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AN-004: Pre-treatment placebo tests

Intuition (plain-language)

If the price jump were really a pre-existing trend, then pretending the policy happened on an earlier (fake) date would also 'find' an effect. It does not — placebo price effects are tiny and insignificant — which supports parallel trends. The firm- and bid-count placebos that do fire reflect the controls' gradual SME rollout, not a Group-65-specific shock.

Reduced-form benchmark layer

The price placebos below are the v8 canonical numbers reported in §5.1 (reduced-form robustness), which the manuscript uses to discipline the timing-and-sign benchmark — not the headline. The canonical policy result is the structural counterfactual decomposition — see AN-010 (decomposition) and AN-011 (welfare arithmetic).

Question

If the reduced-form price benchmark (AN-001) were driven by a differential pre-existing trend in group 65, applying the same specification with a fake treatment date inside the pre-period should detect that trend. A small placebo coefficient on prices supports parallel trends; a large one does not.

Design

  • Sample: pre-treatment data only, restricted to ensure the fake post-period stays inside the pre-period.
  • Variation: placebo cutoffs Sep 2017, Mar 2017, and Jun 2017, substituted for the real March 2018 cutoff.
  • Specification: the reduced-form DiD on \(\log p^{\mathrm{final}}\).
  • Outcomes: log prices (primary); log firms, log valid bids, distance reported in the broader reduced-form battery below.
  • Identification threats: cost shocks or trends inside the pre-period itself.

Results

Canonical v8 price placebos (§5.1), in the same DiD-in-reverse sign convention as the real cutoff:

Placebo cutoff \(g65 \times Pre\) on \(\log p^{\mathrm{final}}\)
Sep 2017 −0.013
Mar 2017 −0.030
Jun 2017 −0.034
Real cutoff (Mar 2018) −0.108 to −0.142

The placebo coefficients are far smaller in magnitude than the real-cutoff range, supporting parallel trends on the price margin.

Earlier reduced-form pipeline (fuller battery)

The v1–v4 pipeline (scripts/05_robustness.R → tab_placebo.tex) ran a two-date × four-outcome placebo battery. Its price placebos were −0.0145 (Sep 2017) and +0.0206 (Mar 2017) — slightly different point estimates from the v8 spec but the same qualitative conclusion (small, near-zero on the price margin). The firm- and bid-count placebos were significant and negative (e.g. log firms −0.104/−0.135; log bids −0.136/−0.134 at Sep/Mar 2017), and the distance placebo was null (+3.8 / −1.2 km).

Interpretation

The price-margin placebos are small relative to the real cutoff: all three pre-reform dates (−0.013, −0.030, −0.034) sit far below the −0.108 to −0.142 real-cutoff range (~10–11% movement). This is the load-bearing piece supporting parallel trends on the price margin.

The firm-count and bid-count placebos are significant — but the direction is informative. Both go in the same direction (negative) as the main DiDiR coefficient would predict if the policy effect started early. The reading is not that there was a pre-treatment cost shock specific to group 65; it is that the control groups were on a gradual SME-restriction rollout throughout the pre-period, so the cross-group DiDiR contrast captures the secular convergence trend rather than a clean policy effect on firm counts. This is documented in docs/robustness.md and is consistent with the firm-count attenuation pattern across windows in AN-002.

The distance placebo is null at both fake dates, ruling out a freight or logistics shock specific to group 65 around the policy break.

Confidence: yellow. The price-margin null is clean and load-bearing. The firm-count placebos are significant but interpreted as a documented secular trend in controls, not as a confound. The interpretation depends on accepting that reading rather than treating the firm-count placebo as a refutation of parallel trends; the price-margin null is the strict test.

Follow-ups

  • Goodman-Bacon decomposition (scripts/21_goodman_bacon.R) of the firm-count DiDiR coefficient into 2×2 building-block comparisons would directly expose how much of the firm-count effect comes from the policy switch vs the secular control-group rollout.
  • Synthetic-control (scripts/09_synth_control.R) reproduction: matches group 65 to a weighted combination of control groups on pre-treatment outcomes; should produce a similar price coefficient if parallel trends hold.