<p>It works the same way, you can use the same table but replace Year 1 with Quarter 1, Year 2 with Quarter 2, etc. And you probably want the data to be seasonally adjusted.</p>
<p>Side note: usually the chain-weighted approach uses both Laspeyres and Paasche indexes. To do that, you would repeat the above with <em>following</em> year prices, and then take the geometric average of the two results.</p>

CC BY-SA 4.0
2023-07-04T06:13:28.723Z
Could you elaborate further? I mean if I consider quarters, let us say Year 2, Q1, then I need to take previous year's prices, right? But I do not take Year 1 Q1 prices but the overall (volume based) price of Year 1, so total cost of the product over the whole year 1 divided by total quantity over year 1; 
Therefore, I take the the same prices for Year 2, Q1 and Year 2, Q4 when calculating previous year's prices, right? But how do I proceed from there?
Johannes
CC BY-SA 4.0
2023-07-03T22:17:26.790Z
2023-07-03T22:23:07.483Z
2023-07-03T22:23:07.483Z
Daniel
<p>Assume we have given apples and oranges; If we only consider annual chain-linking, it is pretty simple, e.g. let us have the following values:</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;"></th>
<th style="text-align: center;">Year 1</th>
<th style="text-align: right;">Year 2</th>
<th style="text-align: right;">Year 3</th>
<th style="text-align: right;">Year 4</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">Apples</td>
<td style="text-align: center;">Amount: 10, Price:3, Total 10*3=30</td>
<td style="text-align: right;">Amount: 8, Price:4, Total 8*4=32</td>
<td style="text-align: right;">Amount: 7, Price:5, Total 7*5=35</td>
<td style="text-align: right;">Amount: 5, Price:10, Total 5*10=50</td>
</tr>
<tr>
<td style="text-align: left;">Oranges</td>
<td style="text-align: center;">Amount: 5, Price:4, Total 5*4=20</td>
<td style="text-align: right;">Amount: 7, Price:4, Total 7*4=28</td>
<td style="text-align: right;">Amount: 7, Price:4, Total 7*4=28</td>
<td style="text-align: right;">Amount: 10, Price:3, Total 10*3=30</td>
</tr>
<tr>
<td style="text-align: left;">Total</td>
<td style="text-align: center;">30+20=50</td>
<td style="text-align: right;">32+28=60</td>
<td style="text-align: right;">35+28=63</td>
<td style="text-align: right;">50+30=80</td>
</tr>
</tbody>
</table>
</div>
<p>I now want to get the chain linked volumes with the reference year 1; To do so I first calculate for each year  &quot;Current volume * previous year price&quot;</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;"></th>
<th style="text-align: center;">Year 1</th>
<th style="text-align: right;">Year 2</th>
<th style="text-align: right;">Year 3</th>
<th style="text-align: right;">Year 4</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">Apples</td>
<td style="text-align: center;">Amount: 10</td>
<td style="text-align: right;">Amount: 8, Previous Price:3, Total 8*3=24</td>
<td style="text-align: right;">Amount: 7, Previous Price:4, Total 7*4=28</td>
<td style="text-align: right;">Amount: 5, Previous Price:5, Total 5*5=25</td>
</tr>
<tr>
<td style="text-align: left;">Oranges</td>
<td style="text-align: center;">Amount: 5</td>
<td style="text-align: right;">Amount: 7, Previous Price:4, Total 7*4=28</td>
<td style="text-align: right;">Amount: 7, Previous Price:4, Total 7*4=28</td>
<td style="text-align: right;">Amount: 10, Previous Price:4, Total 10*4=40</td>
</tr>
<tr>
<td style="text-align: left;">Total</td>
<td style="text-align: center;"></td>
<td style="text-align: right;">24+28=52</td>
<td style="text-align: right;">28+28=56</td>
<td style="text-align: right;">25+40=65</td>
</tr>
</tbody>
</table>
</div>
<p>Now to get the chain-linked volumes with Year 1 as a reference Year I simply use that for the reference year, chain-linked volumes are equal to current prices and for Year 2,3 and 4 I can use that &quot;Current volume * previous year price&quot; / &quot;Previous year's price * previous year's volume&quot; = Chain linked volume of current year/Chain linked volume of previous year (all with same reference year);</p>
<p>So e.g. for Year 2, I just take 52/50 * Chain Linked volume year 1 = 52/50*50 = 52; This leads to the following table for the total of oranges+apples</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;"></th>
<th style="text-align: center;">Year 1</th>
<th style="text-align: right;">Year 2</th>
<th style="text-align: right;">Year 3</th>
<th style="text-align: right;">Year 4</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">Total</td>
<td style="text-align: center;">50</td>
<td style="text-align: right;">52/50*50=52</td>
<td style="text-align: right;">56/60*52=48.53333</td>
<td style="text-align: right;">65/63*48.53333= 50.07</td>
</tr>
</tbody>
</table>
</div>
<p>Of course, one could do something similar not just for the total but also for oranges and apples itself but this would just give volume*price of the base year (Year 1), so chain-linking would be identical to calculating with prices of a base year;</p>
<p>As easy as this is, I am now trying to understand how quarterly chain-linking works; Assume we have again 4 years but with quarters 1,2,3,4 and for each quarter, we have an amount of apples, an amount of oranges, a price per apple and a price per orange;</p>
<p>How would I then calculate the quarterly chain-linked volume?</p>

