0
Social_motivation_tot EV_risk_tot EV_awareness_tot
Min. : 3.00 Min. : 2.000 Min. : 3.000
1st Qu.: 9.00 1st Qu.: 8.000 1st Qu.: 4.000
Median :11.00 Median : 9.000 Median : 5.000
Mean :10.62 Mean : 8.661 Mean : 5.419
3rd Qu.:12.00 3rd Qu.:10.000 3rd Qu.: 6.000
Max. :15.00 Max. :10.000 Max. :15.000
On Tue, Sep 22, 2020 at 2:07 AM Rahul Chakraborty <chakrarahul at gmail.com>
wrote:
Hello,
Here is the result of summary(mydata)
summary(mydata)
IND Block QES STR ALT
Min. : 1.0 Min. :1.000 Min. :1 Min. : 101 Min. :1
1st Qu.:129.8 1st Qu.:1.000 1st Qu.:3 1st Qu.:12978 1st Qu.:1
Median :258.5 Median :2.000 Median :5 Median :25855 Median :2
Mean :258.5 Mean :2.467 Mean :5 Mean :25855 Mean :2
3rd Qu.:387.2 3rd Qu.:4.000 3rd Qu.:7 3rd Qu.:38732 3rd Qu.:3
Max. :516.0 Max. :4.000 Max. :9 Max. :51609 Max. :3
ALT_name ASC Choice Choice_binary
Length:13932 Min. :0.0000 Min. :1.000 Min. :0.0000
Class :character 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.0000
Mode :character Median :1.0000 Median :1.000 Median :0.0000
Mean :0.6667 Mean :1.626 Mean :0.3333
3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.:1.0000
Max. :1.0000 Max. :3.000 Max. :1.0000
Price Refuel_availability Registration_charges Running_cost
Min. : 9.00 Min. :0.25 Min. :0.00000 Min. :115.0
1st Qu.:10.00 1st Qu.:0.75 1st Qu.:0.04000 1st Qu.:192.0
Median :10.00 Median :0.90 Median :0.06000 Median :268.0
Mean :10.33 Mean :0.80 Mean :0.05333 Mean :268.2
3rd Qu.:11.00 3rd Qu.:1.00 3rd Qu.:0.08000 3rd Qu.:383.0
Max. :12.00 Max. :1.00 Max. :0.08000 Max. :383.0
Market_share Friends_share Refuel_time Emission
Min. :0.0500 Min. :0.0000 Min. : 5.00 Min. :0.0000
1st Qu.:0.1500 1st Qu.:0.1500 1st Qu.: 5.00 1st Qu.:0.0000
Median :0.2500 Median :0.3000 Median : 5.00 Median :0.7500
Mean :0.3333 Mean :0.3333 Mean :13.33 Mean :0.5833
3rd Qu.:0.6000 3rd Qu.:0.5500 3rd Qu.:30.00 3rd Qu.:1.0000
Max. :0.9000 Max. :1.0000 Max. :30.00 Max. :1.0000
Sex Age2 Age3 Age4
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :1.0000 Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.7791 Mean :0.4574 Mean :0.2326 Mean :0.1531
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
Edu_PG Edu_Oth Occu_Pvt Occu_Pub
Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
Median :0.0000 Median :0.0000 Median :0.000 Median :0.0000
Mean :0.4147 Mean :0.1841 Mean :0.376 Mean :0.2733
3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
Occu_SE Location_metro Location_majorcity Ahm
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.00000
Median :0.0000 Median :1.0000 Median :0.0000 Median :0.00000
Mean :0.2655 Mean :0.7655 Mean :0.1453 Mean :0.04457
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.00000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
Ben Chen NCR Hyd
Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.00000
1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000
Median :0.00000 Median :0.00000 Median :0.0000 Median :0.00000
Mean :0.06977 Mean :0.04651 Mean :0.2558 Mean :0.03682
3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:0.00000
Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.00000
Kol Mum MajCity HH_size
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. : 1.000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.: 3.000
Median :0.0000 Median :0.0000 Median :0.0000 Median : 5.000
Mean :0.2016 Mean :0.1105 Mean :0.1453 Mean : 4.463
3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.: 6.000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :10.000
Children IG2 IG3 IG4
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :1.0000 Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.8721 Mean :0.3818 Mean :0.4109 Mean :0.1841
