`fit_w` in second stage is decay (or "treatment effect", i.e., effect of t1 on t2, for t2 ~ t1 + t0 + all the other covariates)
```r
IV: First stage: w
TSLS estimation - Dep. Var.: w
Endo. : w
Instr. : z, topicD, z:topicD
First stage: Dep. Var.: w
Observations: 1,842
Standard-errors: IID
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.392368 2.174427 -1.560121 1.1891e-01
zpersuadeTrump 1.486017 0.656344 2.264082 2.3686e-02 *
topicD -2.060479 0.651412 -3.163098 1.5868e-03 **
zpersuadeTrump:topicD 1.943982 0.926202 2.098875 3.5966e-02 *
lean_bidentrump_1 0.901837 0.011114 81.144516 < 2.2e-16 ***
policy_imp_1 0.032688 0.018002 1.815786 6.9568e-02 .
per_imp_1 -0.013116 0.009797 -1.338670 1.8085e-01
politics_involve 0.004378 0.008919 0.490821 6.2361e-01
ai_general_1 0.004933 0.008871 0.556052 5.7824e-01
income -0.017928 0.075303 -0.238077 8.1185e-01
edu -0.142196 0.185706 -0.765701 4.4395e-01
god -0.050233 0.098115 -0.511980 6.0873e-01
pol 0.606229 0.298130 2.033440 4.2153e-02 *
orient -0.380840 0.383529 -0.992988 3.2085e-01
politics_interest -0.004855 0.009484 -0.511873 6.0880e-01
social_conserv 0.055094 0.411761 0.133801 8.9358e-01
economic_conserv 1.148012 0.350041 3.279654 1.0590e-03 **
therm_dem_1 -0.058554 0.011559 -5.065711 4.4815e-07 ***
therm_repub_1 0.015894 0.011924 1.332924 1.8272e-01
vote_chance_1 0.015433 0.010062 1.533801 1.2525e-01
ethnicity 0.512111 0.548552 0.933570 3.5065e-01
area 0.826241 0.543338 1.520677 1.2851e-01
age 0.053926 0.020148 2.676564 7.5050e-03 **
gender -0.488726 0.481113 -1.015824 3.0985e-01
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RMSE: 9.81575 Adj. R2: 0.94692
F-test (1st stage): stat = 12.8, p = 2.751e-8, on 3 and 1,818 DoF.
IV: Second stage
TSLS estimation - Dep. Var.: y
Endo. : w
Instr. : z, topicD, z:topicD
Second stage: Dep. Var.: y
Observations: 1,842
Standard-errors: IID
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.180190 2.843276 1.118495 0.2635033
fit_w 0.436940 0.209077 2.089847 0.0367701 *
lean_bidentrump_1 0.422675 0.189515 2.230298 0.0258492 *
policy_imp_1 -0.038992 0.024218 -1.610046 0.1075612
per_imp_1 -0.004770 0.012861 -0.370885 0.7107666
politics_involve 0.003999 0.011602 0.344694 0.7303646
ai_general_1 0.023314 0.011542 2.019866 0.0435436 *
income -0.162043 0.097804 -1.656813 0.0977296 .
edu 0.122628 0.241477 0.507825 0.6116378
god 0.107518 0.127517 0.843168 0.3992451
pol 0.510198 0.405550 1.258038 0.2085395
orient 0.896086 0.502617 1.782840 0.0747790 .
politics_interest 0.015487 0.012338 1.255252 0.2095484
social_conserv 0.577501 0.533484 1.082508 0.2791704
economic_conserv -0.039037 0.517181 -0.075481 0.9398404
therm_dem_1 -0.026240 0.019387 -1.353499 0.1760645
therm_repub_1 0.030232 0.015698 1.925838 0.0542802 .
vote_chance_1 -0.013008 0.013378 -0.972380 0.3309907
ethnicity 0.792552 0.717114 1.105197 0.2692203
area -1.017530 0.729475 -1.394880 0.1632222
age -0.005490 0.028548 -0.192317 0.8475157
gender -1.932568 0.630199 -3.066601 0.0021969 **
```