<blockquote>
<p>Shouldn't it be the case that the &quot;Commodities less food&quot; inflation rate is some kind of average or convex combination of &quot;Energy commodities&quot; and &quot;Commodities less food and energy commodities&quot;?</p>
</blockquote>
<p>CPI is a weighted average of prices, inflation is  change in that weighted average over time. If you want to combine different inflation rates you need to adjust them by their relative weights.</p>
<p>For example, in table 1 if you would multiply all inflation rates by their weights then you would get the overall inflation rate. If you would want to do it for some subcategories you would first have to know what weight is that subcategory given in the overall category.</p>
<p>Moreover, I wanted to check your numbers and it seems you got the last two numbers (-2% and -1.9%) from table I which has more expenditure categories, and you got the -1.7% from table III which has special aggregate indexes.</p>
<p>There is no reason to assume, unless the document somewhere states otherwise, that the expenditure categories from table I somehow can neatly add up to the special aggregate indexes in table III.</p>
<p>In fact, it would not even be true that the expenditure categories between the more macro table I and more detailed breakdown II would neatly add up since it is not necessary true that macro expenditure category commodities less food and energy commodities combined with another macro expenditure category energy commodities would result in category with the same items as some micro category called commodities less food. Generally unless somewhere stated otherwise, you should not assume that the category labels between multiple tables focusing on different level of analysis are consistent.</p>
<blockquote>
<p>In terms of the commodities themselves, isn't &quot;Commodities less food&quot; equal to &quot;Energy commodities&quot; plus &quot;Commodities less food and energy commodities&quot;?</p>
</blockquote>
<p>No. Again you have to adjust CPI by their relative weights. Moreover, in your case the last two categories are expenditure categories and the first one is special aggregated index.</p>

CC BY-SA 4.0
2024-08-26T13:03:28.080Z
The relative weights for the three categories add up, suggesting that the categories are equal in terms of commodities. From the column for "Relative Importance June 2024": Commodities less food = 22.304; Commodities less food and energy commodities = 18.545; Energy commodities = 3.758
deflator123
CC BY-SA 4.0
2024-08-26T13:27:19.963Z
@deflator123 even if the relative weights add up you can’t just sum those numbers, you need to know what weights those categories have relative to the category you want to add them up to as explained above
1muflon1
CC BY-SA 4.0
2024-08-26T13:46:40.560Z
Are you suggesting to use another series as the weights, instead of "relative importance"?