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
Max. :4.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
HH_cars PPC_morethan10 PPC_gr1 PPC_gr2
Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.00000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.00000
Median :0.0000 Median :0.0000 Median :0.000 Median :0.00000
Mean :0.4864 Mean :0.4516 Mean :0.405 Mean :0.04651
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:0.00000
Max. :3.0000 Max. :1.0000 Max. :1.000 Max. :1.00000
Body_Sedan Body_SUV Daily_travel_medium Daily_travel_long
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
Median :0.0000 Median :0.0000 Median :0.0000 Median :0.00000
Mean :0.3178 Mean :0.2364 Mean :0.3702 Mean :0.02713
3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:0.00000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
Long_drive Mode_Carpool Mode_PB Mode_PV
Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.0000
1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
Median :0.00000 Median :0.00000 Median :0.0000 Median :0.0000
Mean :0.03488 Mean :0.02519 Mean :0.2907 Mean :0.4419
3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.0000
Mode_WRC Garage_y DL_y Own_accom
Min. :0.000000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.000000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :0.000000 Median :1.0000 Median :1.0000 Median :1.0000
Mean :0.007752 Mean :0.7267 Mean :0.6357 Mean :0.6647
3rd Qu.:0.000000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. :1.000000 Max. :1.0000 Max. :1.0000 Max. :1.0000
Freerider_water_electricity Freerider_tot Freerider_avg
Satisfaction_tot
Min. :1.000 Min. :2.000 Min. :1.000 Min. :
2.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:
3.000
Median :3.000 Median :2.000 Median :1.000 Median :
4.000
Mean :3.002 Mean :2.244 Mean :1.122 Mean :
4.264
3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:
5.000
Max. :5.000 Max. :8.000 Max. :4.000 Max.
:10.000
Satisfaction_avg Political_view Meet_friends Meet_colleagues
Min. :1.000 Min. :1.000 Length:13932 Length:13932
1st Qu.:1.500 1st Qu.:3.000 Class :character Class :character
Median :2.000 Median :3.000 Mode :character Mode :character
Mean :2.132 Mean :3.258
3rd Qu.:2.500 3rd Qu.:4.000
Max. :5.000 Max. :5.000
Meet_relatives Invite_colleagues Invite_friends Invite_relatives
Length:13932 Length:13932 Length:13932 Length:13932
Class :character Class :character Class :character Class :character
Mode :character Mode :character Mode :character Mode :character
Lending_relatives Lending_friends Lending_colleagues
Length:13932 Length:13932 Length:13932
Class :character Class :character Class :character
Mode :character Mode :character Mode :character
Willingness_Purchase_Env_frnd EVuse_pollution WTP_env_tot
WTP_env_avg
Min. :1.000 Min. :1.000 Min. : 2.000 Min.
:1.000
1st Qu.:4.000 1st Qu.:3.000 1st Qu.: 7.000 1st
Qu.:3.500
Median :4.000 Median :4.000 Median : 8.000 Median
:4.000
Mean :4.132 Mean :3.992 Mean : 8.124 Mean
:4.062
3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.: 9.000 3rd
Qu.:4.500
Max. :5.000 Max. :5.000 Max. :10.000 Max.
:5.000
Social_recognition Car_social_status Warmglow_tot Warmglow_avg
Min. :1.000 Min. :1.00 Min. : 2.00 Min. :1.000
1st Qu.:3.000 1st Qu.:4.00 1st Qu.: 6.00 1st Qu.:3.000
Median :4.000 Median :4.00 Median : 8.00 Median :4.000
Mean :3.541 Mean :4.07 Mean : 7.61 Mean :3.805
3rd Qu.:4.000 3rd Qu.:5.00 3rd Qu.: 9.00 3rd Qu.:4.500
Max. :5.000 Max. :5.00 Max. :10.00 Max. :5.000
Standout Acceptance_new Climate_perception Env_pref
Tech_leader
Min. :1.000 Min. :1.0 Min. :1.000 Min. :1.000 Min.
