The Bureau of Labor Statistics (BLS) released the December 2014 CPI this past week. I expect to report on weightings changes with next month’s release, but for today, I want to write about the concept of a Personal Price Index. I have written a few times about how people experience inflation depending upon their age. I have been critical of the Federal Reserve targeting Core inflation when the elderly typically have higher than average medical, energy, and food expenses. By removing those items from Core inflation, Social Security benefits get indexed at a lower rate than inflation experienced by the people who receive it.
|Component||2013 Weight||2014 Weight||Importance|
|Food & Beverage||18.9%||15.3%||14.9%|
|Education & Communication||8.3||10.7||7.1|
For myself, I started with expenses in 2013 and 2014. I sub-totaled my expenses based on the naming convention of the BLS and compared it to the Importance factor in the latest release. You can see the results in Table 1. Right away, you can see I spend significantly less than average on Housing and significantly more on Other. I used Other for cash withdrawals as well as other miscellaneous items since I did not itemize how I spent cash.
|Component||2014 CPI||Weight Impact||CPI Impact||Expected CPI|
|Food & Beverage||3.27%||-29.7%||-0.97%||0.62%|
|Education & Communication||0.40||15.6||0.06||0.03|
Constructing Table 2 where I calculate my Personal Price Index will take some explanation. The concept of constructing the index is based on the choices I have made regarding purchases and how those choices shift as I age. The calculation starts with the 2013 weightings of my expenses and that becomes step 1. Step 2 takes those expenditures by component and inflates them using the 2014 CPI by component. The result is Expected Expenditures for 2014. For step 3, we need to find out the impact of the changes in expenditures. To do this, I took my actual expenses by component for 2014 and subtracted the result of step 2 and finally dividing by the result of step 2. In table 2, you can see the result in the column labeled Weight Impact.
Let’s spend some time on this column and grab the first row, Food & Beverage. By reducing my expenditure weighting from 18.9% to 15.3%, the impact from the change in weighting is -29.7%. Similarly, the Education & Communication line is impacted by 15.6% due to the increase in relative expenditures from 2013 to 2014.
The next column is titled CPI impact and the calculation is step 4. By multiplying the 2014 CPI for each component by the Weight Impact column, we get the impact on the Personal Price Index by component. Staying with the two example lines, the Food & Beverage component has a -0.97% impact to my Personal Price Index because my decrease in expenditures offset the large increase in the 2014 CPI. For Education & Communication, the large increase in weighting was offset by the small increase in 2014 CPI resulting in a 0.06% impact to me.
The opposite side shows up in the Transportation component where I had a substantial decrease in weighting from 2013 to 2014 which results in a -20.7% weight impact. Due to the -6.17% CPI in 2014, the impact to my personal price index becomes 1.28%. By decreasing my expenditures in Transportation, in effect I did not get to enjoy the decrease in prices.
Let me take a side note to explain why this calculation is odd and almost misleading. If I purchased 1000 gallons of gasoline in both 2013 and 2014, my expenditures in 2014 would have decreased in dollar terms compared to 2013 because prices went down. Notice the quantity of goods I purchased remained constant, but the value of those goods decreased. The purpose of the personal price index is to show how my choices affected my budget. By not increasing the quantity of goods that were decreasing in cost, the impact would be to increase my price index relative to the average consumer’s price index.
By adding the values of the CPI Impact column together, we arrive at my Personal Price Index for 2014 of 1.65%. The CPI reported by the BLS was 0.80% for 2014. While my price index was higher, it is not significantly out of line.
One last item to calculate: if we take the 2013 expenditure weighting and multiply it by the 2014 CPI, we get the final column titled Expected CPI. Summing the components together creates the expected personal price index of -0.07% for 2014. In other words, if my expenditure weights in 2014 matched my expenditure weights of 2013, I would have experienced a personal price index of -0.07% in 2014. The swing in the impact from the Transportation component is greatly felt through this result. Because of the choices I made in 2014, I felt the effects of inflation more than I should have.