Changes in Inventories

What are inventories?

Inventories exist because of a time lag between production and sale of outputs and acquisition and use of products. Because of this time lag goods are held in storage. Inventories therefore consist of:

Stocks of outputs prior to further use such as sales
Stocks of products acquired from other units for intermediate consumption or resale

Goods in storage are treated as inventories if no change in quality results from being held in storage. Such goods are therefore non-productive. Of course the price of the product may change while in storage. As we will see later this causes the so called holding gains. Goods in storage may be productive as well, i.e. generate additional output while in storage. SNA mentions the following possibilities:

Goods involving a long production process, generating work-in-progress instead of finished goods at the end of the accounting period; an example is the case of construction where during a number of periods part of the construction is “put in place”; each of these parts put in place in turn will generate value (i.e. be productive) in the next periods as we will explain below
Quality improvement during storage, e.g. maturation as in the case of wine; the matured wine will increase in value because it is held to be of more valuable quality by consumers
Seasonality in supply and demand, e.g. staple crops which will be scarce outside harvest time so that they are again effectively of different quality, commanding a higher price

Let us examine the first case in detail (SNA 20.63). Assume a building with a final value of 200 that is to be constructed over a period of four years. One could be inclined to think that work-in-progress of 200/4 = 50 should be recorded for each year. But this is not correct. As an asset this amount can be used by an investor to generate income for the remaining three years that needs to be added to the initial amount. Hence the initial amount needs to be lower to generate the 50 that contributes to the 200 at the end of the four years. This technique is called discounting and is commonly used in finance. If we take as discount rate 5% then the discounting formula for the present value of the value 200 in four years time is:

Here n is the year. We can apply this also to take into account inflation. So the work put in place for year 1 is not 50 but PV(1)/4 = 43.2 which after three more years of 5% inflation would be worth 50 at the end of year 4. Similarly, for year 2 the work put in place is PV(2)/4 = 45.4. However, there could be income accruing on the work put in place during year 1 as well, if this was properly invested. Using the same 5% rate the return on this investment is equal to 43.2*((1+0.05)1 -1) = 2.2 making the total for year 2 equal to 45.4 + 2.2 = 47.6. For year 3 the work put in place is PV(3)/4 = 47.6 plus the return of two years on the work put in place during year 1 plus the return of one year on the work put in place during year 2.

As this example illustrates inventories of output do not only consist of finished goods but also of work-in progress. On the input side inventories can consist of materials and supplies and of goods for resale. A special type of inventory mentioned separately by SNA are military inventories. These consist of single-use items, such as ammunition, missiles, rockets, bombs, etc., delivered by weapons or weapons systems (SNA 10.144).

It should be noted that apart from enterprises, inventories can also be held by government and by households as producers. Only products acquired by final users cannot be part of inventories, even when a time lag exists between acquisition and use.

Changes in inventories

Changes in inventories are measured by the value of the entries into inventories less the value of withdrawals and less the value of any recurrent losses of goods held in inventories during the accounting period (SNA 10.118). Recurrent losses are losses due to wastage, theft or accidental damage that are taking place each accounting period.

In accordance with the accrual principle the additions and withdrawals need to be valued at actual prices. Finished goods transferred into inventories are valued as if they were sold at that time, while additions to work-in-progress are given the value they have at the time they are added to inventories (SNA 10.125). And the goods transferred out of inventories are valued at purchasers’ prices current at the time of the withdrawal from inventories (10.124).

Let us see how changes in inventories are calculated from data on production, uses, sales and purchases. The following table gives price and quantity data. Inputs are imported and output sold to households.

Not all inputs are used so that at the end of the accounting period an inventory of materials will exist. Also, not all output is sold so that at the end of the accounting period an inventory of finished goods will exist. It is assumed that no inventories exist at the beginning of the accounting period.

As is illustrated in the following table changes in inventories are calculated separately for finished goods and for materials. In each case they are calculated as the difference between additions and withdrawals.

Note that in accordance with the accrual principle the withdrawal price 11 for finished goods is the price relevant at the time of sale, not the time of production. Similarly, for materials the withdrawal price 6 is the price at the time of use, not at the time of purchase. For the addition of finished goods, the price 10 is the price at the time of production and for materials the addition price 5 is the price at the time of purchase.

