Hi all,
While running random effects regression with panel setting I'm experiencing the sign of the coefficient changing when I include the interaction term.
Here is brief introduction of the data I'm working with [dataex attached at the end of the post]:
1. OVERLAP_1 is a "time invariant" continuous variable (0 to 11).
This is the main reason why I'm estimating with the random effects model, since fixed effects model would omit the results of time-invariant variables (due to collinearity).
2. year variable is a binary indicator variable (0 if 2019 & 1 if 2020).
3. OFF_AMT is the dependent variable.
[Question]
w/o the interaction term, the code goes:
which returns, negative coefficient for i.year & positive coefficient for OVERLAP_1.
However, when I add an interaction term and change the code to:
it would return positive coefficient for both individual i.year and OVERLAP_1, and negative coefficient for the interaction term i.year#c.OVERLAP_1
Why does the sign on the coefficient for the i.year by itself changes when interaction term is included?
As far as my understanding goes for interpreting the interaction term, the coefficient for the i.year represents the result for 1.year compared to 0.year, which to my understanding it should stay the same regardless of whether it is included in the interaction or not.
My best guess so far is that including the interaction term:
In the regression equation (I'm not 100% sure if this is the right equation): y = a + b1x1ti + b2x2ti +b3x1tix2ti + ei +ui
"b3" the interaction term absorbs the portion of the explanation power which would otherwise have belonged to b1 & b2, thus causing the problem.
However, something tells me that this is not the case...
Could anyone shed further light on what is really going on here?
Any advices or helps are appreciated in advance.
I'm pretty new to STATA so this might not be the perfect representation of the original data, but here is the dataex example generated from the original dataset
Thank you.
My data looks like this:
While running random effects regression with panel setting I'm experiencing the sign of the coefficient changing when I include the interaction term.
Here is brief introduction of the data I'm working with [dataex attached at the end of the post]:
1. OVERLAP_1 is a "time invariant" continuous variable (0 to 11).
This is the main reason why I'm estimating with the random effects model, since fixed effects model would omit the results of time-invariant variables (due to collinearity).
2. year variable is a binary indicator variable (0 if 2019 & 1 if 2020).
3. OFF_AMT is the dependent variable.
[Question]
w/o the interaction term, the code goes:
Code:
xtset id date xtreg OFF_AMT i.year OVERLAP_1, re
However, when I add an interaction term and change the code to:
Code:
xtset id date xtreg OFF_AMT i.year##c.OVERLAP_1, re
Why does the sign on the coefficient for the i.year by itself changes when interaction term is included?
As far as my understanding goes for interpreting the interaction term, the coefficient for the i.year represents the result for 1.year compared to 0.year, which to my understanding it should stay the same regardless of whether it is included in the interaction or not.
My best guess so far is that including the interaction term:
In the regression equation (I'm not 100% sure if this is the right equation): y = a + b1x1ti + b2x2ti +b3x1tix2ti + ei +ui
"b3" the interaction term absorbs the portion of the explanation power which would otherwise have belonged to b1 & b2, thus causing the problem.
However, something tells me that this is not the case...
Could anyone shed further light on what is really going on here?
Any advices or helps are appreciated in advance.
I'm pretty new to STATA so this might not be the perfect representation of the original data, but here is the dataex example generated from the original dataset
Thank you.
