Homework 3 — Hospital Competition and Pricing

Instructions

This homework covers hospital market structure, competition, and pricing. It is empirical only — the theory for this module is assessed in class (quizzes and the midterm).

You are required to use an AI coding assistant for this assignment. Use GitHub Copilot (free with your Emory GitHub account) or your tool of choice, and let it write the R or Python. Your job is not to produce the code. Your job is to direct the tool, check what it returns, and interpret it as a health economist. The AI will frequently hand you a confident, clean, and wrong answer. Catching that is the assignment.

Submit a rendered notebook (Quarto, R Markdown, or Jupyter) containing your code, its output, and your written answers. Each part is worth 3 points, graded:

  • 3 points: correct, with sound economic reasoning
  • 2 points: close, minor error or thin reasoning
  • 1 point: attempted but the economic judgment is missing or wrong
  • 0 points: no work, or the unexamined AI output pasted in

Verification note (required, embedded): somewhere in your notebook, flag one specific point where the AI’s first output was wrong, incomplete, or misleading, and explain in economic terms how you knew. “It ran without errors” does not count.

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

Data for both questions: the hospital file on the shared OneDrive (link on Canvas), built from the Hospital Cost Report Information System (HCRIS) and the Hospital Service Area Files. Markets are defined three ways: zip code, HRR, and a pre-computed “market” from a community-detection algorithm. 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.

Q4 — Market definition and concentration (15 pts)

  1. Have the AI 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. 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. Your part (a) averages HHI across markets. Single-hospital markets have HHI = 10,000 and, in a simple unweighted average, dominate the result. Show what the AI’s default unweighted average hides, and how weighting (or excluding trivial markets) changes the picture.

  4. Market share’s denominator is total discharges in the correctly grouped market. Add a sanity 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. 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?

Q5 — Prices and market structure (15 pts)

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

  1. Have the AI compute the average hospital price in each year and plot it. Then look at the price variable: check its min, max, and share missing, and flag impossible or implausible values (HCRIS price fields mix charges and payments and contain negatives and extreme outliers). Decide on a cleaning rule, apply it, and show how the average changes.

  2. 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. 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. Concentrated markets differ systematically from competitive ones — they tend 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. State your bottom line: is the price-concentration correlation you found causal evidence that concentration raises prices? Use this question for your required verification note.