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Methodology for compiling the producers price index

This chapter describes the methods we use to compile the producers price index (PPI), including the index formula, and how we collect prices of goods and services and account for quality change over time.

Topics covered in this chapter are:

Price index formula

Price indexes are the result of mathematical formulae that bring together information on individual prices, allowing them to be compared in a meaningful way. This is achieved by assigning a weight to each priced item, which reflects the relative importance of that item in the index being calculated. These weights are based on the comparative value of the item in either a business’s inputs or outputs. The indexes are formulated to measure change in the level of prices.

The price index formula most commonly used in New Zealand and internationally is the Laspeyres formula. We compile the PPI indexes using a variant of this base-weighted formula. Due to the substantial amount of time required to collect weighting and pricing information from respondents, the weight reference period in which we collect the quantities is not exactly the same as the period in which we collect the reference period prices. Additionally, we ‘price update’ the weights in the annual reweight (ie express the quantities of the weight reference period in the prices of the price reference period) which makes our index technically a Lowe price index, rather than a pure Laspeyres price index.

Laspeyres price index

A base-weighted Laspeyres price index measures the changing cost over time of a fixed ‘basket’ of goods and services. A PPI outputs index measures the revenue from selling, while a PPI inputs index measures the cost of purchasing, a basket of goods. The expenditure aggregate form of the Laspeyres formula is:

Formula, 14.1


Where

ILpt = Laspeyres Price Index Number at time t
Pit = The price of good or service i in period t (the price reference period)
Pi0 = The price of good or service i in period 0 (the price reference period)
n = The number of goods and services in the basket
qi0 = The quantity of good or service i in period 0 

The Laspeyres index can also be expressed in an equivalent form called the weighted price relatives form. The derivation of this form is given below:  

Formula, 15.1


In words, the relative price of item i in period t when compared with the price reference period 0 is multiplied by Wi, the weight of item i in the basket. The weight of each item i represents the total revenue or cost of qi0 units of good i at price reference period prices.

The numerator of the index’s expenditure aggregate gives the total cost of the fixed basket of goods in the current period t while the denominator gives the total cost of the fixed basket of goods in the price reference period 0. The ratio of these two costs (multiplied by 1000) gives the price index number.

Using the Laspeyres formula assumes, through fixed reference period weights, inelastic demand. That is, there are no quantity changes or substitution of products in response to price changes or changes in taste and fashion. Purchases and sellers do respond to relative price changes, and the impact of this can be mitigated by reweighting the index frequently.

Example of calculating a Laspeyres price index

Two items, A and B, make up index C. Assume that we will construct an output price index. In the base period, 2,500 units of A are sold for $1 each, while 1,500 units of B are sold for $5 each. That is: 

Formula, 16.1


A weight describes the relative importance of an item in the make-up of the final index. In this example, item B is more important than A, being 75 percent of the total reference period weight. Item A accounts for 25 percent.

In period 1, the price of A increases to $2 and the price of B increases to $6. Using these weights and prices in the weighted price relatives Laspeyres formula, we get: 

Formula, 16.2

In period 2, the price of A remains at $2, and the price of B falls back to $5. Using these prices, we get:

Formula, 16.3

From this example we can see that movements in a Laspeyres index are the result of changes in relative prices. Once the weights for a Laspeyres index are set, movements in that index are driven by changes in the comparative prices charged by businesses.

Price collection

The PPI measures price change, over time, in broad industries of the New Zealand economy. Transactions for each of those industries may cover purchases and sales of thousands of different goods and services at a wide variety of prices. The sheer volume and complexity of these transactions means it is impossible to collect prices for every good or service or to take into account every price at which they are sold. Consequently, we need to adopt a sampling approach, pricing a sample of products from a sample of respondents.

Sample approach used

The PPI is based on ‘purposive’ or judgement samples, where the sample is selected on the basis of the knowledge and judgement of staff compiling the index. The alternative of using probability sampling (having some random aspect to it) would be more difficult and expensive to use. In particular:

  • Factors other than sales volume are important when selecting items and businesses. These include availability of prices on an ongoing basis, degree of price dispersion, and the pricing behaviour of businesses.
  • Judgement sampling is more practical in the day-to-day operations of price collection, as the selection of items and suppliers regularly needs to be updated as businesses close or items are no longer produced.

We use business directories, market reports, our Commodity Data Collection Survey, and other information to select and maintain samples of suppliers and products (specifications) for pricing.