My data looks like this:
Code:
* Example generated by -dataex-. For more info, type help dataex clear input double OFF_AMT float(id date year OVERLAP_1) 1100 1183 3100 0 3 1300 1257 3139 1 3 1300 273 3116 0 0 1300 689 3142 1 1 1300 660 3072 0 6 1300 1163 3082 0 6 1400 1214 3084 0 6 1400 1291 3082 0 5 1500 545 3127 1 2 2500 595 3123 1 10 3500 1368 3077 0 4 3700 591 3153 1 1 4300 1010 3098 0 1 4700 1256 3075 0 2 5600 25 3156 1 8 10400 716 3155 1 4 11600 767 3108 0 4 12000 442 3134 1 4 13350 837 3099 0 3 15400 1363 3129 1 4 29500 1050 3101 0 3 42600 884 3091 0 3 45600 715 3109 0 0 47800 570 3084 0 3 70150 645 3096 0 8 76900 398 3161 1 6 85900 1167 3081 0 1 130000 386 3159 1 6 273500 1398 3089 0 2 290200 1271 3163 1 0 389600 937 3076 0 5 398400 102 3136 1 9 410450 869 3127 1 4 890650 189 3095 0 3 906300 169 3137 1 6 1037300 1059 3129 1 6 1048250 556 3104 0 1 1112200 879 3079 0 3 1123640 792 3148 1 2 1198530 824 3103 0 4 1217800 556 3159 1 1 1238250 169 3159 1 6 1242800 551 3120 1 5 1320850 138 3159 1 0 1382400 1321 3159 1 5 1384800 556 3137 1 1 1495264 169 3098 0 6 1544800 264 3073 0 3 1545200 803 3092 0 8 1568500 668 3123 1 1 1578750 541 3154 1 7 1601500 101 3127 1 5 1659600 1205 3154 1 5 1681680 1205 3155 1 5 1703200 1321 3123 1 5 1711050 556 3073 0 1 1729080 1366 3129 1 4 1799700 541 3135 1 7 1843870 541 3159 1 7 1847600 541 3155 1 7 1929550 944 3164 1 3 1933970 541 3157 1 7 1952400 668 3104 0 1 1958150 541 3137 1 7 1966600 1321 3104 0 5 1985300 541 3134 1 7 1996150 541 3158 1 7 2011200 10 3159 1 3 2022650 1268 3159 1 1 2037450 1183 3098 0 3 2042400 541 3153 1 7 2073900 541 3150 1 7 2090750 190 3073 0 3 2095750 667 3151 1 2 2100050 541 3147 1 7 2118200 1407 3164 1 5 2122460 541 3162 1 7 2174400 541 3136 1 7 2201900 169 3073 0 6 2202040 1205 3165 1 5 2205930 556 3123 1 1 2212500 178 3070 0 4 2215050 1205 3153 1 5 2230650 541 3131 1 7 2242070 1205 3157 1 5 2256750 541 3156 1 7 2257200 10 3137 1 3 2264300 812 3123 1 4 2267400 541 3170 1 7 2269980 541 3142 1 7 2274800 541 3163 1 7 2286550 541 3148 1 7 2309200 541 3146 1 7 2314810 826 3159 1 0 2317600 1205 3159 1 5 2325400 541 3133 1 7 2338950 1205 3156 1 5 2339750 541 3141 1 7 2344700 1257 3137 1 3 2360600 541 3166 1 7 2386650 541 3132 1 7 2389900 541 3149 1 7 2390500 541 3160 1 7 2394750 589 3124 1 6 2405750 660 3070 0 6 2407600 541 3169 1 7 2410900 541 3143 1 7 2430550 541 3151 1 7 2436730 1205 3161 1 5 2443050 684 3159 1 1 2445190 541 3145 1 7 2446550 660 3123 1 6 2447860 1205 3150 1 5 2450200 541 3165 1 7 2461320 541 3164 1 7 2510850 720 3090 0 0 2515850 541 3140 1 7 2524550 541 3144 1 7 2528380 1205 3152 1 5 2530700 541 3152 1 7 2538950 138 3123 1 0 2549050 1375 3135 1 5 2550980 1205 3163 1 5 2564050 541 3128 1 7 2584690 169 3150 1 6 2585240 541 3138 1 7 2591450 541 3168 1 7 2605810 1205 3148 1 5 2646530 1205 3162 1 5 2653150 1113 3104 0 3 2666950 541 3139 1 7 2668950 556 3107 0 1 2675100 556 3090 0 1 2680450 1113 3159 1 3 2681000 660 3159 1 6 2683300 684 3123 1 1 2704050 541 3130 1 7 2713930 1205 3151 1 5 2730400 556 3138 1 1 2740750 592 3159 1 6 2744300 1291 3080 0 