Specific Factors Model — Interactive Graphs

ECON 171 · Spring 2026 · Week 3

Sasha Petrov

// ── SVG text helper: handles `_{..}` / `^{..}` scripts, `$..$` italic math ──
// Mirrors the helper used on other interactive decks in this project so that
// figure labels look consistent across weeks. No external KaTeX dependency
// for SVG-internal text (KaTeX is still available for Markdown slide text).
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// ── U.S. goods imports from China, 1991–2015 ($B nominal, annual) ──
// Source: FRED series IMPCH (U.S. Imports of Goods from China, NSA).
// Values rounded to 0.1 $B.
chinaImports = [
  {year: 1991, value: 19.0},  {year: 1992, value: 25.7},
  {year: 1993, value: 31.5},  {year: 1994, value: 38.8},
  {year: 1995, value: 45.6},  {year: 1996, value: 51.5},
  {year: 1997, value: 62.6},  {year: 1998, value: 71.2},
  {year: 1999, value: 81.8},  {year: 2000, value: 100.1},
  {year: 2001, value: 102.3}, {year: 2002, value: 125.2},
  {year: 2003, value: 152.4}, {year: 2004, value: 196.7},
  {year: 2005, value: 243.5}, {year: 2006, value: 287.8},
  {year: 2007, value: 321.4}, {year: 2008, value: 337.8},
  {year: 2009, value: 296.4}, {year: 2010, value: 364.9},
  {year: 2011, value: 399.4}, {year: 2012, value: 425.6},
  {year: 2013, value: 440.4}, {year: 2014, value: 468.5},
  {year: 2015, value: 483.2}
]

Today’s Agenda

1. Mobile vs. immobile (specific) factors
2. Average vs. marginal product of labor
3. Deriving the concave PPF
4. Winners and losers from trade
5. Incomplete specialization
6. Case study: The “China shock” in the United States

Structure of the Economy

Average vs. Marginal Product

Deriving the Concave PPF

Labor Market Equilibrium

Winners and Losers from Trade

Incomplete Specialization

Effects of Technology and Endowment Changes

Case Study: The China Shock

What happened after China joined the WTO?

• December 2001: China joined the WTO — locking in permanent normal trade relations with the U.S.
• U.S. goods imports from China tripled between 2000 and 2007 (~$100B → ~$320B)
• Competition fell heavily on labor-intensive manufacturing: apparel, furniture, toys, electronics
• Local labor markets (“commuting zones”) varied enormously in exposure — the variation Autor, Dorn & Hanson (2013) exploit

{
  const w = 560, h = 360;
  const margin = {top: 28, right: 20, bottom: 44, left: 56};
  const iw = w - margin.left - margin.right;
  const ih = h - margin.top - margin.bottom;

  const svg = d3.create("svg").attr("viewBox", [0, 0, w, h]).style("max-width", "100%");
  const g = svg.append("g").attr("transform", `translate(${margin.left},${margin.top})`);

  texLabel(g, iw / 2, -14, "U.S. goods imports from China, 1991–2015",
    {fontSize: 12, bold: true, anchor: "middle"});

  const x = d3.scaleLinear().domain([1990, 2016]).range([0, iw]);
  const y = d3.scaleLinear().domain([0, 520]).range([ih, 0]);

  g.append("g").attr("transform", `translate(0,${ih})`)
    .call(d3.axisBottom(x)
      .tickValues([1990, 1995, 2000, 2005, 2010, 2015])
      .tickFormat(d3.format("d")));
  g.append("g").call(d3.axisLeft(y).ticks(5));

  texLabel(g, iw / 2, ih + 34, "Year", {fontSize: 11});
  texLabel(g, -44, ih / 2, "$B (nominal)", {rotated: true, fontSize: 11});

  // Faint horizontal gridlines
  g.append("g").attr("opacity", 0.15).selectAll("line")
    .data(y.ticks(5)).join("line")
    .attr("x1", 0).attr("x2", iw)
    .attr("y1", d => y(d)).attr("y2", d => y(d))
    .attr("stroke", "#3e3e3e").attr("stroke-width", 0.5);

  // 2001: WTO accession reference
  g.append("line")
    .attr("x1", x(2001)).attr("x2", x(2001))
    .attr("y1", 0).attr("y2", ih)
    .attr("stroke", "#800000").attr("stroke-width", 1.2)
    .attr("stroke-dasharray", "4,3").attr("opacity", 0.8);
  texLabel(g, x(2001) + 4, 10, "WTO accession (Dec 2001)",
    {fontSize: 10, anchor: "start", color: "#800000", bold: true});

