quantative_writing - what to control

model1 graph

model1 simulation

	Model 1	Model 2
(Intercept)	−0.024	−0.014
	(0.012)	(0.010)
x	1.491	0.983
	(0.009)	(0.010)
z		1.002
		(0.014)
Num.Obs.	10000	10000
R2	0.744	0.829
R2 Adj.	0.744	0.829
AIC	32532.9	28504.3
BIC	32554.6	28533.2
Log.Lik.	−16263.471	−14248.173
F	29089.849	24244.025
RMSE	1.23	1.01

model2 graph

model2 simulation

	Model 1	Model 2
(Intercept)	−0.007	−0.004
	(0.013)	(0.012)
x	1.318	1.001
	(0.007)	(0.012)
z		0.476
		(0.015)
Num.Obs.	10000	10000
R2	0.757	0.779
R2 Adj.	0.757	0.779
AIC	33432.8	32487.5
BIC	33454.5	32516.4
Log.Lik.	−16713.411	−16239.758
F	31070.506	17573.832
RMSE	1.29	1.23

model3 graph

model3 simulation

	Model 1	Model 2
(Intercept)	0.022	0.006
	(0.016)	(0.010)
x	1.491	0.988
	(0.011)	(0.008)
z		1.016
		(0.008)
Num.Obs.	10000	10000
R2	0.632	0.862
R2 Adj.	0.632	0.862
AIC	37886.5	28088.1
BIC	37908.1	28116.9
Log.Lik.	−18940.256	−14040.037
F	17169.383	31192.617
RMSE	1.61	0.99

model4 graph

model4 simulation

	Model 1	Model 2
(Intercept)	0.001	−0.004
	(0.016)	(0.014)
x	1.503	0.999
	(0.011)	(0.014)
z		1.004
		(0.020)
Num.Obs.	10000	10000
R2	0.638	0.712
R2 Adj.	0.638	0.712
AIC	37442.2	35159.2
BIC	37463.8	35188.1
Log.Lik.	−18718.085	−17575.611
F	17653.439	12374.642
RMSE	1.57	1.40

model5 graph

model5 simulation

	Model 1	Model 2
(Intercept)	−0.001	−0.006
	(0.016)	(0.016)
x	1.332	1.009
	(0.009)	(0.016)
z		0.484
		(0.020)
Num.Obs.	10000	10000
R2	0.667	0.686
R2 Adj.	0.667	0.686
AIC	38298.3	37707.7
BIC	38320.0	37736.6
Log.Lik.	−19146.172	−18849.875
F	20040.935	10936.319
RMSE	1.64	1.59

model6 graph

model6 simulation

	Model 1	Model 2
(Intercept)	−0.004	0.010
	(0.019)	(0.014)
x	1.479	0.972
	(0.013)	(0.012)
z		1.030
		(0.012)
Num.Obs.	10000	10000
R2	0.548	0.748
R2 Adj.	0.548	0.748
AIC	41141.0	35326.4
BIC	41162.6	35355.2
Log.Lik.	−20567.482	−17659.199
F	12145.668	14807.028
RMSE	1.89	1.42

model7 graph

mdoel7 simulation

	Model 1	Model 2
(Intercept)	−0.069	−0.032
	(0.041)	(0.032)
x	0.989	1.801
	(0.029)	(0.025)
z		−1.601
		(0.020)
Num.Obs.	10000	10000
R2	0.102	0.444
R2 Adj.	0.102	0.444
AIC	56684.5	51890.4
BIC	56706.1	51919.2
Log.Lik.	−28339.226	−25941.183
F	1132.397	3990.857
RMSE	4.12	3.24

model8 graph

model8 simulation

unadjusted.x   adjusted.x 
   0.9998296    0.9998023

model9 graph

model 9 simulation

unadjusted.x   adjusted.x 
    1.000257     1.000017

model10 graph

model10 simulation

	Model 1	Model 2
(Intercept)	−0.005	0.001
	(0.021)	(0.017)
x	1.328	2.018
	(0.009)	(0.012)
z		−2.066
		(0.030)
Num.Obs.	10000	10000
R2	0.702	0.798
R2 Adj.	0.702	0.798
AIC	43309.4	39426.6
BIC	43331.0	39455.5
Log.Lik.	−21651.693	−19709.323
F	23589.619	19765.335
RMSE	2.11	1.74