5 2746850 1205 3160 1 5 2760650 1205 3168 1 5 2769650 1113 3123 1 3 2770510 247 3083 0 4 2770950 541 3129 1 7 2794050 169 3160 1 6 2797400 1205 3128 1 5 2832300 541 3167 1 7 2841600 1205 3166 1 5 2846600 1045 3159 1 4 2847450 556 3120 1 1 2862100 1205 3169 1 5 2862428 443 3159 1 0 2879350 138 3104 0 0 2879900 1010 3096 0 1 2888921 1255 3159 1 10 2898450 541 3127 1 7 2899500 412 3104 0 6 2901700 169 3085 0 6 2913300 35 3091 0 3 2924000 991 3159 1 4 2937370 541 3123 1 7 2949550 556 3108 0 1 2954650 1408 3159 1 1 2965610 1205 3140 1 5 2993200 322 3068 0 1 2995600 866 3159 1 5 3007240 1205 3132 1 5 3007500 1253 3159 1 7 3015000 684 3104 0 1 3026800 643 3104 0 4 3041850 93 3146 1 3 3042250 1205 3146 1 5 3044000 169 3162 1 6 3050000 812 3159 1 4 3069700 812 3104 0 4 3073400 488 3123 1 2 3092200 991 3123 1 4 3100950 970 3159 1 1 3101960 970 3123 1 1 3109700 1282 3073 0 2 3130450 556 3152 1 1 3140000 781 3123 1 2 3147400 850 3123 1 6 3149300 556 3100 0 1 3184420 1205 3133 1 5 3186300 556 3109 0 1 3191700 1205 3164 1 5 3207000 541 3161 1 7 3208800 169 3151 1 6 3214550 215 3123 1 6 3224900 1268 3123 1 1 3228700 10 3123 1 3 3232250 826 3123 1 0 3233520 541 3126 1 7 3234810 1205 3167 1 5 3245450 1205 3147 1 5 3256000 1205 3134 1 5 3259350 169 3166 1 6 3259980 1205 3149 1 5 3264600 541 3120 1 7 3265520 1205 3145 1 5 3280300 826 3137 1 0 3295070 1205 3143 1 5 3299900 379 3084 0 0 3300550 556 3146 1 1 3314090 655 3123 1 4 3315300 169 3135 1 6 3318950 169 3143 1 6 3320750 1165 3081 0 2 3323000 556 3122 1 1 3325960 1205 3142 1 5 3330800 668 3159 1 1 3332500 488 3073 0 2 3333440 1205 3139 1 5 3334300 541 3125 1 7 3336850 556 3070 0 1 3360810 556 3129 1 1 3362450 1241 3159 1 9 3368880 1205 3136 1 5 3377100 286 3149 1 4 3389500 169 3123 1 6 3390760 1205 3131 1 5 3391850 169 3161 1 6 3392800 1408 3104 0 1 3400950 10 3104 0 3 3405250 517 3159 1 4 3405500 169 3163 1 6 3405500 368 3123 1 2 3411450 556 3081 0 1 3412100 169 3142 1 6 3414280 556 3128 1 1 3422400 1205 3129 1 5 3426670 1282 3114 0 2 3434450 286 3164 1 4 3435900 1205 3144 1 5 3438460 1205 3141 1 5 3438620 1205 3104 0 5 3453350 286 3162 1 4 3457650 1150 3091 0 6 3459400 1205 3135 1 5 3472219 169 3100 0 6 3473900 1023 3104 0 2 3474750 169 3120 1 6 3478300 655 3159 1 4 3487730 353 3123 1 3 3496900 1268 3104 0 1 3499650 1378 3123 1 3 3501900 169 3156 1 6 3509700 1205 3127 1 5 3510050 329 3080 0 6 3524920 1205 3130 1 5 3526650 169 3152 1 6 3530960 556 3135 1 1 3536400 1321 3072 0 5 3540350 10 3073 0 3 3546650 26 3159 1 7 3549160 169 3145 1 6 3567800 541 3124 1 7 3568450 541 3104 0 7 3568800 688 3159 1 6 3568850 169 3090 0 6 3572840 556 3160 1 1 3577040 541 3117 0 7 3577300 165 3159 1 4 3579150 1132 3135 1 6 3583700 286 3163 1 4 3603200 541 3122 1 7 3608560 556 3121 1 1 3615550 10 3100 0 3 3619650 169 3155 1 6 3621750 556 3125 1 1 3627800 541 3108 0 7 3630600 286 3147 1 4 3632200 556 3103 0 1 3638100 1000 3104 0 6 3639400 1205 3125 1 5 3643350 1268 3073 0 1 3669770 169 3153 1 6 3678000 556 3126 1 1 3678100 488 3120 1 2 3679500 345 3159 1 5 3682000 286 3166 1 4 3686350 286 3142 1 4 3698650 