U.S. Merger Retrospectives

A living Bayesian meta-analysis of merger price effects

Andrew Olsen  ·  Reed Orchinik  ·  Marc Remer

This project collects reduced-form, difference-in-differences estimates of the price effects of U.S. horizontal mergers and synthesizes them in a Bayesian hierarchical model. The website summarizes the results, shows where the literature is concentrated, and accepts submissions of new estimates so the synthesis can stay current.

Read the paper (SSRN)

7.1% Mean post-merger price increase across log-price retrospectives (95% CrI: 2.0% to 12.0%)

1.7x In a broader analysis, anticompetitive price outcomes are about 1.7 times more likely than procompetitive ones

Posterior distribution of the average price effect

muData = FileAttachment("draws_mu.csv").csv({typed: true})

muModels = ["Simple", "Intermediate", "Full"]
muColors = ["#9aa7b1", "#c98a3a", "#1c3d5a"]

// Shared bin edges so every model's area and line use the *same* bins —
// otherwise each series would bin over its own range and not line up.
muThresholds = d3.range(57).map(i => -0.05 + i * (0.225 / 56))

muSummary = muModels.map(m => {
  const v = muData.filter(d => d.model === m).map(d => d.mu).sort(d3.ascending);
  return {
    model: m,
    median: d3.quantile(v, 0.5),
    lo: d3.quantile(v, 0.025),
    hi: d3.quantile(v, 0.975),
    pPos: d3.sum(v, x => x > 0) / v.length
  };
})

Plot.plot({
  height: 300,
  marginLeft: 48,
  marginBottom: 42,
  x: {label: "Average merger price effect (μ) →", tickFormat: "+.0%",
      grid: true, domain: [-0.05, 0.175]},
  y: {label: "posterior density", ticks: []},
  color: {domain: muModels, range: muColors, legend: true},
  marks: [
    Plot.ruleX([0], {strokeDasharray: "4 3", stroke: "#888"}),
    // One area + one line per model, as separate marks, so the fills OVERLAP
    // rather than stack. Each line traces the top of its own fill exactly.
    ...muModels.flatMap(m => {
      const d = muData.filter(r => r.model === m);
      return [
        Plot.areaY(d, Plot.binX({y: "count"},
          {x: "mu", fill: () => m, curve: "basis", fillOpacity: 0.2,
           thresholds: muThresholds})),
        Plot.lineY(d, Plot.binX({y: "count"},
          {x: "mu", stroke: () => m, curve: "basis", strokeWidth: 2.2,
           thresholds: muThresholds}))
      ];
    }),
    Plot.dot(muSummary, {x: "median", y: () => 0, fill: "model", r: 4.5,
      stroke: "white", strokeWidth: 1.5,
      title: d => `${d.model} model\nMedian: ${(d.median*100).toFixed(1)}%\n` +
                  `95% CrI: ${(d.lo*100).toFixed(1)}% to ${(d.hi*100).toFixed(1)}%`,
      tip: true})
  ]
})

html`<p class="fig-note">
In the full model, the average merger raised prices by an estimated
<strong>${(muSummary[2].median*100).toFixed(1)}%</strong>
(95% credible interval ${(muSummary[2].lo*100).toFixed(1)}% to
${(muSummary[2].hi*100).toFixed(1)}%). The posterior places
<strong>${(muSummary[2].pPos*100).toFixed(1)}%</strong> of its mass above zero.
Hover any point for that model's estimate.
</p>`

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