Superlative Index Research Articles

Price Index Numbers under Large-Scale Demand Shocks–The Japanese Experience of the COVID-19 Pandemic

Abstract We investigate the prices and quantities of face masks when the 2020 COVID-19 pandemic was particularly serious to understand the impact of demand shocks on the cost of living index (COLI). Using a recently developed index number formula that is exact for the constant elasticity of substitution utility function with variable preferences, we quantified the degree of demand shock caused by the pandemic. Our empirical analysis revealed that shifts in preferences during the pandemic were so large that the COLI with variable tastes became very different from the standard superlative indexes. While the prices of face masks decreased in the Fisher index in May 2020 by 0.76% per week, the COLI increased by 1.92% per week.

Quadratic-mean-of-order-r indexes of output, input and productivity

This paper deals with the quadratic-mean-of-order-r indexes of output, input and productivity. Each index is a family of indexes that unify many of the existing indexes, including the most popular ones. We show that all index number formulae belonging to these families are superlative indexes. This is considered as a generalization of the equivalence of Fisher and Malmquist indexes, shown by Diewert (1992).

Multilateral Methods, Substitution Bias, and Chain Drift: Some Empirical Comparisons

Multilateral methods are increasingly being used in the computation of official price indexes such as the consumer price index (CPI). This reflects the growing use of scanner data by statistical agencies and the fact that fixed‐based or chained price comparisons perform poorly in this context. A range of multilateral approaches have been pursued by different statistical agencies. Yet, it can be shown that some of these methods, at least theoretically, could suffer from substitution bias. We investigate this as well as the drivers of chain drift. We adopt a simulation‐based approach using actual scanner data prices with the corresponding quantities being generated assuming constant elasticity of substitution (CES) preferences. We find that most methods systematically deviate from the exact CES benchmark index. This is even the case for the superlative index methods, which should not exhibit substitution bias. Interestingly, we also find significant chain drift even in the exact CES indexes. We argue this reflects life cycle pricing and particularly run‐out sales at the end of a product's life.

Index Numbers and Revealed Preference Rankings

For previously identified weakly separable blockings of goods and assets, we construct aggregates using four superlative index numbers, the Fisher, Sato-Vartia, Tornqvist and Walsh, two non-superlative indexes, the Laspeyres and Paasche and the atheoretical simple summation. We conduct several tests to examine how well each of these aggregates “fit” the data. These tests are how close the aggregates come to solving the revealed preference conditions for weak separability, how often each aggregate gets the direction of change correct and how well the aggregates mimic the preference ranking from revealed preference tests. We find that, as the number of goods and assets being aggregated increases, the problems with simple summation manifest.

INDEX NUMBERS AND REVEALED PREFERENCE RANKINGS

For previously identified weakly separable blockings of goods and assets, we construct aggregates using four superlative index numbers, the Fisher, Sato-Vartia, Törnqvist, and Walsh, two non-superlative indexes, the Laspeyres and Paasche, and the atheoretical simple summation. We conduct several tests to examine how well each of these aggregates “fit” the data. These tests are how close the aggregates come to solving the revealed preference conditions for weak separability, how often each aggregate gets the direction of change correct, and how well the aggregates mimic the preference ranking from revealed preference tests. We find that, as the number of goods and assets being aggregated increases, the problems with simple summation manifest.

“Risky” monetary aggregates for the UK and US

We extend the scope of monetary aggregation beyond capital certain assets that make up central bank data sets and identify groups of assets that form monetary aggregates composed of both capital certain and risky, capital uncertain, assets. We construct monetary aggregates for the US and UK using a superlative index and relax a key assumption of the Consumption Capital Asset Pricing Model (CCAPM), a one year planning horizon, by using forecasted returns on risky assets. Our new risky monetary aggregates perform well in VAR tests. We recommended exploring risky assets as providers of liquidity services in future research on this topic.