286 3152 1 4 3707300 169 3141 1 6 3719850 558 3159 1 4 3726650 1282 3104 0 2 3729800 828 3159 1 8 3733000 368 3159 1 2 3734800 995 3113 0 8 3736560 169 3076 0 6 3741450 541 3107 0 7 3748400 660 3128 1 6 3750200 655 3104 0 4 3756250 1000 3159 1 6 3758750 1190 3168 1 1 3760000 169 3107 0 6 3764850 169 3140 1 6 3765420 556 3133 1 1 3765550 286 3169 1 4 3766800 1282 3109 0 2 3776700 541 3111 0 7 3779400 556 3094 0 1 3780350 541 3116 0 7 3786750 138 3072 0 0 3787150 286 3160 1 4 3790500 1321 3073 0 5 3798750 169 3134 1 6 3802250 556 3101 0 1 3810500 1256 3073 0 2 3814150 286 3143 1 4 3814800 608 3159 1 4 3815250 169 3068 0 6 3820650 763 3123 1 0 3823250 443 3104 0 0 3833150 1166 3159 1 8 3833700 1035 3104 0 2 3834900 1241 3104 0 9 3843300 700 3159 1 2 3845050 590 3120 1 7 3845250 10 3085 0 3 3849850 27 3123 1 6 3850040 1268 3137 1 1 3852700 286 3144 1 4 3858740 556 3147 1 1 3862650 933 3159 1 9 3870320 933 3123 1 9 3871600 556 3139 1 1 3881550 556 3095 0 1 3882050 215 3104 0 6 3883250 286 3150 1 4 3885580 1205 3124 1 5 3886550 169 3133 1 6 3897250 88 3159 1 7 3908500 11 3159 1 2 3909930 169 3147 1 6 3913450 1282 3072 0 2 3913600 286 3151 1 4 3919750 556 3127 1 1 3920650 488 3121 1 2 3920900 541 3112 0 7 3927950 1282 3124 1 2 3930650 98 3159 1 5 3932200 822 3102 0 6 3932900 556 3087 0 1 3935850 169 3164 1 6 3935950 169 3154 1 6 3936850 286 3115 0 4 3937000 556 3156 1 1 3945200 919 3114 0 3 3953150 169 3169 1 6 3954400 541 3118 0 7 3960250 686 3159 1 2 3965200 443 3123 1 0 3975350 169 3108 0 6 3978050 1282 3108 0 2 3979700 286 3148 1 4 3986550 368 3104 0 2 3986600 556 3150 1 1 3992000 169 3138 1 6 4002700 556 3083 0 1 4008900 488 3069 0 2 4010150 286 3145 1 4 4015450 850 3104 0 6 4017450 1282 3120 1 2 4017700 1282 3116 0 2 4021200 169 3157 1 6 4022750 999 3123 1 1 4031250 440 3145 1 4 4031500 388 3159 1 7 4031700 488 3104 0 2 4036550 556 3077 0 1 4037100 368 3073 0 2 4038100 397 3159 1 4 4039420 1205 3126 1 5 4040050 286 3161 1 4 4043600 286 3159 1 4 4043700 286 3153 1 4 4048300 169 3144 1 6 4049200 541 3115 0 7 4053750 1282 3125 1 2 4054650 1000 3123 1 6 4055440 556 3102 0 1 4056100 169 3124 1 6 4059450 488 3068 0 2 4059550 169 3136 1 6 4062130 169 3149 1 6 4062900 120 3159 1 6 4063650 668 3072 0 1 4066330 556 3164 1 1 4066800 556 3096 0 1 4074450 541 3121 1 7 4075050 820 3123 1 1 4076500 1271 3165 1 0 4080500 10 3152 1 3 4084450 556 3151 1 1 4085750 739 3123 1 4 4089150 10 3072 0 3 4090200 647 3070 0 7 4090350 286 3155 1 4 4098150 264 3159 1 3 4102750 1282 3107 0 2 4104100 286 3141 1 4 4105010 1205 3094 0 5 4109150 556 3140 1 1 4109650 169 3110 0 6 4116750 551 3122 1 5 4118000 169 3165 1 6 4119850 169 3148 1 6 4122650 169 3128 1 6 4128750 1282 3097 0 2 4131150 660 3129 1 6 4133150 169 3086 0 6 4133800 1282 3094 0 2 4135750 541 3109 0 7 4140730 556 3110 0 1 4142330 1205 3100 0 5 4145050 286 3104 0 4 4148500 286 3146 1 4 4152850 1268 3072 0 1 4155600 592 3123 1 6 4156840 1282 3110 0 2 4158450 1113 3099 0 3 4158850 488 3072 0 2 4163100 488 3114 0 2 4163850 1282 3090 0 2 4163950 286 3165 1 4 4164800 1378 3159 1 3 4166750 850 