The effectiveness of this sample approach depends on the representativeness at each hierarchical level of an index. In our approach:

  • key commodities are selected to adequately represent the price movements for all the commodities that come within the scope of the particular price index
  • businesses are selected to adequately represent all the suppliers/users of the selected commodities
  • product specifications are determined for each surveyed business to adequately represent the product range of that business within the selected commodity description
  • transaction prices that best represent the price movements of all transactions for the selected product specification are obtained.

Our use of judgement sampling has implications for the selection of replacement product specifications or businesses. Individual specifications and businesses may be representing a category of specifications or businesses, not just themselves (for example, a selected business may represent medium-sized firms or a specification may represent a broader product grouping).

Therefore the selection of replacement specifications takes into account these characteristics and, as far as possible, ensures that the category is still covered by the new specifications or businesses.

Establishing and maintaining samples

Price indexes are only as valid as the price samples they are based on. Consequently, in selecting the samples for basket items with a large weight in a published series, our aim is to cover those businesses accounting for a high proportion of sales or purchases of the products making up the index item. For less significant items, coverage may be lower. We take care to ensure the selected businesses are representative of all the businesses trading in the less significant item.

Price indexes aim to reflect changes in market transaction prices. Therefore, the specifications identify the precise terms under which transactions are typically made. Prices collected take account of the discounts, surcharges, conditions of sale, order sizes, type of customer etc. We use list prices when most transactions in a specification occur at the list price or no alternative is available.

When selecting specifications to be priced, we consider the following factors:

  • The relative importance of the item in an index – more important items (ie higher weights) are given greater representation.
  • The degree of homogeneity within the index item – more homogeneous items require smaller samples.
  • Influences that can cause prices of some specifications to move differently from others within the category. It is important to reflect all the significant influences in the sample.
  • The extent to which the specification is expected to be continuously available for pricing. Preference is given to specifications for which transaction prices are available on a continuous basis.
  • Whether the specification can be clearly described in terms of quantity and quality, so those prices can be collected over time for an item of constant quality.

Over time, the samples of businesses and specifications may become unrepresentative, or the proportions in which they are combined to calculate the index numbers may become outdated. Therefore we review the samples of businesses and specifications on a rolling basis to ensure they remain representative. When new or changed samples are incorporated in the index, we link the resulting index numbers using an overlap period. This ensures that only price movements, and not any effect of the sample change, are shown in the index.

Price collection procedures and timetable

We source most PPI prices by quarterly postal survey. The pricing date is the 15th of the middle month in the calendar quarter. This approach assumes that movements in prices between two dates that are three months apart adequately represent quarterly price movements.

The survey we use is called the Commodity Price Survey. We obtain individual price quotes for the PPI from about 2,200 different businesses and cover about 300 NA06CC commodity groups. Many prices are also used in other business price index series, such as the capital goods price index (CGPI) and the farm expenses price index (FEPI). Some prices that we principally collect for other indexes, including the consumers price index (CPI), are also used in the PPI. A small, but growing, number of prices are also collected from administrative sources such as the Internet. Our rationale for sharing prices between indexes or using other sources, where appropriate, is to minimise the administrative load placed on surveyed businesses and to optimise coherence across all our price indexes.

Some items are subject to significant price variation, such as agricultural outputs. In these cases we collect prices at more regular intervals, rather than quarterly. In a small number of cases, such as local authority rates, prices are known to be set once each year, so we collect prices annually.

Special pricing treatments

Foreign currency pricing

The Commodity Price Survey asks respondents to quote prices in New Zealand dollars. However, some prices are provided in foreign currencies (eg US$), which we convert to New Zealand dollar prices when the questionnaires are returned.

We convert these prices using the mid-quarter exchange rate for that currency (that is, divided by the bank selling rate at the 15th day of the middle month of the quarter).

Seasonal treatment

Some commodities are produced for only part of the year (for example, strawberries). The practice we adopt in these cases is to repeat (carry forward) the last reported price until the next season’s trading occurs and a new price can be collected.

This practice means that when we make a quarterly comparison, the not-in-season commodities contribute no change to the index movement. For any comparison of the latest quarter with a period a year or more earlier, all commodities will have a bearing on the index movement. While this practice has some weaknesses, we chose it in preference to having variable weights on a commodity depending on the quarter (for example, giving commodities a weight of zero when they are not in season). This approach makes our analysis of contributions to index movements more straightforward.

