Price Index

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Expenditure vs. Price Index

August 18, 2011 in Economics - General | 2 comments

Can health care productivity be increasing even as costs are rising so fast?  This may be the case.   One study by Aizcorbe and Nestoriak (2011) examines this phenomenon.

“Using retrospective claims data for a sample of commercially insured patients, we find that, on average, expenditures to treat diseases rose 11% from 2003Q1 to 2005Q4 and would have risen even faster, 18%, had the mix of services remained fixed at the 2003Q1 levels.  This suggests that fixed-basket price indexes, as are used in the official statistics, could overstate true price growth significantly.”

Much of the decrease in cost to treat specific conditions come from a shift of patients from inpatient care to outpatient surgical centers.  The question is, was this change a one time productivity gain, or does the health care system have other options for improving productivity (in the sense of reducing cost for the same quality).  It could be the case that Health IT and electronic medical records could produce synergies.  Alternatively, more intensive use of physician assistants and nurse practitioners could reduce the cost of treating many conditions.  We will see what the future holds.

Notes: The authors analysis uses the Symmetry grouping algorithm to define episodes of care.  By using the groupers, the authors are not required to have extensive medical knowledge to perform this analysis.   On the other hand, because the groupers are proprietary, the algorithms can be seen as a ‘black box.’

The formula used to estimate the expenditure and price indices are:

  • Price: {Σcd2xd1/N1}/ {Σcd1xd1/N1}
  • Expenditure: {Σcd2xd2/N2}/ {Σcd1xd1/Nd1}

Where cdt is the cost per episode of type d in year t, xdt is the number of episodes with disease d in time t, and
Nt is the total number of beneficiaries in time t.

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Substitution and Price Indices

April 15, 2010 in Economics - General | No comments

In this post, I discussed how to construct the Laspeyres, the Paasche, and the Fisher price index.  In practice, the Laspeyres tends to overstate the price increase and the Paasche tends to understate the price increases.  Let us look at the following example to see why this is the case.

In this spreadsheet, I use the example of a doctor’s visit to an internist and a doctor’s visit to a nurse practitioner.  Assume that there is no health insurance.  In the first period, it costs $200 to see the internist and $100 to see the nurse practitioner.  In this case, 10 patients visit each type of provider (20 total visits).  However, in the second period, the price for an internist visit rises to $350 (75% increase) while the price of a visit to a nurse practitioner only rises to $125 (25% increase).  Because of the difference in both the rate and level of price increases, some patients will stop seeing the internist and will instead visit the nurse practitioner.

Because the change in prices is between 25% (for the NP) and 75% (for the internist), we know the resulting price index value will be between 1.25 and 1.75.  If we use the Laspeyres index and weight the price changes by the initial quantities, the value of the price index in period 2 is 1.58.  However, if we use the Paasche index and weight the price changes by the terminal quantities, then the price index value in the second period is only 1.45.

The Laspeyres overstates the price increase, because it does not take into account the fact that people switched from the expensive internist to the cheaper nurse practitioner.  On the other hand, the Paache index understate the price increases because it ignores the fact that some people had to switch from their preferred provider (internist) to a less preferred provider (NP) because of the price change.  It ignores that some people are getting lower quality care when they switch to the NP.  [Disclaimer! This is just a simple example where I assume internists care is superior to NP care when I realize that in reality, this may or may not be the case].

One could apply the Fisher index as well which is the geometric mean of the Laspeyres and the Paasche.   The Fisher index takes into account the substitution between goods or services over time.  In this case, the price index value is a more reasonable 1.52.

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How to construct a Price Index

February 8, 2010 in Econometrics, Economics - General | No comments

Price indices are useful for calculating inflation over time.  The consumer price index (CPI) measures changes in prices for the overall economy.  Researchers can also use price indices to understand the evolution of the price of health care over time.  For instance, the Bureau of Labor Statistics also calculates a CPI for Medical Care and Medical Care Services.

The question of how to calculate a price index is far from trivial however.  To calculate the change in the price of any good between years 1 and T, one could simply use the following formula:

  • Psimple=piT/pi1

However, a price index indicates the change in prices for a basket of goods.  If you are considering the change in price of 10 medical services, how much weight to you give to each one?

Economists have generally come up with the solution: the goods that make up a large share of total expenditures should be weighed more than those that make up a small share.  For instance, let us imagine a simple example where you have two expenses: food and medical care.  The price of food goes up by 10% and the price of medical care goes up by 20%.  Let us assume that food makes up a larger share of your budget than medical expenses and that the initial value of the price index is 1.0 (i.e., T=1).  Thus, if 80% of your income goes to food and 20% of your income goes to medical expenses, than the value of the price index one year from now would be would be 80%*1.1+20%*1.2=1.12.

Sounds easy right?  Not so fast.