How can an weighted average of -1.9% and -2.0% turn out to be equal to -1.7%?
deflator123
CC BY-SA 4.0
2024-08-26T15:09:33.937Z
@deflator123 1. What I am saying is that to combine those inflation rates you would need to know the weights of them as if the largest category was the total category. With provided weights you are given them you can construct just the overall inflation or a portion of total inflation coming from some category. 2. As I keep explaining the table III uses aggregated index, even if it uses same weight I do not think you should use it in calculation for the categories in table I even if the weights match. Just because the weights match doesn't mean the methodologies are same for the SAI
1muflon1
CC BY-SA 4.0
2024-08-26T15:29:01.150Z
1. What are the weights you're referring to, different than the 'relative importance?' 2. How are the methodologies different for tables 1 and 3?
deflator123
CC BY-SA 4.0
2024-08-26T18:43:24.113Z
@deflator123 every CPI or sub-CPI will be constructed based on weighting prices of items according to certain rules. The reason why I am being vague about it is that there are multitudes of ways how to determine those weights. Two different CPIs will not necessary construct these weights in the same way. 2. As mentioned before table III shows the special  aggregated index construction of which BLS describes here; https://www.bls.gov/cpi/factsheets/constructing-special-cpis.htm
1muflon1
CC BY-SA 4.0
2024-08-27T00:20:47.773Z
The first paragraph on the page that you link mentions the series "all items less food and energy". That series is in Table 1, not Table 3. Are you suggesting that page is relevant to Table 1 or Table 3, or both?
deflator123
CC BY-SA 4.0
2024-08-27T07:47:35.983Z
@deflator123 the first paragraph also says that is just an example. It is relevant for the special aggregated indexes so Table 3.
1muflon1
CC BY-SA 4.0
2024-08-27T13:59:04.893Z
Any reasonable reading of the page you linked suggests that the same methodology is used to calculate the aggregates in both Table 1 and Table 3. The only weights that we have discussed with any specificity suggest that the three categories in OP are precisely equal. Do you have any evidence to support your comments in this thread?
deflator123
CC BY-SA 4.0
2024-08-27T15:38:06.037Z
@deflator123 Aside from that link also BLS handbook ch 17 part I states; “BLS also calculates and publishes indexes for special aggregations, such as energy items, that cut across preexisting classification scheme.” The preceding classification scheme they list includes the expenditure class. In addition I do not understand what makes you think they are the same. Generally, unless stated otherwise if in one document uses different name for different variable then conventionally they are not same unless stated otherwise. I see nothing in the document you post that would suggest
1muflon1
CC BY-SA 4.0
2024-08-27T15:38:39.833Z
Expenditure categories are somehow equivalent to special aggregated indexes when you add them up based on the qualitative description of category, even if in this case those two categories together have the same weight for overall CPI.
1muflon1
CC BY-SA 4.0
2024-08-26T09:59:54.133Z
2024-08-26T09:59:54.133Z
1muflon1
<p>The latest CPI report shows inflation for these line items (12 month unadjusted change to July 2024):</p>
<p>Commodities less food: -1.7%</p>
<p>Commodities less food and energy commodities: -1.9%</p>
<p>Energy commodities: -2.0%</p>
<p>Why is the inflation rate of &quot;commodities less food&quot; greater than both &quot;Energy commodities&quot; and &quot;Commodities less food and energy commodities?</p>
<p>Shouldn't it be the case that the &quot;Commodities less food&quot; inflation rate is some kind of average or convex combination of &quot;Energy commodities&quot; and &quot;Commodities less food and energy commodities&quot;?</p>
<p>In terms of the commodities themselves, isn't &quot;Commodities less food&quot; equal to &quot;Energy commodities&quot; plus &quot;Commodities less food and energy commodities&quot;?</p>
<p>[ https://www.bls.gov/news.release/pdf/cpi.pdf ]</p>

<macroeconomics><inflation><data>
CPI: Why is the inflation rate of "commodities less food" greater than both "Energy commodities" and "Commodities less food and energy commodities"?
deflator123
# CPI: Why is the inflation rate of "commodities less food" greater than both "Energy commodities" and "Commodities less food and energy commodities"?

(Asked by: username_0 on 2024-08-26)

The latest CPI report shows inflation for these line items (12 month unadjusted change to July 2024):

Commodities less food: -1.7%

Commodities less food and energy commodities: -1.9%

Energy commodities: -2.0%

Why is the inflation rate of "commodities less food" greater than both "Energy commodities" and "Commodities less food and energy commodities?

Shouldn't it be the case that the "Commodities less food" inflation rate is some kind of average or convex combination of "Energy commodities" and "Commodities less food and energy commodities"?

In terms of the commodities themselves, isn't "Commodities less food" equal to "Energy commodities" plus "Commodities less food and energy commodities"?

[ https://www.bls.gov/news.release/pdf/cpi.pdf ]

**Tags:** macroeconomics, inflation, data


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## 1 answers

### Answer by username_1 on 2024-08-26. Score: 0

> Shouldn't it be the case that the "Commodities less food" inflation rate is some kind of average or convex combination of "Energy commodities" and "Commodities less food and energy commodities"?

CPI is a weighted average of prices, inflation is change in that weighted average over time. If you want to combine different inflation rates you need to adjust them by their relative weights.