<macroeconomics>
Can someone help me how to perform quarterly chain linking?
Johannes
# Can someone help me how to perform quarterly chain linking?

(Asked by: username_0 on 2023-07-03)

Assume we have given apples and oranges; If we only consider annual chain-linking, it is pretty simple, e.g. let us have the following values:

|  | Year 1 | Year 2 | Year 3 | Year 4 |
| --- | --- | --- | --- | --- |
| Apples | Amount: 10, Price:3, Total 10\*3=30 | Amount: 8, Price:4, Total 8\*4=32 | Amount: 7, Price:5, Total 7\*5=35 | Amount: 5, Price:10, Total 5\*10=50 |
| Oranges | Amount: 5, Price:4, Total 5\*4=20 | Amount: 7, Price:4, Total 7\*4=28 | Amount: 7, Price:4, Total 7\*4=28 | Amount: 10, Price:3, Total 10\*3=30 |
| Total | 30+20=50 | 32+28=60 | 35+28=63 | 50+30=80 |

I now want to get the chain linked volumes with the reference year 1; To do so I first calculate for each year "Current volume \* previous year price"

|  | Year 1 | Year 2 | Year 3 | Year 4 |
| --- | --- | --- | --- | --- |
| Apples | Amount: 10 | Amount: 8, Previous Price:3, Total 8\*3=24 | Amount: 7, Previous Price:4, Total 7\*4=28 | Amount: 5, Previous Price:5, Total 5\*5=25 |
| Oranges | Amount: 5 | Amount: 7, Previous Price:4, Total 7\*4=28 | Amount: 7, Previous Price:4, Total 7\*4=28 | Amount: 10, Previous Price:4, Total 10\*4=40 |
| Total |  | 24+28=52 | 28+28=56 | 25+40=65 |

Now to get the chain-linked volumes with Year 1 as a reference Year I simply use that for the reference year, chain-linked volumes are equal to current prices and for Year 2,3 and 4 I can use that "Current volume \* previous year price" / "Previous year's price \* previous year's volume" = Chain linked volume of current year/Chain linked volume of previous year (all with same reference year);

So e.g. for Year 2, I just take 52/50 \* Chain Linked volume year 1 = 52/50\*50 = 52; This leads to the following table for the total of oranges+apples

|  | Year 1 | Year 2 | Year 3 | Year 4 |
| --- | --- | --- | --- | --- |
| Total | 50 | 52/50\*50=52 | 56/60\*52=48.53333 | 65/63\*48.53333= 50.07 |

Of course, one could do something similar not just for the total but also for oranges and apples itself but this would just give volume\*price of the base year (Year 1), so chain-linking would be identical to calculating with prices of a base year;

As easy as this is, I am now trying to understand how quarterly chain-linking works; Assume we have again 4 years but with quarters 1,2,3,4 and for each quarter, we have an amount of apples, an amount of oranges, a price per apple and a price per orange;

How would I then calculate the quarterly chain-linked volume?

**Tags:** macroeconomics


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## 1 answers

### Answer by username_1 on 2023-07-03. Score: 0

It works the same way, you can use the same table but replace Year 1 with Quarter 1, Year 2 with Quarter 2, etc. And you probably want the data to be seasonally adjusted.

Side note: usually the chain-weighted approach uses both Laspeyres and Paasche indexes. To do that, you would repeat the above with *following* year prices, and then take the geometric average of the two results.

> **Comments:**
> **username_0**: Could you elaborate further? I mean if I consider quarters, let us say Year 2, Q1, then I need to take previous year's prices, right? But I do not take Year 1 Q1 prices but the overall (volume based) price of Year 1, so total cost of the product over the whole year 1 divided by total quantity over year 1;  Therefore, I take the the same prices for Year 2, Q1 and Year 2, Q4 when calculating previous year's prices, right? But how do I proceed from there?  

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