model11 graph

model11 simulation

	Model 1	Model 2
(Intercept)	−0.016	0.003
	(0.014)	(0.010)
x	0.992	−0.025
	(0.014)	(0.014)
z		1.016
		(0.010)
Num.Obs.	10000	10000
R2	0.327	0.671
R2 Adj.	0.327	0.671
AIC	35509.5	28363.6
BIC	35531.1	28392.4
Log.Lik.	−17751.747	−14177.786
F	4855.772	10178.769
RMSE	1.43	1.00

model12 graph

model12 simulation

	Model 1	Model 2
(Intercept)	−0.030	−0.024
	(0.014)	(0.012)
x	0.999	0.486
	(0.014)	(0.015)
z		0.517
		(0.009)
Num.Obs.	10000	10000
R2	0.332	0.507
R2 Adj.	0.332	0.507
AIC	35481.0	32438.9
BIC	35502.6	32467.8
Log.Lik.	−17737.498	−16215.455
F	4970.258	5147.640
RMSE	1.43	1.22

variation of model11

variation of model11 simulation

	Model 1	Model 2
(Intercept)	−0.071	−0.016
	(0.025)	(0.012)
x	0.971	−0.502
	(0.025)	(0.015)
z		1.504
		(0.009)
Num.Obs.	10000	10000
R2	0.135	0.789
R2 Adj.	0.135	0.789
AIC	46359.9	32270.8
BIC	46381.5	32299.6
Log.Lik.	−23176.929	−16131.390
F	1559.325	18647.167
RMSE	2.46	1.21

model13 graph

model13 simulation

unadjusted.x   adjusted.x 
   0.9997093    1.0005497

model14 graph

model14 simulation

unadjusted.x   adjusted.x 
   0.9995661    1.0012137

model15 graph

model15 simulation

	Model 1	Model 2	Model 3
(Intercept)	−0.011	−0.017	−0.005
	(0.019)	(0.017)	(0.022)
x	1.668	1.003	1.033
	(0.022)	(0.025)	(0.022)
w	−0.655	−0.984
	(0.011)	(0.012)
z		0.993
		(0.021)
Num.Obs.	10000	10000	10000
R2	0.389	0.498	0.175
R2 Adj.	0.389	0.498	0.175
AIC	41371.2	39414.0	44375.7
BIC	41400.0	39450.1	44397.3
Log.Lik.	−20681.595	−19702.017	−22184.825
F	3187.958	3306.140	2124.734
RMSE	1.91	1.74	2.22

model16 graph

model16 simulation

	Model 1	Model 2
(Intercept)	0.001	−0.015
	(0.022)	(0.017)
x	0.982	−0.011
	(0.022)	(0.021)
z		0.989
		(0.012)
Num.Obs.	10000	10000
R2	0.165	0.494
R2 Adj.	0.165	0.494
AIC	44426.2	39422.9
BIC	44447.9	39451.7
Log.Lik.	−22210.111	−19707.429
F	1978.339	4878.632
RMSE	2.23	1.74

model17 graph

model17 simulation

	Model 1	Model 2
(Intercept)	−0.008	−0.004
	(0.010)	(0.007)
x	1.000	−0.023
	(0.010)	(0.012)
z		0.506
		(0.005)
Num.Obs.	10000	10000
R2	0.498	0.754
R2 Adj.	0.498	0.754
AIC	28518.5	21384.8
BIC	28540.2	21413.6
Log.Lik.	−14256.267	−10688.394
F	9909.296	15317.599
RMSE	1.01	0.70

model18 graph

model18 simulation

	Model 1	Model 2
(Intercept)	0.006	0.005
	(0.010)	(0.007)
x	1.008	0.512
	(0.010)	(0.009)
z		0.496
		(0.005)
Num.Obs.	10000	10000
R2	0.504	0.751
R2 Adj.	0.504	0.751
AIC	28377.1	21478.5
BIC	28398.8	21507.4
Log.Lik.	−14185.574	−10735.258
F	10159.905	15095.323
RMSE	1.00	0.71

This notebook contains R code with numerical simulations for all the examples discussed in:

Cinelli et al (2020). A Crash Course in Good and Bad Controls. Available at SSRN: https://ssrn.com/abstract=3689437

what to control