For example, in table 1 if you would multiply all inflation rates by their weights then you would get the overall inflation rate. If you would want to do it for some subcategories you would first have to know what weight is that subcategory given in the overall category.

Moreover, I wanted to check your numbers and it seems you got the last two numbers (-2% and -1.9%) from table I which has more expenditure categories, and you got the -1.7% from table III which has special aggregate indexes.

There is no reason to assume, unless the document somewhere states otherwise, that the expenditure categories from table I somehow can neatly add up to the special aggregate indexes in table III.

In fact, it would not even be true that the expenditure categories between the more macro table I and more detailed breakdown II would neatly add up since it is not necessary true that macro expenditure category commodities less food and energy commodities combined with another macro expenditure category energy commodities would result in category with the same items as some micro category called commodities less food. Generally unless somewhere stated otherwise, you should not assume that the category labels between multiple tables focusing on different level of analysis are consistent.

> In terms of the commodities themselves, isn't "Commodities less food" equal to "Energy commodities" plus "Commodities less food and energy commodities"?

No. Again you have to adjust CPI by their relative weights. Moreover, in your case the last two categories are expenditure categories and the first one is special aggregated index.

> **Comments:**
> **username_0**: The relative weights for the three categories add up, suggesting that the categories are equal in terms of commodities. From the column for "Relative Importance June 2024": Commodities less food = 22.304; Commodities less food and energy commodities = 18.545; Energy commodities = 3.758  
> **username_1**: @username_0 even if the relative weights add up you can’t just sum those numbers, you need to know what weights those categories have relative to the category you want to add them up to as explained above  
> **username_0**: Are you suggesting to use another series as the weights, instead of "relative importance"?  How can an weighted average of -1.9% and -2.0% turn out to be equal to -1.7%?  
> **username_1**: @username_0 1. What I am saying is that to combine those inflation rates you would need to know the weights of them as if the largest category was the total category. With provided weights you are given them you can construct just the overall inflation or a portion of total inflation coming from some category. 2. As I keep explaining the table III uses aggregated index, even if it uses same weight I do not think you should use it in calculation for the categories in table I even if the weights match. Just because the weights match doesn't mean the methodologies are same for the SAI  
> **username_0**: 1. What are the weights you're referring to, different than the 'relative importance?' 2. How are the methodologies different for tables 1 and 3?  
> **username_1**: @username_0 every CPI or sub-CPI will be constructed based on weighting prices of items according to certain rules. The reason why I am being vague about it is that there are multitudes of ways how to determine those weights. Two different CPIs will not necessary construct these weights in the same way. 2. As mentioned before table III shows the special  aggregated index construction of which BLS describes here; https://www.bls.gov/cpi/factsheets/constructing-special-cpis.htm  
> **username_0**: The first paragraph on the page that you link mentions the series "all items less food and energy". That series is in Table 1, not Table 3. Are you suggesting that page is relevant to Table 1 or Table 3, or both?  
> **username_1**: @username_0 the first paragraph also says that is just an example. It is relevant for the special aggregated indexes so Table 3.  
> **username_0**: Any reasonable reading of the page you linked suggests that the same methodology is used to calculate the aggregates in both Table 1 and Table 3. The only weights that we have discussed with any specificity suggest that the three categories in OP are precisely equal. Do you have any evidence to support your comments in this thread?  
> **username_1**: @username_0 Aside from that link also BLS handbook ch 17 part I states; “BLS also calculates and publishes indexes for special aggregations, such as energy items, that cut across preexisting classification scheme.” The preceding classification scheme they list includes the expenditure class. In addition I do not understand what makes you think they are the same. Generally, unless stated otherwise if in one document uses different name for different variable then conventionally they are not same unless stated otherwise. I see nothing in the document you post that would suggest  
> **username_1**: Expenditure categories are somehow equivalent to special aggregated indexes when you add them up based on the qualitative description of category, even if in this case those two categories together have the same weight for overall CPI.  

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