Aggregation of the generalized fractional processes

The paper studies the interaction between aggregation and persistence pertaining to skip sampling of stock variables as well as temporal aggregation of flow variables for the generalized fractional processes. We show that, for skip sampling, the long memory feature at the zero frequency can arise from the aggregation of a generalized fractional series, while temporal aggregation does not induce such phenomenon. Simulation results are included to demonstrate the practical relevance of the theoretical results.     

Time Aggregation and the Money-Real GDP Relationship

This paper investigates the influence of temporal aggregation and systematic sampling on conclusions about the money-output relationship. We find that a causal relationship from M2 to real output is more likely detected using systematic sampling rather than temporal aggregation. Systematic sampled M2 has greater variation concentrated at business cycle frequencies, and this frequency band is important in explaining movements in output. In the case of M1, we find that temporal aggregation introduces a spurious causal relationship, and that the relationship between M1 and output is not stable. We find little evidence that base money or M3 help predict output.     

Detecting periods of exuberance: A look at the role of aggregation with an application to house prices

The recently developed SADF and GSADF unit root tests of Phillips and Yu (2011) and Phillips et al. (2015a,b) have become popular in the literature for detecting exuberance in asset prices. In this paper, we examine through simulation experiments the effect of cross-sectional aggregation on the power properties of these tests. The simulation design considered is based on simulated data and actual housing data for both U.S. metropolitan areas and international housing markets and thus allows us to draw conclusions for different levels of aggregation. Our findings suggest that aggregation lowers the power of both the SADF and GSADF tests. The effect, however, is much larger for the SADF test. We also provide evidence that tests based on panel data techniques, namely the panel GSADF test recently proposed by Pavlidis et al. (2016), can perform substantially better than univariate tests applied to aggregated series. Furthermore, we also illustrate the date-stamping procedure under the univariate/panel GSADF procedure uncovering novel evidence on the role of interest rates and policy uncertainty as factors explaining episodes of widespread mildly explosive dynamics in housing markets.     

Habit,aggregation and long memory: evidence from television audience data

Many economic outcomes appear to be influenced by habit or commitment, giving rise to persistence. In cases where the decision is binary and persistent, the aggregation of individual time series can result in a fractionally integrated process for the aggregate data. Certain television programmes appear to engender commitment on the part of viewers and the decision to watch or not is clearly binary. We report an empirical analysis of television audience data and show that these series can be modelled as I(d) processes. We also investigate the proposition that temporal aggregation of a fractionally-integrated series leaves the value of d unchanged.     

Linear aggregation of vector autoregressive moving average processes

A framework is developed in which to analyze both temporal and contemporaneous linear aggregation of vector autoregressive moving average processes. An aggregated finite order process is shown to be again a finite order process, and upper bounds for the autoregressive and moving average order are given.     

EstimatingJ (>1) quarterly time series in fulfilling annual and quarterly constraints

This paper addresses the problem of joint disaggregating a group of time series when their temporal aggregation values and their contemporaneous aggregation are known and when a number of related series in the desired frequency are available. The focus is on temporal distribution of annual series. This problem was treated before by other authors but they did not solve the problem of spurious steps which usually emerge in this framework. Proposed here is the simplest hypothesis congruent with reality that solves this difficulty. An algorithm is proposed to use these hypotheses in empirical works.     

Aggregation biases in production functions: a panel data analysis of Translog models

The value of panel data for micro-units in exploring aggregated relationships empirically is substantial, since such data are not only useful for estimation at both the micro- and the macro-level, but also allow comparison of properties of relationships aggregated formally from the micro-level with those resulting from aggregation by analogy in an informal way. Using panel data from manufacturing plants, we consider biases in the aggregation of the Translog production function, which does not generally satisfy the strict mathematical conditions for perfect aggregation. Linear and log-linear aggregation in the presence of random coefficients are considered. Under linear aggregation across plants, departures between geometric and arithmetic means of inputs as well as correlation between log-inputs, contribute substantially not only to biases in the output volume, but also to instability in derived input and scale elasticities and biases in total factor productivity growth. Overall, the biases under log-linear aggregation are smaller.     