3159 1 6 4167050 286 3122 1 4 4168050 928 3102 0 1 4172050 286 3102 0 4 4178300 541 3110 0 7 4183350 556 3079 0 1 4183750 488 3095 0 2 4188250 1268 3152 1 1 4189250 488 3159 1 2 4189600 556 3071 0 1 4189830 556 3076 0 1 4190050 286 3158 1 4 4191350 1266 3141 1 4 4192530 1205 3138 1 5 4199600 1113 3148 1 3 4202850 169 3139 1 6 4210500 488 3115 0 2 4210950 999 3159 1 1 4212150 613 3123 1 2 4212300 1205 3137 1 5 4214100 556 3149 1 1 4214800 936 3159 1 10 4218300 556 3088 0 1 4222200 541 3114 0 7 4223100 1282 3095 0 2 4223300 286 3113 0 4 4223550 1411 3070 0 0 4225500 556 3097 0 1 4228100 182 3135 1 3 4230400 593 3159 1 9 4234850 518 3123 1 4 4242350 1378 3104 0 3 4242950 937 3074 0 5 4243100 1282 3096 0 2 4254740 286 3107 0 4 4255050 286 3095 0 4 4260850 286 3156 1 4 4261250 286 3105 0 4 4262700 556 3085 0 1 4263050 541 3105 0 7 4264020 1282 3103 0 2 4264750 556 3165 1 1 4267700 1321 3098 0 5 4270680 556 3072 0 1 4272750 826 3104 0 0 4274000 1113 3147 1 3 4274750 1282 3098 0 2 4275400 556 3155 1 1 4279800 1321 3097 0 5 4280750 1282 3091 0 2 4283260 169 3111 0 6 4285510 169 3081 0 6 4286500 286 3109 0 4 4286750 286 3111 0 4 4288150 608 3137 1 4 4291450 1113 3142 1 3 4293200 1113 3163 1 3 4294100 1113 3103 0 3 4296250 1282 3127 1 2 4297100 286 3137 1 4 4298750 120 3151 1 6 4301350 286 3114 0 4 4301400 169 3091 0 6 4303500 10 3135 1 3 4307120 556 3082 0 1 4312250 613 3159 1 2 4318450 1045 3123 1 4 4319450 286 3101 0 4 4321600 286 3131 1 4 4323600 169 3129 1 6 4325550 286 3092 0 4 4328100 1113 3114 0 3 4333900 739 3104 0 4 4335000 169 3168 1 6 4338350 1113 3141 1 3 4339050 286 3093 0 4 4339850 169 3146 1 6 4341150 286 3168 1 4 4341700 286 3167 1 4 4343450 1321 3099 0 5 4348700 169 3115 0 6 4348940 556 3143 1 1 4354700 1408 3123 1 1 4358390 1205 3103 0 5 4359750 970 3104 0 1 4362150 1282 3123 1 2 4364250 286 3123 1 4 4365000 169 3077 0 6 4366250 4 3097 0 1 4367750 1321 3100 0 5 4370350 488 3070 0 2 4371300 541 3106 0 7 4371750 541 3096 0 7 4373300 541 3085 0 7 4375900 1321 3096 0 5 4375960 1205 3170 1 5 4376400 488 3100 0 2 4380300 169 3116 0 6 4384600 488 3111 0 2 4385800 1205 3121 1 5 4391450 286 3100 0 4 4393250 784 3098 0 4 4393350 169 3087 0 6 4402850 286 3170 1 4 4403500 1282 3111 0 2 4404800 1113 3107 0 3 4404800 660 3153 1 6 4409250 286 3099 0 4 4409900 1282 3115 0 2 4410050 138 3073 0 0 4412200 264 3123 1 3 4412800 1113 3121 1 3 4413800 264 3104 0 3 4414200 286 3127 1 4 4418200 668 3153 1 1 4418850 1282 3122 1 2 4420700 1282 3093 0 2 4421530 541 3113 0 7 4421650 286 3097 0 4 4427450 682 3152 1 8 4429350 684 3073 0 1 4431250 682 3104 0 8 4431350 398 3104 0 6 4432000 1113 3108 0 3 4436000 826 3073 0 0 4437150 488 3071 0 2 4440950 1321 3149 1 5 4441030 556 3105 0 1 4441600 1113 3116 0 3 4444950 286 3121 1 4 4446650 488 3110 0 2 4448350 286 3096 0 4 4448800 541 3093 0 7 4449150 1282 3117 0 2 4453500 1241 3123 1 9 4455080 556 3141 1 1 4455700 668 3154 1 1 4455800 169 3132 1 6 4457850 1113 3166 1 3 4460300 286 3091 0 4 4460900 725 3099 0 2 4462130 556 3124 1 1 4462950 488 3098 0 2 4464950 286 3117 0 4 4465250 1321 3126 1 5 