We trialled the two methods and saw no significant difference in the index movements using fixed and variable weights. The fixed weights approach is easier to administer, resulting in less potential for error.

Weighted average quarterly prices

Most commodities in the PPI are priced at the 15th day of the middle month in each quarter. Movements in these mid-quarter prices are then taken to represent movements in weighted average prices for the whole quarter. This assumption is acceptable for the majority of commodities. For those commodities with particularly volatile prices and/or high weights, we aim to collect or calculate average prices over the whole quarter. Examples include fuel, dairy products, and some commodities sold at auction, including fresh fruit and vegetables, livestock, and wool.

Additionally, we use weighted average quarterly prices for many exported and imported products we collect from the Overseas Trade Index (OTI). These prices are a unit value calculated as the total imports/exports of a product, divided by the total quantity of the product imported or exported.

Quality change

Our price indexes measure the extent to which the cost of an identical basket of goods and services changes over time, unaffected by changes in quality, quantity, or terms of sale. This is often referred to as ‘pricing to constant quality’. This is a difficult objective for us to achieve because the characteristics of the good being sold in the market place, and its terms of sale, often change over time. Frequently the precise commodity priced in one period is no longer available in the next period. Either there has been some change in the characteristics of the commodity or something new has taken its place. Therefore, we need to use statistical techniques to identify quality differences and eliminate their effect on the calculation of price change.

The concept of quality

To identify and assess quality change in our price indexes we consider:

  • how changes in commodity specifications affect the utility or usefulness of the good or service to the purchaser
  • the cost of actually producing the item.

For goods where quality is closely associated with the quantitative characteristics of the product, an assessment of quality change is relatively straightforward because we can usually measure these characteristics objectively. For example, if a $4.00 box of chocolates increases in price by $1.00 and the quantity of chocolates also increases by 25 percent, it is easy to see that no price change has occurred from the purchaser’s point of view.

It is more difficult to assess quality change when it is not purely quantitative, or involves a number of quantitative variables that may conflict in terms of their effect on quality. For example, an increase in the power of a car engine which improves performance but increases fuel consumption – it would be difficult to determine whether there is a net increase or decrease in value to the purchaser.

Identifying changes in quality

To identify changes in quality, we need to collect a considerable amount of detailed information about the goods we price. We obtain some of this information while collecting and checking price data during compilation of the price indexes. We check instances of unexplained price change with surveyed businesses to determine whether they represent a genuine price change or a change in quality.

Taking account of quality change

Whenever we determine that a change in quality has occurred in a product being priced, we aim to eliminate the effect that the quality change has on the price. This must not interfere with the measurement of any true price movement that might have occurred over the same period. The way we do this depends on the circumstances of the quality change. There are three common situations:

  • Overlapping sales – where one product is replaced by another of different quality, but both have sold during an overlapping period.
  • Not sold at the same time – where one product is replaced by another of different quality, but the two have not been available at the same time.
  • Change in composition – where there are some changes in the composition of a particular product.
Overlapping sales

The first common situation where we aim to eliminate the effect that quality change has on the price is when the brand or model being priced ceases to be available. But there is another similar item which has been, and continues to be, available in the same market as the first item and is expected to be a substitute for the first item.

In this situation, we collect prices for both items at the one date – provided the two items have sold side by side for some time in the same market and both have sold in reasonable quantities.

Here we assume that the difference in prices at that date represents the difference in quality between the two. Our assumption is that the market has adequate knowledge of the qualities and prices of each product and that it regards the price difference as a reasonable measure of the quality difference. We then substitute the second item for the first by linking the price series, as shown in Table 2.

Table 2
Example: Overlapping sales

  Period 1  Period 2  Period 3 
Price of harvester A  $80,000  $82,000  
Price of harvester B    $95,000  $98,000 
Price relative for harvester  80,000/
80,000
= 1
85,000/
$80,000
= 1.063 
[98,000x(85,000/95,000)]/
80,000
=1.096 
Product total  1x1000
=1000
1.063x1000
= 1063 
1.096x1000
= 1096 

 
The price movement reflected in the index from period 1 to period 2 is the movement in the price of harvester A. The price movement from period 2 to period 3 is based on harvester B, which we will price in subsequent periods to replace harvester A. The difference in price between harvester A and harvester B has been eliminated through the process of linking the new price series to the old price series.

