**_Poish_** _Fical_ **_Crisis 29_**

Finally, we divide the total of gross-up inventories by monthly turnover to get inventory life in months. Monthly turnover is approximated from monthly sales of own production plus 46% (see above).

Two methods of grossing up are used. (1) Materials are grossed-up by the ratio of monthly material costs to monthly sales of own production. Finished goods and commodities are gross up by the ratio of "monthly costs of own sales' to monthly sales of own production. This method will tend to overstate somewhat gross-up inventories because of the downward bias in historical costs.' (2) Materials are grossed-up by the ratio of monthly material expenditures (i.e. spending on materials on a CF basis) to monthly sales of own production.' Finished goods and commodities are grossed-up by 15% to allow for missing costs and a profit margin. This method will tend to understate somewhat grossup inventories because of the inflation bias in inventories.

The results, on a month-by-month basis for 1989-90, are shown in. Inventory life is seen to be between 1.5 and 3 months, with estimates near the lower end of the range at the end of 1989 (the critical point estimate). NB: I do not think the estimates are accurate enough to be able to learn much from interpretations of month-to-month movements.

A check on this estimate is to calculate the implicit inventory life from the estimated inflation biases and observed costs. The idea is most clearly expressed if we consider the steady state (constant output, costs and inventories). In the steady state, inventories = ctC, where a is the inventory life. Furthermore, the paper capital gain on inventories (the inflation bias) is just the inflation rate times .nventories, and so

**_lB_** - QC **_* p_**

This equation, together with the estimates of the inflation bias, can be used to calculate the implied life in inventories. The results are variable but are generally one month or less. I conclude that the estimated life in inventory in the Polish enterprise sector is 1-3 months.

Inventory price deflators are constructed from weighted averages of the industrial price index. The weights are calculated using a rough estimate of the distribution over time of value added in inventories. These are derived as follows. The ratio of total value to the value of materials in finished goods is about 2 (i.e. it takes one zloty of materials and one zloty of value added to make 2 zloty of finished goods). Reported inventories of materials are roughly equal to reported inventories of finished goods and commodities. Consider now a simple example. Life in inventory is 3 periods. Production is instantaLiowus. One zloty of materials is held for 2 periods, one zloty of value is then added in production, the resulting finished good is held for one more period and then sold. In a steady state with no inflation, inventories will be 2 zloty of materials + 2 zloty of finished goods = 4 zloty. (Note that both the shares of materials and finished goods in total inventories and the ratio of materials to value

- W.,. Both inventoriea **and** costs **arm** biated downwards, but (assuming LIFO) **the is** gratcr **fo.** .osts **bc.._'.-** .osts of sold production reflect the fuU time spent in production (inventory **life).**

**25.** Material expenditur **amr** calculated using **an** identity **similar** to the CF identity (see Schaffer 1992). **There** is **a** residual inflation **bias** remining in **thi esimate** of **matrial** expenditures, but it **is likely** to be **small.**