  // 2008 GFC marker
  g.append("line")
    .attr("x1", x(2008)).attr("x2", x(2008))
    .attr("y1", 0).attr("y2", ih)
    .attr("stroke", "#666").attr("stroke-width", 0.9)
    .attr("stroke-dasharray", "3,3").attr("opacity", 0.6);
  texLabel(g, x(2008) + 4, 26, "GFC", {fontSize: 9, anchor: "start", color: "#666"});

  // Series line
  const line = d3.line().x(d => x(d.year)).y(d => y(d.value)).curve(d3.curveMonotoneX);
  g.append("path").datum(chinaImports).attr("d", line)
    .attr("fill", "none").attr("stroke", "#005ab5").attr("stroke-width", 2.2);

  // Annotated endpoints
  g.append("circle").attr("cx", x(2000)).attr("cy", y(100.1)).attr("r", 3.5)
    .attr("fill", "#005ab5");
  texLabel(g, x(2000) - 4, y(100.1) - 12, "$100B in 2000",
    {fontSize: 10, anchor: "end"});

  g.append("circle").attr("cx", x(2007)).attr("cy", y(321.4)).attr("r", 3.5)
    .attr("fill", "#005ab5");
  texLabel(g, x(2007) + 6, y(321.4) - 6, "$321B in 2007",
    {fontSize: 10, anchor: "start"});

  texLabel(g, iw, ih + 34, "Source: FRED IMPCH",
    {fontSize: 9, color: "#555", anchor: "end"});

  return svg.node();
}

What does the SF model predict?

• The China shock is a negative relative price shock on U.S. import-competing manufacturing: \(p_M \downarrow\) (apparel, furniture, low-tech electronics)

• Two factors are effectively specific to manufacturing in the short/medium run:

  • Physical capital embedded in plants — cannot be repurposed for services
  • Workers with sector-specific human capital — skills, tenure, local networks

• Import-competing specific factors lose (wages in manufacturing fall; manufacturing capital returns fall); export-sector specific factors gain; mobile labor’s real wage is ambiguous

Testable prediction: losses should be concentrated by sector and geography — falling on workers, plants, and communities that cannot reallocate.

How exposed were different U.S. regions?

• CZ exposure = Chinese imports per worker, weighted by each CZ’s pre-shock industry mix

• Darker shading = highest quartile of exposure

• Concentrated across the industrial Midwest and Southeast; much of the West barely touched

Source: Autor, Dorn & Hanson (2013), Figure 1a.

What did Autor, Dorn & Hanson (2013) find?

• Exposed CZs: sharper declines in manufacturing employment share, lower wages, higher unemployment, lower LFP, higher per-capita transfers

• Headline magnitude: each extra $1,000 / worker of predicted exposure \(\Rightarrow\) ~0.3 pp fall in the manufacturing share of CZ working-age population

• Sharp (\(t = -4.77\)) and economically large in aggregate

Source: Autor, Dorn & Hanson (2013), Figure 2 — added-variable plot of the reduced-form relationship.

Why does SF fit where Ricardian and H-O don’t?

Ricardian

• Costless reallocation of labor from manufacturing to the expanding sector
• No concentrated losses — displaced workers simply move
• Aggregate gains from trade with essentially uniform incidence

Heckscher-Ohlin (Stolper-Samuelson)

• Losses fall on the scarce factor as a class — in the U.S., unskilled labor broadly
• All unskilled workers should see real wages fall, regardless of sector or location
• Incidence runs along factor-type lines, not geography

Specific factors — and what ADH observe. Losses are concentrated in the workers, capital, and places attached to the import-competing sector. Geography matters precisely because specific factors can’t move. Only the SF model delivers this sharp, localized incidence pattern — and that is the pattern the data actually show.

What does the SF model still miss?

• Slow, incomplete adjustment. SF is comparative-static; the data show a decade later, exposed CZs had not recovered manufacturing employment and displaced workers had not relocated

• Diffuse gains vs. concentrated losses. Every consumer benefits a little from cheaper goods; a small set of workers and communities bear nearly all of the cost

• Second-order effects the SF model is silent on: declines in marriage and fertility; rising “deaths of despair”; political polarization

• Policy implication. A trade shock can be Kaldor-Hicks efficient in aggregate yet deeply destabilizing when losers are concentrated and transfers do not follow them

SF gets the first-order distributional story right: losses are localized and persistent. The open frontier is the mechanisms behind slow adjustment.

Further reading: Autor, Dorn & Hanson, The China Syndrome (AER 2013).