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1. COMMUNITY-CLUSTERED SE  (vs HC3)
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Baseline (full sample):
  Internet (preferred)       b=+0.1032  HC3 SE=0.0301 (p=0.001)  | CLUST SE=0.0320 (p=0.001)
Use-type (users only):
  Online learning            b=+0.0814  HC3 SE=0.0261 (p=0.002)  | CLUST SE=0.0253 (p=0.001)
  Online shopping            b=+0.0815  HC3 SE=0.0237 (p=0.001)  | CLUST SE=0.0231 (p=0.000)
  Online gaming              b=-0.0021  HC3 SE=0.0267 (p=0.937)  | CLUST SE=0.0314 (p=0.946)
Joint use-type:
  use_learn                  b=+0.0757  CLUST SE=0.0255 (p=0.003)
  use_shop                   b=+0.0770  CLUST SE=0.0235 (p=0.001)
  use_game                   b=-0.0081  CLUST SE=0.0314 (p=0.795)
  Wald H0: learn=shop -> F=0.001, p=0.974

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2. OSTER (2019) BOUNDS for use-type effects
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delta* = relative selection on unobs/obs that drives beta to 0;
beta*  = bias-adjusted coefficient assuming delta=1, Rmax=min(1.3*Rtilde,1).
Rule of thumb (Oster): |delta*|>1 and stable sign => robust to omitted-var bias.
  use_learn   [1.3*Rt] b_tilde=+0.0814  b*=+0.0259  delta*=+1.47  (robust: delta*>1, same sign)
  use_learn   [Rmax=1] b_tilde=+0.0814  b*=-0.4711  delta*=+0.15  
  use_shop    [1.3*Rt] b_tilde=+0.0815  b*=+0.0563  delta*=+3.23  (robust: delta*>1, same sign)
  use_shop    [Rmax=1] b_tilde=+0.0815  b*=-0.1687  delta*=+0.33  
  internet    [1.3*Rt] b_tilde=+0.1032  b*=-0.0218  delta*=+0.83  
  internet    [Rmax=1] b_tilde=+0.1032  b*=-1.0752  delta*=+0.09  

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3. LEWBEL (2012) heteroskedasticity-based IV
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Internal instruments Z=(X-Xbar)*e1 from first-stage residuals; needs heterosked.
  internet: heterosked. test (e1^2 on instruments) F=418.0, p=3.46e-323
  internet    Lewbel-IV b=+0.1192 (SE=0.0460, p=0.010)  ~+12.7%
  use_learn: heterosked. test (e1^2 on instruments) F=152.6, p=2.81e-124
  use_learn   Lewbel-IV b=-0.0812 (SE=0.0734, p=0.268)  ~-7.8%

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4. HECKMAN selection correction
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Selection: labour-force participation (emp_income>0) among working age 16-60.
Exclusion restriction: child16n_2 (# co-resident children < 16).
  Working-age sample: 16190,  participation rate=51.3%
  Probit: nchild coef=-0.1053 (p=1e-05)  [exclusion-restriction relevance]
  Heckman-corrected internet b=+0.1004 (SE=0.0305, p=0.001)  ~+10.6%
  Inverse Mills ratio (lambda) coef=+0.3118 (p=0.068)  -> selection bias present

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5. MULTIPLE-TESTING CORRECTION (sharpened FDR q-values)
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  Subgroup               beta        p    FDR q
  Urban·internet      +0.1097    0.008    0.014  *
  Rural·internet      +0.0874    0.064    0.085  
  HighEdu·internet    +0.2265    0.002    0.004  *
  LowEdu·internet     +0.1512    0.000    0.000  *
  Male·internet       +0.1403    0.000    0.001  *
  Female·internet     +0.0538    0.333    0.363  
  Rural·learn         +0.1318    0.005    0.011  *
  Urban·learn         +0.0591    0.037    0.056  
  Female·learn        +0.1249    0.001    0.004  *
  Male·learn          +0.0437    0.171    0.206  
  Age46-60·learn      +0.2328    0.000    0.000  *
  Age16-30·learn      -0.0194    0.671    0.671  

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6. POOLED INTERACTION TESTS for the reversal
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  Internet x Urban (vs rural)        interaction b=+0.0696 (p=0.224)
  Internet x Male (vs female)        interaction b=-0.0706 (p=0.224)
  Learning x Age46-60 (vs younger)   interaction b=+0.1732 (p=0.002)
  Learning x Female (vs male)        interaction b=+0.2047 (p=0.000)
  Learning x Rural (vs urban)        interaction b=-0.0210 (p=0.693)

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ENHANCEMENTS COMPLETE
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