TFP estimation at firm level: The fiscal aspect of productivity convergence in the UK

This paper reviews the state of the art in firm-level Total Factor Productivity (TFP) estimation employing an unbalanced panel of 7400 manufacturing firms in the UK during 2004–2011. The five methodologies considered are Superlative Index Numbers, System-GMM, Olley and Pakes (1996), Levisohn and Petrin (2003) and Ackerberg et al. (2015). Each of these estimators assumes different underlying properties for some inputs, which potentially affect the TFP measurements. We analyze the role of corporate taxation within a TFP catch-up model, providing new insights on the unexplored fiscal aspect of the UK productivity puzzle. Our findings are summarized as: (i) the Ackerberg et al. (2015) algorithm is the cutting-edge estimation technique with most plausible results, while GMM system (GMM-SYS) is the second best estimator; (ii) the global financial crisis in 2009 impacted negatively on TFP; (iii) corporate tax adversely affects TFP growth as it induces distortive effects on productivity enhancing investment; (iv) the adverse effect is found to be severe in the groups of R&D and exporting firms, suggesting that the distortive nature of corporate tax affects disproportionately the firms that are more financially constrained and more exposed to risk.

Scanner data, time aggregation and the construction of price indexes

We examine the impact of time aggregation on price change estimates for 19 supermarket item categories using scanner data. Time aggregation choices lead to a difference in price change estimates for chained indexes which ranged from 0.28% to 29.73% for a superlative index and an incredible 14.88%–46,463.71% for a non-superlative index. Traditional index number theory appears to break down with weekly data, even for superlative indexes. Monthly and (in some cases) quarterly time aggregation were insufficient to eliminate downward drift in superlative indexes. To eliminate drift, a novel adaptation of a multilateral index number method is proposed.

Consumer Substitution, Cost of Living Indices and Exchange Rate in Argentina - First Part: 1960-1995

This paper reviews the theory of the true cost of living index and its approximation through superlative index numbers, as well as the Vartia quantum theory of bias in index numbers as applied to substitution bias in consumer price indices. Estimated adjustments are proposed for the Argentine Consumer Price Index on account of consumer substitution, for the period 1960-1995. Annual substitution is shown to be a relatively minor proportion of annual inflation, but to accumulate a sizable effect over the years. The absolute effect varies with the absolute size of annual inflation. Substitution bias in the CPI is shown to have a strong effect on estimates of the historical inflation record and the PPP exchange rates in the 1990s.

An Index Number Formula Problem: The Aggregation of Broadly Comparable items

Index number theory informs us that if data on matched prices and quantities are available, a superlative index number formula is best to aggregate heterogeneous items, and a unit value index to aggregate homogeneous ones. The formulas can give very different results. Neglected is the practical case of broadly comparable items. This paper provides a formal analysis as to why such formulas differ and proposes a solution to this index number problem.

An Index Number Formula Problem: The Aggregation of Broadly Comparable Items

Index number theory informs us that if data on matched prices and quantities are available, a superlative index number formula is best to aggregate heterogeneous items, and a unit value index to aggregate homogeneous ones. The formulas can give very different results. Neglected is the practical case of broadly comparable items, for which price dispersion can be decomposed into a quality component, say due to product differentiation, and a component that is stochastic or due to price discrimination. This paper analyses why such formulas differ and proposes a solution to this index number problem. JEL Classification Numbers: C43, C81, E31, L11, L15.

Measuring the substitution bias in Japan: the demand system approach and a superlative index

This study estimates the demand system using Japanese micro data and calculates the cost of living index (COLI) to assess the substitution bias in the Consumer Price Index. The estimated bias during the sample period of 1982–2000 is about 0.06 percentage points, which is larger than the estimates calculated from a superlative index. The difference between the COLI and a superlative index can be explained with the upward movements of the average utility level in Japan, since the cost of living for the rich has grown more rapidly than that for the poor.

PROBLEM AND METHODOLOGICAL SOLUTION FOR CALCULATIONS ALTOGETHER PRODUCTIVITY IN AGRICULTURE

Author is engaged with problems of incorporating intermediate inputs in productivity measurements in agriculture, i.e. including intermediate inputs in a function of attached value because in that way it’s more comprehensively showing structure of agriculture production. The importance of use of superlative indexes that display qualitative changes in measurement of partial productivity is short analyzed. It’s overlooked the influence of technical-technological progress on altogether productivity adequately measure the importance in growth of production. It’s obverse that the problems of productivity measurement in agriculture are more complex than in other sectors of production. Main cause of that condition is, beside other, acceptation and use of different models and procedures at determination of productivity parameters.