The price movement reflected in the index from period 1 to period 2 is the movement in the price of harvester A. The price movement from period 2 to period 3 is based on harvester B, which we will price in subsequent periods to replace harvester A. The difference in price between harvester A and harvester B has been eliminated through the process of linking the new price series to the old price series.

We have to take care when selecting the linking period. Because in many instances, an older model may be discounted following the introduction of a new model. And if we use a discounted price in the link between the old and new models, an unrepresentative price movement may result.

In some cases, linking the price of the new specification to the existing price series is not a satisfactory way of eliminating changes in quality. This situation occurs, for example, when the price of a new model reflects not only the extent of modifications but also a degree of price change, upwards or downwards, for reasons distinct from these modifications. Linking the old and new prices would eliminate the elements of pure price change as well as the elements of quality change.

In these cases, we assess the degree of pure price change involved, and ensure this is reflected in the price series after linking. How we do this is described in ‘Not sold at same time’ below.

Not sold at same time

The second common situation where we aim to eliminate the effect that quality change has on the price is where one product replaces another, but the two products have not sold side by side in the market place.

In this situation, we identify any quality differences between the old and new products and estimate the value of these differences. A simple example of this sort of quality change is the replacement of a 50-litre drum of industrial solvent by a 45-litre drum. In such cases, where the proportionate change in quantity is relatively small, it is reasonable to assume that the value of the change is directly proportional to the change in quality. That is, we can make the price of the 45-litre drum comparable with the previous price of the 50-litre drum by applying a factor of 50/45. Therefore, we calculate a price relative for industrial solvent as shown in Table 3.

 

Table 3
Example: Not sold at same time
  Period 1  Period 2  Period 3 
Price of 50 litre drum 
$40 
   
Price of 45 litre drum    $40  $42 
Price relative for solvent  40/40
=1 
[40x(50/45)]/40
= 1.111 
[42x(50/45)]/40 
Product total    1.111x1000
= 1111 
1.167x1000
= 1168 

However, if the proportionate change in the unit of quantity is large, this technique is not appropriate. For example, the unit price of a kilogram of cement when purchased in a 25-kilogram bag cannot be directly compared with the unit price of a kilogram of cement purchased as part of a truckload. The two products are different in the sense that they would usually sell in different markets and to different kinds of users. In these circumstances we estimate the difference in quality using different methods, and sometimes also use expert judgement.

Change in composition

The third common situation where we aim to eliminate the effect that quality change has on the price is where there are changes in the composition of a product.

In this situation, we identify the quality differences and place a value on them. Frequently the composition of a product changes as a result of adding or removing features, or using different materials. For example, a change in the wool/synthetic mix of yarn. In these cases, we estimate the value of the quality change to the purchaser by determining the additional cost (or saving) to the manufacturer and examining the prices of broadly comparable items (for example, yarns containing various proportions of pure wool and synthetic fibres).

Sometimes the modified product differs substantially from the previously priced product – as occurs with a change in models for a particular brand of motor vehicle. To take account of this type of quality change, we collect a considerable amount of information on the products from suppliers, and in some cases use our judgement, to estimate a monetary value by which to adjust the price.

Our first step is to determine the differences between the old and new models as precisely as possible. Then we determine which of these differences represent changes in quality, and estimate the monetary value of each change. Some changes are relatively simple to quantify. For example, changing the type of tyres on a new model car when both types of tyres are sold separately on the market – the value of the quality change can be assessed as the difference in the selling prices of the tyres. Other changes require more detailed examination, for example, if a new model car has eight airbags while the old model has four airbags.

While there is some subjectivity involved in placing a dollar value on the changes in a product, quality adjustment procedures mitigate potential long-term bias in the price series. But ignoring quality changes altogether could result in significant biases in the price indexes.

Styling and packaging changes

We do not consider product changes that are purely styling changes to be changes in quality. For example, we regard the current year’s range of bricks as being equivalent to last year’s if the general quality of workmanship and function is similar, regardless of the actual colour, texture etc. Similarly, we do not regard styling changes in the external trim on an escalator to be quality change. We adopt this approach because it is not really possible to estimate an objective value for something as subjective as a change in styling.

Changes in packaging that do not affect the quality of the package contents have no effect on quality. However, if a different type of packaging for building materials, for example, resulted in less damage to the product while being transported, we would take this into account as a quality change. 
 

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