Eliminating chain drift in price indexes based on scanner data

The use of scanner data in the CPI makes it possible to compile superlative price indexes at detailed aggregation levels since prices and quantities are available. A potential drawback is the high attrition rate of items. The usual solution to handle this problem, high-frequency chaining, can create drift in the index series due to price and quantity bouncing arising from sales. Ivancic, Diewert and Fox (2009) have recently proposed an approach that provides drift free, superlative-type indexes through adapting multilateral index number theory. In this paper we apply their proposal to seven product groups and find promising results. We compare the results with those obtained by using the Dutch method to deal with supermarket scanner data.     

Superlative index numbers: not all of them are super

This paper shows that just because superlative index numbers approximate each other to the second order does not necessarily imply that they are numerically similar. In fact, the spread between the largest and smallest superlative indexes sometimes even exceeds that between Paasche and Laspeyres indexes. This result has significant implications for the index number literature. It shows that the economic approach does not by itself solve the index number problem, since it does not tell us which superlative index should be used. It may be necessary to combine the economic and axiomatic approaches to arrive at an answer.     

The index of decent subsistence

The index of decent subsistence (IDS) is a price index that allows for purchasing substitutions when food prices change. The consumer's food basket is represented by a utility maximizing quadratic program that computes the cost of decent subsistence (CDS) and assures gastronomic equivalence among the food baskets optimized at various price levels. This IDS is the ratio of respective CDS measures. IDS estimates from USDA food group data are presented for the 1965–1975 and 1978–1989 time periods. These estimates are shown to be inconsistent with fixed weight price indexes computed for the same periods. Implications for the food stamp program and institution feeding systems are discussed.     

Why elementary price index number formulas differ: Evidence on price dispersion

Most countries use either the Dutot or Jevons index number formula for the compilation of their consumer price index at the elementary level of aggregation. The difference between the formulas is shown to be accounted for by changes in price dispersion. In turn, some of this difference is shown to be explained by product heterogeneity. Scanner data on television sets (TVs) are used to calculate Dutot and Jevons indexes. The difference between them is successfully explained in terms of changes in price dispersion and much reduced using an hedonic, heterogeneity-controlled Dutot index.     

An Implicit Törnqvist Index of Real GDP

Recently much attention has been devoted to superlative indexes in the context of the national accounts. In this paper we advocate the use of the implicit Törnqvist quantity index to measure real GDP. This index, which has been proposed by Diewert and Morrison (1986), has never received serious consideration in the literature. Yet, compared to the better-known Fisher index, the implicit Törnqvist index of real GDP has a number of advantages. Thus, it can be shown to be exact for the Translog GDP function, it allows for a complete multiplicative decomposition of nominal and real GDP, and it is consistent with state-of-the-art measures of total factor productivity that typically rely on the Törnqvist aggregation. Estimates for a sample of 26 countries are reported. We find that the Laspeyres quantity index still used by the statistical agencies of most countries tends to underestimate real growth. Over the 1960–1996 period, the cumulated shortfall was as much as 13.4% of GDP in the case of Japan.     

The Sato–Vartia index and the monotonicity axiom

The Sato–Vartia index is believed to be on a par with the Fisher ideal index in terms of its ability to satisfy index number axioms or tests. Yet we show that this index fails to satisfy the monotonicity axiom, and we provide formulas for the point at which a Sato–Vartia price index becomes non-monotonic in prices. In fact, requiring monotonicity for initial as well as final prices rules out not only the Sato–Vartia index but all log-change price indexes whose weights depend upon initial or final expenditure shares. Since cost of living index theory leads naturally to the Sato–Vartia index, as well as to other log-change indexes, there is an irreconcilable tension between the standard axiomatics for indexes, and cost of living index theory.     

Indirect productivity measurement

Caves, Christensen and Diewert [1982a] showed that the Törnqvist productivity index is superlative in a considerably more general sense than had been previously believed. We examine the allocative and technical efficiency hypotheses on which their finding rests. We show that the allocative efficiency hypothesis can be modified, which makes the Törnqvist index superlative in a wider sense than even Caves, Christensen and Diewert showed, since it is consistent with a type of allocative efficiency other than the standard cost minimization and revenue maximization hypotheses considered by Caves, Christensen and Diewert. We also show that if the technical efficiency hypothesis is relaxed, the CCD result may no longer hold, and the distance functions that form the basis of the Malmquist productivity indexes, and hence of the Törnqvist productivity index, must be calculated. We then show how to calculate the underlying distance functions, and we argue that there are real advantages to doing so.The refereeing process of this paper was handled through N.R. Adam.     