4465300 1113 3146 1 3 4467250 120 3154 1 6 4469220 402 3137 1 7 4470350 169 3109 0 6 4470800 826 3120 1 0 4472500 556 3086 0 1 4474100 286 3094 0 4 4477250 286 3116 0 4 4478400 1282 3099 0 2 4479750 169 3125 1 6 4484130 1366 3099 0 4 4485120 120 3152 1 6 4488080 556 3098 0 1 4489000 1282 3102 0 2 4493300 215 3159 1 6 4493500 1321 3143 1 5 4498000 1282 3088 0 2 4498550 1256 3123 1 2 4500400 886 3107 0 4 4500750 592 3104 0 6 4502000 488 3103 0 2 4504450 301 3109 0 0 4506100 792 3150 1 2 4506650 556 3131 1 1 4506800 88 3123 1 7 4507000 541 3103 0 7 4508100 1113 3150 1 3 4509050 286 3090 0 4 4509200 286 3140 1 4 4509400 286 3133 1 4 4510050 1035 3159 1 2 4510300 784 3104 0 4 4513700 541 3091 0 7 4514500 1282 3113 0 2 4515350 286 3098 0 4 4515400 1113 3149 1 3 4519400 286 3103 0 4 4520950 684 3164 1 1 4521400 488 3125 1 2 4521900 556 3069 0 1 4526580 556 3080 0 1 4527100 541 3090 0 7 4528000 1282 3082 0 2 4532850 660 3130 1 6 4535950 169 3099 0 6 4536300 1282 3068 0 2 4537100 1326 3123 1 3 4538880 541 3094 0 7 4542100 120 3164 1 6 4542300 660 3154 1 6 4546870 541 3089 0 7 4550600 882 3159 1 3 4552900 120 3115 0 6 4557000 1282 3100 0 2 4558800 649 3073 0 6 4560400 1282 3081 0 2 4561750 1282 3083 0 2 4563300 1113 3109 0 3 4566760 1321 3117 0 5 4568950 286 3134 1 4 4571300 169 3131 1 6 4573600 1113 3158 1 3 4574750 541 3100 0 7 4576800 286 3088 0 4 4576905 488 3128 1 2 4578250 286 3157 1 4 4580400 286 3120 1 4 4582050 10 3156 1 3 4588350 1282 3101 0 2 4593150 286 3106 0 4 4593410 1270 3088 0 1 4595400 120 3163 1 6 4598400 286 3110 0 4 4600690 169 3102 0 6 4606650 286 3108 0 4 4609600 286 3136 1 4 4613850 286 3124 1 4 4614250 488 3099 0 2 4616450 197 3123 1 6 4617100 1113 3143 1 3 4617100 944 3165 1 3 4618000 488 3090 0 2 4619410 1205 3122 1 5 4619700 1321 3146 1 5 4621250 613 3104 0 2 4621950 1321 3122 1 5 4623700 402 3159 1 7 4625950 286 3125 1 4 4630675 1205 3088 0 5 4631950 1321 3120 1 5 4632700 1113 3165 1 3 4633060 1189 3159 1 3 4633350 1321 3151 1 5 4633650 682 3123 1 8 4635000 120 3150 1 6 4642750 120 3153 1 6 4645050 1113 3164 1 3 4645950 286 3139 1 4 4646040 1321 3147 1 5 4647750 1282 3121 1 2 4648450 1321 3152 1 5 4650400 596 3159 1 10 4650642 169 3083 0 6 4651550 88 3073 0 7 4653100 488 3124 1 2 4653550 556 3144 1 1 4655900 1321 3153 1 5 4657460 353 3159 1 3 4661750 286 3128 1 4 4662700 169 3101 0 6 4663300 120 3104 0 6 4663750 541 3095 0 7 4665750 556 3142 1 1 4668600 688 3123 1 6 4668950 169 3167 1 6 4670842 169 3082 0 6 4672900 1321 3103 0 5 4674550 1282 3105 0 2 4677500 1282 3106 0 2 4678050 120 3160 1 6 4685200 1321 3145 1 5 4685300 704 3123 1 4 4685550 870 3159 1 6 4685900 660 3135 1 6 4687000 1175 3159 1 8 4688400 1175 3068 0 8 4689750 541 3097 0 7 4691100 1113 3160 1 3 4692350 649 3123 1 6 4695700 763 3104 0 0 4696300 1321 3142 1 5 4697900 488 3112 0 2 4703740 541 3102 0 7 4706250 668 3073 0 1 4707950 25 3159 1 8 4709700 945 3159 1 4 4713950 649 3159 1 6 4718000 286 3080 0 4 4719550 169 3095 0 6 4720840 1205 3087 0 5 4721200 1113 3131 1 3 4722000 1205 3107 0 5 4722100 1321 3162 1 5 4723200 1113 3117 0 3 4724840 