Aggregation of Price Risk over Commodities: An Economic Index Number Approach

AbstractThis article extends the economic theory of index numbers to the aggregation of price risk over commodities in production. Superlative indexes of aggregate price risk are related to Tornqvist and Fisher—type output quantity indexes. An application to major crops in Manitoba illustrates the empirical importance of the analysis.

Analytical Bias Reduction for Small Samples in the U.S. Consumer Price Index

The U.S. Bureau of Labor Statistics (BLS) faces sample size constraints when computing its Consumer Price Index (CPI–U). The samples are not sufficiently large for the index to equal a true “fixed basket” price index. This study adjusts for this small-sample bias by estimating the second order of a stochastic expansion of the index. Unlike increasing sample size, this adjustment is inexpensive because it uses the same data used to compute the CPI–U. From the beginning of 1999 to the end of 2003, we estimate that 63% of the difference between the BLS superlative index (C–CPI–U) and the CPI–U is the result of finite-sample bias, and the other 37% is commodity substitution bias.

Operational identification of the complete class of superlative index numbers: An application of Galois theory

We provide an operational identification of the complete class of superlative index numbers to track the exact aggregator functions of economic aggregation theory. If an index number is linearly homogeneous and a second order approximation in a formal manner that we define, we prove the index to be in the superlative index number class of nonparametric functions. Our definition is mathematically equivalent to Diewert's most general definition. But when operationalized in practice, our definition permits use of the full class, while Diewert's definition, in practice, spans only a strict subset of the general class. The relationship between the general class and that strict subset is a consequence of Galois theory. Only a very small number of elements of the general class have been found by Diewert's method, despite the fact that the general class contains an infinite number of functions. We illustrate our operational, general approach by proving for the first time that a particular family of nonparametric functions, including the Sato-Vartia index, is within the superlative index number class.

The Difference Between Hedonic Imputation Indexes and Time Dummy Hedonic Indexes

Statistical offices try to match item models when measuring inflation between two periods. For product areas with a high turnover of differentiated models, however, the use of hedonic indexes is more appropriate since they include the prices and quantities of unmatched new and old models. The two main approaches to hedonic indexes are hedonic imputation (HI) indexes and dummy time hedonic (DTH) indexes. This study provides a formal analysis of the difference between the two approaches for alternative implementations of the Tornqvist superlative index. It shows why the results may differ and discusses the issue of choice between these approaches.

Substitution biases in price indices during transition

The rapidly changing environment of the transition may create special problems for calculation of index numbers that require a fixed basket of goods and retail outlets. Using referent-level data we find that fixed-weight Laspeyres index on average overstated cost of living increases by approximately 5 per cent a year when compared with a superlative index in the Czech Republic. This difference is smaller than might be expected given the large changes in relative prices that occurred during transition and suggests that consumer substitution impacts may have been largely offset by other factors, especially rising prices combined with increased consumption of some goods as artificial shortages under communism were removed. Indeed, in the period of greatest supply response to price liberalization, the Laspeyres index appears to understate increases in the cost of living.

The Theory of Exact and Superlative Index Numbers Revisited

This paper proposes to clarify some important questions that are still open in thefield of index number theory. The main results are the following: (i) the so-called Quadratic Identity on which the superlative index numbers are based can be applied in more general cases than those traditionally considered; (ii) it is not only the Tornqvist index number that does not rely on separability restrictions, but also some other indicators of absolute or relative changes are not based on such restrictions; (iii) in practice, however, all the index numbers or indicators that are considered to be superlative in Diewert’s (1976) sense generally fail by construction to be really superlative; (iv )t hese hybrid index numbers may be far from providing the expected secondorder approximation to the true index and may be found beyond the Laspeyres-Paasche interval even in the homothetic case. In conclusion, it would be more appropriate to construct a range of alternative index numbers (including even those that are not superlative) rather than follow the common practice of searching for only one optimal formula.

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.