Substitution Bias and Cost of Living Variability for U.S. Demographic Groups:

A bstract . Intertemporal cost of living variability is analyzed for households with differing income levels and family characteristics. These indexes are based upon the parameter estimates of a comprehensive system of expenditure equations, the quadratic expenditure system. Despite considerable differences in the group-specific share parameters as well as nonlinearities in the Engle curves for each group, little variation occurs in these indexes for several U.S. price series over the 1967–1984 time period. As a result, we find little evidence that group-specific fixed weight indexes are better cost of living approximations than a general Consumer Price Index even though all substitution bias estimates, by income and household type, are quite small.     

Measuring the diffusion of housing prices across space and over time: Replication and further evidence

Brady (Journal of Applied Econometrics, 2011, 26(2), 213–231) studies how fast and how long a change in housing prices in one region affects its neighbors by estimating the impulse response functions using a spatial autoregressive model (SAR). This paper replicates Brady's empirical results, but reports different SAR test statistics. Additional robustness checks are conducted by analyzing three different housing price indexes covering a more extensive period. Analysis shows that the model specifications and model estimates vary with the housing price indexes.     

The biennial Malmquist productivity change index

In this paper we introduce a new Malmquist productivity index that has three attractive features: it avoids linear programming infeasibilities under variable returns to scale, it allows for technical regress, and it does not need to be recomputed when a new time period is added to the data set. The proposed index is compared to both the adjacent Malmquist index and the global Malmquist index in an empirical example, which highlights the drawbacks of the existing indexes compared to the proposed biennial Malmquist index.Our results show that 13% of the observations in the data set may have to be ignored due to infeasibilities when decomposing the adjacent Malmquist index. Using only this reduced data set does at times lead to quite different results than those generated by applying the proposed biennial Malmquist index to the entire data set. The empirical example also shows that productivity change estimated between two time periods using the global Malmquist index change substantially when a third time period is added to the data set, whereas the proposed biennial Malmquist index is immune to this problem.     

Time aggregation and the distributional shape of unemployment duration

This paper reports empirical evidence on the sensitivity of unemployment duration regression estimates to distributional assumptions and to time aggregation. The results indicate that parameter estimates are robust to distributional assumptions, while estimates of duration dependence are not. Time aggregation does not seem to have drastic effects on the estimates in a simple parametric model like the Weibull, but can produce dramatic changes in the more complicated extended generalized gamma model. Semiparametric models for grouped data produce stable estimates, and perform much better than continuous-time models in terms of significance at high levels of time aggregation.     

Hedonic versus repeat-sales housing price indexes for measuring the recent boom-bust cycle

Standard housing price indexes rely on strong constant-quality assumptions and often conflict. Hedonic price indexes overcome limitations of median price and repeat-sales indexes but their implementation has been limited by a lack of data. This paper constructs hedonic indexes at the zip code level for the Los Angeles and San Diego metropolitan areas using considerably more detailed data than previously available. Our sample was collected by a mortgage technology firm, and consists of almost 1.1 million transactions during the boom-bust cycle since 2000. Our hedonic regressions include new spatial models that capture correlations within submarkets (using zip codes as proxies) and allow temporal asymmetry. Compared to a repeat-sales price index constructed from the same data, the hedonic indexes indicate that the market peaked about 11 months later in Los Angeles and about 2 months earlier in San Diego, show less pre-peak appreciation and post-peak depreciation in low-tier housing and more pre-peak appreciation in high-tier housing. We also find that the intensity of the cycle varies greatly across zip codes and price-tiers in a pattern consistent with foreclosure activity.     

Hedonic price and depreciation indexes for residential housing: A longitudinal approach

An equilibrium price relation is derived for price changes in durable goods capable of generating a hedonic, or quality-corrected, price index, and an index of depreciation. The structure proposed is applicable particularly to housing markets, where longitudinal, or repeat-sale data are readily available from assessment or real estate sources. The separation permits not only the construction of a true price index, but also allows tests of various functional forms for depreciation, notably the geometric function. As an application of the proposed structure, estimates are presented for single-family dwellings in surburban London, Ontario, 1967–1975.     

