Key Results

Across the U.S. horizontal mergers that economists have studied, the predicted price effect was about 7% on average. A broader analysis finds that anticompetitive price outcomes are about 1.7 times as common as procompetitive ones. Estimated effects vary across mergers, and the variation within a single merger (across products, geographies, and time) is larger than the variation across mergers.

The average price effect

The meta-analysis uses 273 log-price difference-in-differences estimates drawn from 42 papers, the subset of the literature which reports the price effect in percentage terms. A Bayesian hierarchical random-effects model pools these estimates while weighting each by its precision and accounting for the fact that several estimates can come from the same merger or industry.

Across three nested specifications (Simple, Intermediate, and Full), the posterior mean of the average price effect ranges from about 5% to 7%. The preferred Full Model gives a mean of 7.06% with a 95% credible interval of 2.0% to 12.0%. In none of the specifications does the credible interval cross zero.

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>`

A second result: the direction of effects

The 42-paper meta-analysis is restricted to a single regression specification for comparability. To use the rest of the literature, the paper develops a companion model that aggregates the direction of estimated effects across the larger sample of 68 papers and 444 estimates.

In this broader sample, anticompetitive outcomes are about 1.7 times more likely than procompetitive outcomes. The qualitative conclusion, that studied mergers have on average been anticompetitive with respect to price, holds in the broader sample as well as the log-price subset.

How the effect varies

The model lets us decompose where the variation in estimated price effects comes from: across industries, across mergers within an industry, and across estimates from the same merger.

indData = FileAttachment("draws_industry.csv").csv({typed: true})

indSummary = Array.from(
  d3.group(indData, d => d.industry),
  ([industry, rows]) => {
    const v = rows.map(d => d.eta).sort(d3.ascending);
    return {
      industry,
      median: d3.quantile(v, 0.5),
      lo95: d3.quantile(v, 0.025), hi95: d3.quantile(v, 0.975),
      lo80: d3.quantile(v, 0.10),  hi80: d3.quantile(v, 0.90)
    };
  }
).sort((a, b) => d3.descending(a.median, b.median))

Plot.plot({
  height: 340,
  marginLeft: 175,
  marginBottom: 42,
  x: {label: "Industry mean merger price effect (ηᵢ) →", tickFormat: "+.0%", grid: true},
  y: {label: null, domain: indSummary.map(d => d.industry)},
  marks: [
    Plot.ruleX([0], {strokeDasharray: "4 3", stroke: "#888"}),
    Plot.ruleY(indSummary, {y: "industry", x1: "lo95", x2: "hi95",
      stroke: "#1c3d5a", strokeWidth: 1.6}),
    Plot.ruleY(indSummary, {y: "industry", x1: "lo80", x2: "hi80",
      stroke: "#1c3d5a", strokeWidth: 7, strokeOpacity: 0.32}),
    Plot.dot(indSummary, {y: "industry", x: "median", r: 5.5,
      fill: d => d.median < 0 ? "#7b2d3b" : "#1c3d5a",
      stroke: "white", strokeWidth: 1.5,
      title: d => `${d.industry}\nMedian: ${(d.median*100).toFixed(1)}%\n` +
                  `80% CrI: ${(d.lo80*100).toFixed(1)}% to ${(d.hi80*100).toFixed(1)}%\n` +
                  `95% CrI: ${(d.lo95*100).toFixed(1)}% to ${(d.hi95*100).toFixed(1)}%`,
      tip: true})
  ]
})

html`<p class="fig-note">
Each dot is an industry's estimated mean effect; the thick bar is the 80%
credible interval and the thin line the 95% interval. Estimates range from
<strong>${(d3.min(indSummary, d => d.median)*100).toFixed(1)}%</strong>
(${indSummary[indSummary.length - 1].industry}) to
<strong>${(d3.max(indSummary, d => d.median)*100).toFixed(1)}%</strong>
(${indSummary[0].industry}). Hover a point for its intervals.
</p>`

• Industries. Healthcare mergers, the bulk of which are hospital mergers, have historically had the largest estimated price effects. The industrials sector, mostly airline mergers, also stands out. Excluding both, the average across the remaining mergers is about 4% and still positive with high posterior probability.
• Within vs. across mergers. The largest source of variation in the Meta-Study Sample is within mergers, across the products, geographies, and time windows, rather than across mergers. In the broader-sample direction model, the ordering reverses: estimates within a merger differ in magnitude but tend to agree on sign.

A practical implication discussed in the paper: because effects can vary so much within a single merger, antitrust analysis is usually better done at the level of individual product and geographic markets than by extrapolating from one merger to another.