Although changes in inventories are one of the expenditure categories that make up GDP, they also play a vital role in the output approach to GDP, since output and intermediate consumption are typically calculated from data on sales and purchases. The following tables illustrates this for output, which is calculated from data on sales and inventories, and for intermediate consumption from data on purchases and inventories.

Note the opposite arithmetic in these tables. For output the changes in inventories are added to sales because output can be sold directly or added to inventories, leading to a positive change in inventory. For intermediate consumption used materials can come from purchases or from inventory, leading to a negative change in inventory. These negative changes in inventories are subtracted from the purchases, leading to an increase in intermediate consumption.

The following table shows the calculation of gross value added as the difference between output and intermediate consumption and – assuming no taxes and subsidies on this product – the contribution to GDP by the output approach, GDP(O).

Finally, the following table shows the corresponding calculation of GDP by the expenditure approach, GDP(E) for this example. Apart from the inventory build-up, households consume the sold product and the purchases of materials are subtracted as imports. Note that GDP(O) = GDP(E) as should be the case.

Inventory valuation

As we have seen the accrual principle demands that all entries into and withdrawals from inventories are valued at actual prices. However, enterprises generally value inventories at historic prices, i.e. prices at which the goods where purchased when entering the inventory. The challenge for national accountants is to make the proper adjustments of business accounts data to accord with the accrual principle.

The valuation of inventories in national accounts is based on the Perpetual inventory method (PIM). According to this method inventories on a given date may be considered as the sum of additions and withdrawals, in principle going way back into the past. Entries into inventories must be valued at the prices prevailing at the time of entry, while withdrawals must be valued at the prices at which they are then sold. This requires that all entries into, and withdrawals from, inventories be recorded continuously as they occur. In particular the method values goods withdrawn from inventories at the prices prevailing at the time they are withdrawn and not at the prices at which they are entered (the historic price).

In business accounting stocks are usually valued at historic cost or at the last recorded acquisition price of the individual goods. This may include a holding gain due to price changes which does not reflect any physical change in the inventories or in the output of goods during the accounting period. Holding gains accrue during the accounting period to the owners of assets and liabilities as a result of a change in their prices (SNA 3.105). Holding gains accrue purely as a result of holding assets or liabilities over time without transforming them in any way. Holding gains are very general and include gains on all fixed assets, land and financial assets. A holding gain (loss) is called realized when an asset that has increased (decreased) in value due to holding gains (losses) since the beginning of the accounting period is sold, redeemed, used or otherwise disposed of, or a liability incorporating a holding gain or loss is repaid. If not realized the holding gain or loss is called unrealized.

The above table shows the calculation of holding gains for the example given earlier. For both materials and finished goods the price at the end of the accounting period is different from the price at the beginning of the accounting period, thereby giving rise to holding gains. The realized gains relate to sales and use, the unrealized gain to unsold production.

Holding gains (losses) need to be separated from total changes in inventories. If the general price level rises (inflation) and if the output value in the period is calculated on the basis of uncorrected business accounts data as output = sales + changes in inventories of finished goods, output and value added will be overvalued. Conversely, if prices fall the enterprises’ output will be undervalued. Also, during periods of inflation, holding gains will have an effect on inventories of raw materials, with intermediate consumption being undervalued and value-added overvalued.

Whereas changes in inventories as part of Gross Capital Formation belong to the asset side of the capital account, holding gains are recorded in a special account: the revaluation account. We noted earlier that recurrent losses are included in changes in inventories and hence in the capital account as well. On the other hand, exceptional losses (e.g. due to natural disasters) are recorded in another special account: the other changes in volume of assets account.