A general approach to intertemporal and interspatial productivity comparisons

The purpose of this paper is to introduce a general methodology for analysing the sources of intertemporal or interspatial differences in outputs and costs, general in the sense that our methodology allows the productivity analyst to ‘break out’ of the quadratic ‘straightjacket’ imposed by the class of superlative index number comparisons. Starting fromTaylor's series expansions about the two points to be compared, we develop a general growth accounting equation which can be approximated to any desired degree of accuracy, depending on the information available.The theoretical framework is applied to two recent examples of interspatial comparisons which use the Tornqvist superlative index. In the first example, we show that the biases in regional Canadian total manufacturing cost-efficiency comparisons which result from the use of this index are negligible. However, in the second example, it is shown that the Tornqvist index imparts a substantial bias in United States-Japan total domestic economy productivity comparisons. The index consistently overestimates the relative productivitylevel of the U.S. economy and misses the turning point, when the Japanese economy becomes more efficient, by two years.     

Luenberger Productivity Indicators: Aggregation Across Firms

Two methods of aggregating Luenberger productivity indicators across firms are considered. One method makes use of some rather implausible allocative efficiency assumptions. The second method, a superlative index number approach, relies on more palatable assumptions and is judged to be the more promising of the two methods.     

Estimating the determinants of stock price changes

I develop an approach for estimating the determinants of stock price changes that uses all eligible trade data and other observable parameters of market activity. This approach backs out the unobserved continuous price change distribution from the observable discrete price changes, and does not constrain the determinants to be proportions of the traded bid-ask spread. I show that theoretically impermissible results and skewed estimates of cost components are obtained when the model used for estimating the determinants of stock price changes does not attempt to uncover the mapping between the observed price changes and the underlying unobserved continuous price change process, and does not effectively use all eligible trade data.     

Seasonality, consumer heterogeneity and price indexes: the case of prepackaged software

This paper measures constant-quality price change for prepackaged software in the US using detailed and comprehensive scanner data. Because there is a large sales surge over the winter-holiday, it is important to account for seasonal variation. Using a novel approach to constructing a seasonally-adjusted cost-of-living price index that explicitly accounts for consumer heterogeneity, I find that from 1997 to 2003 constant-quality software prices declined at an average 15.9% at an annual rate. As a point of comparison, the Bureau of Labor Statistics reports average annual price declines of only 7.7% for prepackaged software.     

Prices and Regional Variation in Welfare

One would expect regional differences in prices to influence conclusions concerning levels and distributions of well-being. Although there is anecdotal evidence of significant price dispersion across regions, there is no governmental source of data that measures differences in price levels. In this paper I integrate estimates of regional prices with expenditure data from the Consumer Expenditure Surveys to assess the influence of price differences on living standards in the United States. While prices have little effect on inequality, estimates of poverty and the standard of living change substantially with the inclusion of regional price variation.     

城市住房价格指数编制方法的拓展设计及实证检验

科学监测城市房价走势,在当前环境下尤为重要。为拓展国际通行方法编制国内单一城市房价指数的适用性,引入样本匹配重复交易法构建房价指数,以提高样本容量与可比性。基于上海数据的实证结果表明,相较于传统重复交易法和特征价格法,样本匹配重复交易法能更准确地反映住房价格变动,结果异常波动性更小,噪声影响程度更低,在克服样本代表性误差和变量缺失误差方面效果更显著,对编制国内城市房价指数具有较好应用价值。     

Aggregation in Input–Output Models: Prices and Quantities

This paper develops a joint theory of aggregation of input–output quantity and price models. The main emphasis is on the problem of aggregation of industries in the models. While aggregation of quantity models is a familiar topic in economic literature, the aggregation of price models is a largely unexplored subject. Here, however, quantity and price models are considered as two parts of a single, composite flow model. This understanding implies that each result in the quantity model has dual counterpart in the price model and vice versa. Through consistent use of this duality principle, significant results are developed for both model types, and a number of well-known results can be stated in a simpler way. Specifically, a number of conditions for perfect aggregation of final demands, primary inputs and industries in price models as well as quantity models are formulated. On this basis a new indicator of aggregation bias is suggested. The indicator can be decomposed into the contributions of each detailed industry, enabling the user to identify atypical industries in each group. Furthermore, the indicator can be computed even with no knowledge of the coefficients of the detailed models.