169 3114 0 6 4725850 286 3154 1 4 4725900 27 3100 0 6 4726050 1113 3105 0 3 4728050 169 3106 0 6 4731140 1113 3095 0 3 4731400 1282 3092 0 2 4735800 770 3104 0 1 4737050 488 3127 1 2 4737600 169 3105 0 6 4738460 120 3127 1 6 4739500 1113 3094 0 3 4741450 541 3086 0 7 4747550 933 3104 0 9 4748650 286 3112 0 4 4749650 488 3075 0 2 4750050 1113 3145 1 3 4753300 935 3159 1 10 4753600 345 3123 1 5 4753700 1282 3118 0 2 4754250 120 3149 1 6 4754800 1282 3084 0 2 4755250 1321 3136 1 5 4761250 1282 3143 1 2 4761450 824 3123 1 4 4763100 684 3072 0 1 4763300 739 3159 1 4 4764860 556 3113 0 1 4767250 1205 3120 1 5 4768350 1113 3162 1 3 4770150 286 3126 1 4 4770750 286 3132 1 4 4776500 1282 3071 0 2 4776900 1282 3089 0 2 4779870 660 3155 1 6 4780000 682 3159 1 8 4780550 556 3099 0 1 4784670 1205 3090 0 5 4786450 1321 3107 0 5 4786800 286 3079 0 4 4786950 660 3131 1 6 4794150 541 3080 0 7 4794200 10 3107 0 3 4795150 88 3170 1 7 4799300 1321 3095 0 5 4799750 643 3159 1 4 4800550 98 3104 0 5 4801020 541 3101 0 7 4803000 1321 3144 1 5 4803000 668 3114 0 1 4806800 88 3152 1 7 4809300 286 3089 0 4 4809350 27 3104 0 6 4810300 120 3143 1 6 4810650 1321 3094 0 5 4810900 541 3081 0 7 4811900 286 3138 1 4 4812220 488 3164 1 2 4814400 1113 3169 1 3 4814450 286 3084 0 4 4817150 120 3123 1 6 4818150 1113 3098 0 3 4820800 1205 3082 0 5 4821500 412 3072 0 6 4824740 1282 3142 1 2 4824850 553 3134 1 7 4825650 10 3160 1 3 4830700 1113 3072 0 3 4840100 1113 3111 0 3 4841210 1205 3089 0 5 4842150 1067 3159 1 7 4846750 488 3108 0 2 4847575 1205 3091 0 5 4850200 1321 3118 0 5 4853100 120 3165 1 6 4853284 169 3094 0 6 4854350 1035 3093 0 2 4856200 660 3136 1 6 4858800 286 3081 0 4 4861950 142 3159 1 0 4870150 1035 3091 0 2 4871630 541 3082 0 7 4871700 1321 3101 0 5 4872100 1113 3151 1 3 4873000 169 3130 1 6 4874500 784 3123 1 4 4875350 1113 3100 0 3 4875900 1113 3101 0 3 4877300 169 3084 0 6 4879600 98 3150 1 5 4879930 1113 3152 1 3 4881500 120 3145 1 6 4881550 684 3168 1 1 4882270 805 3123 1 4 4883550 1321 3169 1 5 4884150 1205 3101 0 5 4885250 1282 3070 0 2 4886320 1282 3069 0 2 4886500 88 3098 0 7 4887370 556 3074 0 1 4889910 364 3163 1 3 4890300 386 3160 1 6 4890725 1205 3078 0 5 4891200 1035 3090 0 2 4894250 169 3093 0 6 4895700 541 3099 0 7 4896950 1282 3087 0 2 4898650 983 3123 1 3 4900350 1045 3104 0 4 4901850 10 3090 0 3 4902640 169 3096 0 6 4902990 120 3146 1 6 4903100 1321 3170 1 5 4907150 169 3069 0 6 4908050 1321 3166 1 5 4910150 488 3102 0 2 4910850 1321 3090 0 5 4913900 1271 3123 1 0 4917250 1321 3093 0 5 4917650 541 3087 0 7 4918000 1113 3155 1 3 4921950 1321 3121 1 5 4921950 660 3156 1 6 4923250 541 3088 0 7 4923630 1205 3092 0 5 4926598 556 3148 1 1 4928050 10 3068 0 3 4931150 1035 3123 1 2 4931250 88 3143 1 7 4933700 136 3159 1 0 4933800 1321 3163 1 5 4937030 1035 3096 0 2 4939100 920 3104 0 4 4940250 488 3131 1 2 4940820 169 3127 1 6 4941600 1035 3100 0 2 4942160 556 3084 0 1 4942450 286 3135 1 4 4945400 488 3122 1 2 4946750 286 3085 0 4 4946900 668 3158 1 1 4952000 277 3159 1 4 4955450 541 3092 0 7 4957220 169 3080 0 6 4957900 120 