Homework 3 — Hospital Competition and Pricing

Instructions

This homework is about hospital market structure, competition, and pricing, the material from the third module of the course. It is empirical only. The theory is assessed in class through the quizzes and the midterm. Here you work with real data and interpret it as a health economist.

You are expected to use an AI coding assistant. GitHub Copilot is free with your Emory GitHub account, and you can use another tool if you prefer. It writes most of the code for you, in R or Python. You are graded on your answers, as in any assignment. Read what the assistant gives you, make sure it actually answers the question, and explain what it means in economic terms.

Submit your work as a private GitHub repository. Start from the homework template, do your analysis in the notebook or Quarto starter, and commit both the source file and a rendered copy of your answers. Create the repository as private, add imccart and scai5 as collaborators, and paste the repository link into the Homework submission card on Commons. Full instructions are on the assignments page. Each part is graded on this scale, scaled to the points shown for that part:

  • Full credit: correct, with sound economic reasoning.
  • Partial credit: close, with a minor error or thin reasoning.
  • Little credit: attempted, but the economic reasoning is missing or wrong.
  • No credit: no real work, or output pasted in with no interpretation.

Homework 3 is due by midnight on Friday, November 13.

Both questions use hospital-panel.csv (on the shared OneDrive, linked from Canvas), one row per hospital and year from 1998 through 2017, built from the Hospital Cost Report Information System (HCRIS) and the Hospital Service Area Files. It includes each hospital’s discharges, beds, and a constructed price, along with three ways of defining its market, namely its zip code, its Hospital Referral Region (hrr), and a pre-computed community-detection market (mkt). Throughout, define the market share of hospital \(i\) in market \(m\) in year \(t\) as \(s_{imt} = q_{imt} / \sum_{j} q_{jmt}\), where \(q\) is discharges.

Q1 — Market definition and concentration (15 pts)

  1. (3 points) Compute HHI three ways. Compute the HHI for each market and year under all three market definitions (zip, HRR, community-detection), and plot the average HHI over time for each definition.

  2. (3 points) Why the definition matters. Explain why your assessment of how concentrated hospital markets are changes with the definition. Which definition is “correct,” and why is there no single right answer?

  3. (3 points) The problem with a simple average. Your part (a) averages HHI across markets. Single-hospital markets have HHI = 10,000, and a simple unweighted average gives each of them the same weight as a large market, so the many small markets raise the average. Show how weighting by discharges, or excluding single-hospital markets, changes the result, and what the plain average was leaving out.

  4. (3 points) A sanity check on the join. Market share’s denominator is total discharges in the correctly grouped market. Add a check that shares sum to 1 within each market-year, and explain what a careless join, one that mismatched hospitals to markets, would do to that check and to your HHI.

  5. (3 points) Maximum share instead of HHI. Recompute part (a) using the maximum market share \(s^{max}_{mt} = \max_i s_{imt}\) instead of HHI (average across markets, plot over time). Does your assessment of competitiveness change, and what does the contrast with HHI tell you?

Q2 — Prices and market structure (15 pts)

Use the same hospital data, focusing on the community-detection market measure.

  1. (3 points) The price variable. Compute the average hospital price in each year and plot it. Then look closely at the price variable itself. This price is not a sticker price. It is constructed from HCRIS as adjusted charges net of Medicare payments, divided by non-Medicare discharges, and it is in nominal dollars. Examine its distribution (its range and spread) and explain what this measure does and does not capture as a hospital “price,” and what those limitations mean for how you read the trend you plotted.

  2. (3 points) Concentrated vs competitive markets. Identify market-years that are monopolies or duopolies (exactly one or two hospitals) and those that are “competitive” (at least four hospitals). Plot the count of each type over time.

  3. (3 points) Price by market structure. Compute the average price in each year within the monopoly/duopoly group and within the competitive group. Show the comparison. Does concentration appear to correlate with price?

  4. (3 points) The market-size confound. Concentrated markets differ systematically from competitive ones, tending to be smaller and more rural. Repeat part (c) after limiting to markets with between 10,000 and 50,000 total discharges per year. Explain what changes and why market size confounds the raw price-concentration relationship.

  5. (3 points) Is it causal? State your conclusion. Is the price-concentration correlation you found causal evidence that concentration raises prices, and what would you need to make a causal claim?