Inventory valuation adjustment

How do we calculate changes in inventories on the basis of business accounting data, with stocks valued at historic costs? To do so we need information on the cost flow method used in the business accounts. Cost flow methods can be based on:

First-in-first-out (FIFO) principle: withdrawals are valued at prices of the oldest item; inventories will consist of the most recently acquired items
Last-in-first-out (LIFO) principle: withdrawals are valued at prices of the newest item; inventories relate to the items first purchased
Weighted-average principle (older prices having a steadily decreasing weight); the average is recalculated periodically, e.g. when new goods are received; any subsequent purchase is then valued at that price until the average is recalculated

In practice national accountants often assume the FIFO principle. Let us see what needs to be done to convert stock data based on FIFO valuation into inventory data valued according to SNA. First the SNA calculation. The following table gives some example data for the SNA calculation. Note that for quantities closing stock = opening stock + additions – withdrawals. Note also that the prices listed are actual prices as stipulated by PIM.

In following table we apply the SNA methodology for changes in inventories from the previous section. We also calculate the value change as recorded in the balance sheet.

Because these balance sheet totals include any price changes as well, we can calculate the holding gains indirectly by subtracting the changes in inventories from the changes in the balance sheet. This is done in the following table. Another way of interpreting this table is by noting that the total balance sheet change consists of the change in inventory (recorded in the capital account) and the holding gain (recorded in the revaluation account).

Let us now see how the calculation would go if we had FIFO data from business accounts, as in the following table. Opening stock and additions are the same as in table 8. How the remaining items are valued based on FIFO: the withdrawal of 1 unit at the historic cost 5 (assuming this to be the price used for the opening stock) and closing stock at the price of the last addition 7.

Because the balance sheet closing stock is differently valued from the SNA case, the change in balance sheet as calculated in the following table will be different as well.

The difference between this change in balance sheet and the SNA change in inventory is called the inventory valuation adjustment (IVA). The IVA measures the holding gains included in the change in book values of inventories shown in the balance sheets of enterprises. Different historic cost methods will lead to different IVAs. For the FIFO case above the IVA is calculated in the following table.

Compiling changes in inventories in current and constant prices

As we have seen in the previous section the challenge for the national accountant is to convert book values of stock data at historic costs from business accounts into additions and withdrawals at actual prices. In order to carry out the kind of calculations of the previous section we need to either come to data on quantities or to data on deflated values (volumes) on the one hand and to data on prices on the other hand. We can then convert the prices into actual prices and apply them to the quantities or volumes added to and withdrawn from inventory.

Given the complexity of these calculations, we will not go into any details, but one point should be clear: given that such a methodology works on quantities or volumes and prices, the calculations of changes in inventories at current and constant prices are closely interlinked and constant price estimates may be compiled relatively easy if a good current prices compilation methodology has been set up. For example, opening and closing stocks of inventories can be converted into constant prices by deflation with an appropriate price index and the change in inventories in constant prices derived as the difference between the two. Of course deflators need to be consistent with inventory type. For inventories of finished products, producer price indexes (PPIs) at basic prices are the appropriate choice. For inventories of materials and supplies, similar indices as used for intermediate consumption should be used. For inventories of goods for resale PPIs may be used as well.

Detailed inventory calculations are best done on monthly or quarterly data. In this case an important question relates to the choice in time lag for the deflators. For the FIFO case the question would be what the lag for the oldest item is. One can answer this question by calculating the holding period, i.e. the average time period an item is kept in stock before it is withdrawn. Typically, such holding periods will be a few months at most. Once the holding period is estimated the distribution of the inventory over “vintages” (the set of inventory items of the same age) can be estimated. For example, the total inventory may be split into 40% 1-month old vintage, 40% 2-month old vintage and 20% 3-month old vintage. Suitable deflators can then be applied to each vintage. For example, for an estimate of the first quarter, a March deflator can be used for the vintage smaller than 1 month, the February deflator for the vintages 1 – 2 months, etc.

It should be noted that it is possible that enterprises provide no information on values or quantities of levels or changes in inventories at all. In the absence of direct data, changes in inventories may be estimated in an indirect way, by resorting to the commodity flow method. Changes in inventories are then compiled as the difference between total supply (output and imports) and total use (intermediate consumption, final consumption expenditure, gross fixed capital formation and exports). Of course the calculation of output and intermediate consumption will be approximate only in this case, since these will need inventory data as well, as we have seen.

One last point to be made in relation to changes in inventories is that volume indices (“growth rates”) based on constant price estimates are meaningless in this case, since these would be based on changes (in volume) of changes (in inventories).