3157 1 6 4959900 1113 3093 0 3 4960950 1321 3131 1 5 4961371 1205 3106 0 5 4965600 1282 3135 1 2 4966850 286 3072 0 4 4970000 660 3150 1 6 4970850 1321 3158 1 5 4974650 820 3159 1 1 4975450 684 3134 1 1 4977200 784 3159 1 4 4977300 120 3155 1 6 4978200 488 3086 0 2 4978800 488 3129 1 2 4979650 88 3133 1 7 4980200 556 3089 0 1 4982400 488 3135 1 2 4982960 1205 3083 0 5 4988150 169 3070 0 6 4989800 488 3132 1 2 4993510 169 3088 0 6 4994850 1035 3143 1 2 4995910 266 3098 0 1 4997300 541 3084 0 7 4997700 1035 3142 1 2 4999050 10 3143 1 3 4999700 811 3159 1 5 5003500 1268 3160 1 1 5003850 27 3159 1 6 5004400 882 3104 0 3 5005300 983 3104 0 3 5006000 850 3073 0 6 5006250 10 3150 1 3 5009850 1113 3144 1 3 5010100 828 3104 0 8 5010200 488 3081 0 2 5011500 488 3074 0 2 5012300 488 3109 0 2 5012750 1321 3115 0 5 5013300 1321 3111 0 5 5015000 1113 3127 1 3 5017550 890 3159 1 6 5017850 556 3078 0 1 5018150 266 3149 1 1 5018300 558 3104 0 4 5018450 488 3084 0 2 5019650 660 3134 1 6 5020050 488 3116 0 2 5021250 488 3107 0 2 5023750 1321 3157 1 5 5029350 120 3169 1 6 5030400 1321 3154 1 5 5036450 1159 3108 0 7 5036900 120 3116 0 6 5037950 1282 3085 0 2 5039926 541 3079 0 7 5040350 169 3089 0 6 5040450 1321 3141 1 5 5040700 1166 3123 1 8 5042300 488 3079 0 2 5042338 1205 3073 0 5 5044500 88 3163 1 7 5046100 556 3075 0 1 5046350 1113 3168 1 3 5049550 541 3098 0 7 5052550 1282 3079 0 2 5053100 10 3144 1 3 5055500 1035 3092 0 2 5056200 88 3149 1 7 5057630 933 3073 0 9 5058940 1366 3100 0 4 5059000 1321 3091 0 5 5059550 88 3168 1 7 5060550 306 3123 1 9 5060800 120 3166 1 6 5061100 488 3091 0 2 5062050 488 3097 0 2 5062200 1205 3111 0 5 5062650 169 3121 1 6 5064000 826 3098 0 0 5064300 120 3120 1 6 5066450 556 3116 0 1 5067150 488 3136 1 2 5068500 1205 3102 0 5 5069400 1321 3161 1 5 5070600 1113 3132 1 3 5075150 991 3104 0 4 5077730 1205 3096 0 5 5078350 1113 3124 1 3 5080000 1321 3127 1 5 5081150 1268 3068 0 1 5084950 1113 3106 0 3 5085000 1205 3105 0 5 5085450 330 3159 1 5 5085485 1205 3070 0 5 5087000 98 3123 1 5 5091900 1113 3085 0 3 5092590 556 3161 1 1 5093150 120 3156 1 6 5095650 1321 3110 0 5 5097000 1321 3092 0 5 5097250 10 3108 0 3 5097440 1255 3123 1 10 5099350 1321 3102 0 5 5099750 88 3094 0 7 5099950 169 3079 0 6 5100000 820 3104 0 1 5100750 696 3159 1 6 5100960 169 3097 0 6 5103850 1113 3073 0 3 5104850 684 3166 1 1 5105250 488 3162 1 2 5105320 1205 3086 0 5 5107200 781 3104 0 2 5107550 412 3123 1 6 5108800 136 3104 0 0 5112300 1205 3110 0 5 5112450 1282 3077 0 2 5113350 511 3159 1 6 5115930 556 3130 1 1 5116550 668 3098 0 1 5122600 1205 3117 0 5 5122850 668 3099 0 1 5124450 488 3106 0 2 5125350 1321 3135 1 5 5125450 120 3132 1 6 5125500 154 3159 1 5 5125800 1113 3157 1 3 5127500 1321 3114 0 5 5128650 1113 3153 1 3 5129200 541 3083 0 7 5130400 1035 3150 1 2 5130450 1113 3120 1 3 5130550 1321 3164 1 5 5131600 649 3151 1 6 5132150 120 3162 1 6 5132470 886 3109 0 4 end format %tw date label values year year label def year 0 "2019년도", modify label def year 1 "2020년도", modify
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