How well does a standard price index capture sales--论文代写范文精选

更受欢迎的产品通常是品牌上市,或者因为倾向于购买更多的物品。这表明,国家统计局数据可能歪曲价格。如何计算的问题有一个正确的索引的储备。消费者储备意味着分离，利用价格指数和基于消费价格指数。下面的paper代写范文进行详述。

Abstract
The sales behaviour documented in the previous subsections has several implications for the standard measurement of price indices. First, given the way statistical agencies collect data there is an issue about whether they correctly sample sales. Statistical agencies may over- or undersample items on sale given the products included in the basket of goods relative to the sample of all products purchased by consumers. We provide evidence that this might be the case. Second, even if the correct products are chosen, and hence the true prices observed, there is an issue regarding what is the correct price index formula. We demonstrate the issue in the context of a simple example. 

Finally, there is a question of whether the difference between the ideal measure and the index actually computed varies across time and households. As the previous figures show, sales are a significant factor in the expenditure of most households. In order to examine how the data collected by statistical agencies captures sales we looked at prices of the most commonly purchased (“most popular”) items within each food category, which we took to be an approximation of the set of prices most likely to be sampled by price collectors 5 . We find that the most popular products are more often on sale than the “average” product (see Table 5). This may be because the more popular products are typically branded items which go on sale more often, or perhaps because promoted items tend to be purchased more often. This suggests that the ONS data could misrepresent the distribution of prices paid by consumers.

Putting aside the measurement issue – even if prices are collected in such a way as to accurately capture sale prices – there is an issue of how to compute a correct index in the presence of stockpiling. Consumer stockpiling implies a separation between a purchase-based price index and a consumption-based price index. Standard price indices are purchase-based, some explicitly so, but a utility based cost-of-living index should account for the ability to store the product 6. To illustrate the difference consider the following example. Suppose a consumer consumes two products, A and B, at equal quantities. 

Product A always costs $2, while product B is normally priced at $2, but goes on sale for one period and is sold at a price of $1. Normally, the consumer purchases one unit of each product each period and consumes both products in that period. Suppose the consumer has a storage cost of $0.25 per unit per period. During the sale of product B the consumer purchases 4 units and consumes one unit each week over the next few weeks. We assume there are no consumption effects: the consumer does not increase consumption in response to the sale price. For the calculation that follows we ignore the discount factor. The consumer saves on each of the units he purchases: for the last unit the consumer pays $1.00 and stores it for 3 periods at a cost of $0.75, for a total saving of $0.25 relative to buying the product at the regular $2 price. The consumer, however, will not save from buying additional units because of the storage costs. If the consumer bought a fifth unit on sale the storage costs for 4 periods will exactly equal the savings (and we assume that in this case the consumer will not store the product).

Suppose we want to compute a cost-of-living index for this consumer. We set the base as the prices during non sale periods, so when consuming 1 unit of each product the base is $4. The true consumer’s price index for the period of the sale and the following weeks is (2.00+1.00)/4.00=0.75, (2.00+1.25)/4.00 = 0.8125, (2.00+1.50)/4.00 = 0.875, (2.00+1.75)/4.00 = 0.9375, and 1.00 for every following week. The observed prices of product A are 2.00 at each period and observed purchases are 1 unit each period. The prices of product B are 2.00, 1.00, and 2.00 for every following period, while the purchasing patterns are 1 unit, 4 units, 0, 0, 0 and 1 unit for every following week. 

Consumption is constant every week. A standard price index will capture some price reduction in the week of the sale. The exact reduction in the price index depends on the quantity weight used to compute the index. For example, a fixed weight price index, with equal weights, will yield 0.75, for the week of the sale, and 1 for every following week. However, a standard index will not capture the effective drop in the price index in the weeks following the sale, and the problem cannot be “fixed” by adjusting the weights. The problem is that the price the consumer faces is a shadow price. Note, that aggregation across weeks, to construct a monthly price, will also not solve the problem, even if the timing is captured exactly right. In this case, the aggregation will overestimate the benefits from purchasing on sale since it will ignore the storage cost.

This simple example illustrates the issues with a standard price index. A more realistic model would allow for consumption effects and uncertainty regarding future prices (see Hendel 18 and Nevo, 2006b, for such a model). Such a model allows us to compute the unobserved shadow prices faced by the consumer in each period, but is very computationally intense and cannot be estimated on a large scale. Developing more tractable alternatives is a current area of research.

Bulk Discounting and Choice of Package Size 
Many grocery items are sold at non-linear prices. Larger package sizes are sold at higher prices but at lower per unit price. For example, Hendel and Nevo (2006a) report that the regular, nonsale, price of a 24-pack of soft drinks cans cost 2.7 times more than a 6-pack. This implies a discount of over 30 percent in the per period unit price. A typical treatment of non-linear prices in the price index is to focus on unit values. This corrects for the difference in the actual price between sizes, as opposed to the difference in the size per unit. However, it does not account for the tradeoffs consumers are making (Triplett, 2003).

The tradeoffs facing the consumers are similar to those we discussed in the case of sales. Consider a consumer deciding between purchasing a smaller unit and a larger one at a lower per unit price. Unless she can consume the additional quantity before her next store visit the consumer has to weigh the benefits of the lower price with the costs of storing the product longer and the deprecation in the quality of the product. Different consumers will make different choices depending on their marginal utility from income, the cost of storage and transport of the product, and their future consumption needs. A given consumer will make different choices for different products, depending on storage costs, durability, expected consumption and the price schedule.(论文代写)

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