:1.0
1st Qu.:2.000 1st Qu.:2.0 1st Qu.:4.000 1st Qu.:2.000 1st
Qu.:2.0
Median :3.000 Median :3.0 Median :5.000 Median :3.000 Median
:2.0
Mean :2.657 Mean :2.8 Mean :4.483 Mean :3.093 Mean
:2.5
3rd Qu.:3.000 3rd Qu.:4.0 3rd Qu.:5.000 3rd Qu.:4.000 3rd
Qu.:3.0
Max. :5.000 Max. :5.0 Max. :5.000 Max. :5.000 Max.
:5.0
Social_motivation_tot Social_motivation_avg Social_motivation_median
Min. : 3.00 Min. :1.000 Min. :1.000
1st Qu.: 9.00 1st Qu.:3.000 1st Qu.:3.000
Median :11.00 Median :3.667 Median :3.000
Mean :10.62 Mean :3.539 Mean :3.514
3rd Qu.:12.00 3rd Qu.:4.000 3rd Qu.:4.000
Max. :15.00 Max. :5.000 Max. :5.000
EV_risk_tot EV_risk_avg EV_price EV_awareness_tot
EV_awareness_avg
Min. : 2.000 Min. :1.00 Min. :1.000 Min. : 3.000 Min.
:1.000
1st Qu.: 8.000 1st Qu.:4.00 1st Qu.:1.000 1st Qu.: 4.000 1st
Qu.:1.333
Median : 9.000 Median :4.50 Median :2.000 Median : 5.000 Median
:1.667
Mean : 8.661 Mean :4.33 Mean :2.244 Mean : 5.419 Mean
:1.806
3rd Qu.:10.000 3rd Qu.:5.00 3rd Qu.:3.000 3rd Qu.: 6.000 3rd
Qu.:2.000
Max. :10.000 Max. :5.00 Max. :5.000 Max. :15.000 Max.
:5.000
EV_awareness_median Lost_env Investment_trust Lottery1
Min. :1.000 Min. :1.000 Min. : 0 Length:13932
1st Qu.:1.000 1st Qu.:5.000 1st Qu.: 0 Class :character
Median :2.000 Median :5.000 Median : 0 Mode :character
Mean :1.806 Mean :4.913 Mean : 1345
3rd Qu.:2.000 3rd Qu.:5.000 3rd Qu.: 0
Max. :5.000 Max. :5.000 Max. :100000
Time1 Lottery2 Time2
Length:13932 Length:13932 Length:13932
Class :character Class :character Class :character
Mode :character Mode :character Mode :character
Yes, I have many Likert items and many dummy variables. How do I solve
this issue?
Best regards,
On Tue, Sep 22, 2020 at 1:45 AM David Winsemius <dwinsemius at comcast.net>
wrote:
If you had included output of summary(mydata) we might be more capable of giving a fact-based answer but I'm guessing that you have a lot of catagorical variables with multiple levels and some sort of combinatoric explosion is resulting in too many levels of a constructed factor. -- David. On 9/21/20 12:55 PM, Rahul Chakraborty wrote:
Hello everyone, I am using *mlogit* to analyse my choice experiment data. I have *3 alternatives* for each individual and for each individual I have *9 questions*. I have a response from *516 individuals*. So it is a panel
of
9*516 observations. I have arranged the data in long format (it contains 100 columns indicating different variables and identifiers). In mlogit I tried the following command--- *mldata<- mlogit.data(mydata, shape = "long", alt.var = "Alt_name",
choice
= "Choice_binary", id.var = "IND")* It is giving me the following error message- Error in 1:nchid : result would be too long a vector Could you please help me with this? I don't think it is too big a data
100
ROWS*13932 columns. I faced no issue in Excel. I am stuck due to this
issue.
Thanks in advance.
-- Best Regards,
Rahul Chakraborty
Research Fellow
National Institute of Public Finance and Policy
New Delhi- 110067
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-- Rahul Chakraborty Research Fellow National Institute of Public Finance and Policy New Delhi- 110067
Rahul Chakraborty Research Fellow National Institute of Public Finance and Policy New Delhi- 110067