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I am trying to distribute inflation in a hierarchical model. In both of the following two scenarios, the Laspeyres' Index over the entire data set is 1.8; However, in the first scenario, the inflation is caused by a rise in prices in Florida. i.e. the inflation is 1.8, and is caused by a change in relative prices between states. In the second scenario, the inflation is caused by a rise in the price of Juice everywhere. i.e. the inflation is 1.8 and is caused by a change in relative prices between products.

I would like a metric that captures this intuition in a general scenario that gives a ratio (or something like it) of inflation-causality of price redistribution between states and price redistribution between products. I have not been able to find anything in the literature, and I am having difficulty diving anything. Any direction is appreciated.

(note that the quantity at time 1 doesn't enter into the calculation, it's just displayed for completeness)

SCENARIO 1

+---------+-------+-------------+--+-------------+
|         |       | time 0      |  | time 1      |
+---------+-------+-------------+--+-------------+
|         |       | price | qty |  | price | qty |
+---------+-------+-------+-----+--+-------+-----+
| Florida | Nuts  | 1     | 10  |  | 2.6   | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 5.2   | 40  |
+---------+-------+-------+-----+--+-------+-----+
|         |       |       |     |  |       |     |
+---------+-------+-------+-----+--+-------+-----+
| Alabama | Nuts  | 1     | 10  |  | 1     | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 2     | 40  |
+---------+-------+-------+-----+--+-------+-----+

SCENARIO 2

+---------+-------+-------------+--+-------------+
|         |       | time 0      |  | time 1      |
+---------+-------+-------------+--+-------------+
|         |       | price | qty |  | price | qty |
+---------+-------+-------+-----+--+-------+-----+
| Florida | Nuts  | 1     | 10  |  | 1     | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 4     | 40  |
+---------+-------+-------+-----+--+-------+-----+
|         |       |       |     |  |       |     |
+---------+-------+-------+-----+--+-------+-----+
| Alabama | Nuts  | 1     | 10  |  | 1     | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 4     | 40  |
+---------+-------+-------+-----+--+-------+-----+
$\endgroup$

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