I said that 80% of the person’s budget was made up by food, but does that figure refer to your budget expenditures in the first time period or the second time period?  Let us assume the following:

  • Pfood,1=$1; Qfood,1=800; Efood,1=$800;
  • Pfood,2=$1.1; Qfood,2=800; Efood,2=$880;
  • Pmed,1=$100; Qmed,1=2; Emed,1=$200;
  • Pmed,2=$120; Qmed,2=3; Emed,2=$360;

Above, P, Q and E refers to price, quantity and expenditures respectively; the first subscript in the formulas above refers to the good (food or medicine) and the second subscript refers to the time period (1 or 2).  In the example, 80% of the person’s budget in period 1 is for food and 20% is for medical supplies.  If we use the budget shares in the first period to weight the price changes, then we could calculate the price index as:

  • (800*$1.1+2*$120)/(800*$1+2*$100)=1.120

This method is known as the Laspeyres price index.  The general formula is: [Σ pitqi0]/[Σ pi0qi0].

An alternative measure is the Paasche  price index.  In this case, we weight the price changes depending on the bundle of goods in the last time period under consideration.  In the example, our price index would be:

  • (800*$1.1+3*$120)/(800*$1+3*$100)=1.127

The price index is higher now.  Why?  In the last period, the quantity of medical care we purchased increase (for 2 to 3) compared to the quantity of food purchased (stayed the same at 800).  This means that the Paasche price index will put relatively more weight on the price changes for medicine.  Since the price of medicine increased faster than the price of food, the overall price index level be higher in this example than in the case of the Laspeyres price index.  The general formula for the Paasche price index is: [Σ pitqiT]/[Σ pi0qiT].

However, both the Laspeyres and Paasche indices do not take into account substitution effects between goods. Goods are weighed statically based on the quantity purchased in either the first period (Laspeyres) or last period (Paasche). To solve this problem, one can use the Fisher price index. This index does account for individuals substituting across different types of goods. To calculate the Fischer index, one simply takes the geometric mean of the Laspeyres and Paasche indices. According to the example above, this means the price index would be:

  • Pf=(Pp*Pl)0.5=(1.120*1.127)0.5=1.123

One can also chain the Fisher index calculations from each year in order to produce a chain-weighted Fisher price index, but I’ll save that explanation for another day.

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Calculating zero inflation when drug costs rose from $100 to $36,000

August 23, 2009 in Pharmaceuticals | No comments

A paper by  Claudio Lucarelli and Sean Nicholson  (2009) examines the skyrocketing cost of colorectal cancer treatment.  In 1993, the price of treating these patients with chemotherapy was only $100.  By 2005, this price had skyrocketed to $36,000.  Is this what is wrong with our health care system?

The authors claim that the answer is no.  Although prices increased, so did quality.  Thus, the price per unit of quality has stayed fairly constant over time.  In the author’s words:

“Using discrete choice methods to estimate demand, we construct a price index for colorectal cancer drugs for each quarter between 1993 and 2005 that takes into consideration the quality (i.e., the efficacy and side effects in randomized clinical trials) of each drug on the market and the value that oncologists place on drug quality.  A naive price index, which makes no adjustments for the changing attributes of drugs on the market, greatly overstates the true price increase.  By contrast, a hedonic price index and two quality-adjusted price indices show that prices have actually remained fairly constant over this 13-year period, with slight increases or decreases depending on a model’s assumptions.”

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Estimating Price increases for Medicare using Bundling

June 4, 2009 in HC Statistics | No comments

One question that plagues health economists is estimating the price inflation of medical care.  The output measured in these indices should be “health,” but this is often difficult to measure. Typically, economists simply look at the price increase of different inputs (e.g., the cost of a doctor’s visit, the cost of pharmaceuticals, the cost of different procedures)

In a novel approach, Aizcorbe and Nestoriak (2008) use cost of a bundle of treatments for a given disease as the unit of measurement.  This way, the authors can track how the cost to treat a specific disease changes over time. Even if the input costs for treating a disease increase over time, the mix of inputs used to treat a disease may also shift.  Further, if a new treatment arises, this will be included in the treatment bundles, eliminating the “new goods problem.”  The authors find the following results:

“ While the price of treating diseases grew an average of 12% over this period [2003-2005], costs would have risen even faster, 17%, if the mix of treatments in 2005 had been the same as that in 2003…For example, in the treatment of depression, there  has been a shift away from talk-therapy and towards (the lower cost) drug therapy that has reduced the cost of treating depression…[also, there have been] shifts from care at hospitals towards care at ambulatory surgical centers for orthopedic and gastroenterological conditions…”

In order for this estimation to be valid, a few things must hold.  First, disease severity must be constant over time.   Second, treatment outcomes must be constant over time.  If increase spending leads to a better outcome, this may not be price inflation, but simply a better treatment bundle.  Bundling will not correct this problem.  Third, the period of observation is only over 3 years and the data lacks information on Medicare claims.  Nevertheless, the bundling of treatments provides an attractive option to constructing medical care price indices.

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