How serious is the aggregation problem? An empirical illustration

Heterogeneity in consumer behaviour may create problems with aggregation across consumers. If so, we may not be able to make correct inferences about behaviour based on aggregated data. However, using micro estimates to predict aggregate demand responses to policy changes may also create a bias if not aggregated properly. This may sound like a Catch 22 situation, but it is not, as it is possible to calculate both micro and aggregate demand responses based on microdata. The size of the aggregation bias is an empirical question. In this article, we show how to calculate theoretically consistent aggregate demand responses. We use both micro and macro data for Norwegian household electricity consumption to illustrate the magnitude and direction of different aggregation biases. We find considerable aggregation biases, in particular, when estimating with macro data.     

Implications of seeing economic variables through an aggregation window

A variety of cross-sectional and temporal aggregation cases are considered. It is shown that if cointegration is found at an aggregate level then, strictly, many surprising constraints are implied at the micro level. However, a suitable approximation is suggested using common factors. It is shown that series may not be cointegrated at the time period of generation, but that after temporal aggregation cointegration could occur. This possibility arises because temporal aggregation can move a nuit root at a seasonal frequency to the zero frequency. Finally, the possibility of aggregating income distributions is considered and it is shown that, strictly, the Pareto distribution does not have the required property.     

A Guide To U.S. Chain Aggregated Nipa Data

In 1996, the U.S. Department of Commerce began using a new method to construct all aggregate "real" series in the National Income and Product Accounts (NIPA). This method is based on the so-called "ideal chain index" pioneered by Irving Fisher. The new methodology has some extremely important implications that are unfamiliar to many practicing empirical economists; as a result, mistaken calculations with NIPA data have become very common. This paper explains the motivation for the switch to chain aggregation, and then illustrates the usage of chain–aggregated data with three topical examples, each relating to a different aspect of how information technologies are changing the U.S. economy.     

Aggregated and disaggregated import demand in China: An empirical study

This paper re-estimates both the aggregated and disaggregated import demand functions for China. We consider six groups of goods for the disaggregated imports based on the Standard International Trade Classification (SITC). The empirical findings from the dynamic ordinary least squares and autoregressive distributed lag regressions indicate that there are positive effects of the domestic income on imports. Second, contrary to theory but in line with previous studies, we obtain negative coefficients for the real effective exchange rate—a real appreciation in the Renminbi (RMB) would reduce import demand. Third, the period of the great global recession is negatively associated with the import demand in China. Fourth, the perception of tail risk negatively affects demand for the aggregated imports and five of six groups for the disaggregated imports. Fifth, the exchange rate reform had a positive impact on the aggregated imports, but our estimations report mixed results for the disaggregated imports. Finally, our results indicate that there is no aggregation bias for import demand in China.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Purchasing Power Parity and aggregation bias for a developing country: The case of Mexico

This paper investigates long-run Purchasing Power Parity (PPP) between the US and Mexico. We use a panel of disaggregated price data between the US and Mexico with a long time series to look at two types of aggregation bias. The first is examined in Imbs et al. — which we refer to as estimator aggregation bias — and the second is put forth by Broda and Weinstein — hereafter, data aggregation bias. The findings indicate substantial estimator aggregation bias and data aggregation bias. Although estimates using aggregate data and imposing homogeneous coefficients provide little evidence of PPP, findings with disaggregated data and heterogeneous coefficient estimators offer strong support. The results also suggest the presence of small-sample bias as examined in Chen and Engel, but with little effect on the qualitative results. Tradable goods and non-tradable goods show little distinction in convergence rates. Estimated half-lives are lower under flexible than fixed exchange rates and indicate rapid convergence during the Mexican peso crisis.     

Biases in technical efficiency scores caused by intra-input aggregation: mathematical analysis and a DEA application using simulated data

In Data Envelopment Analysis (DEA) applications involving multiple inputs and outputs, inputs are aggregated into the total amounts of each type of input. For example, if input types ‘labour’ and ‘capital’ are used to produce multiple outputs, the total amount of labour used to produce all outputs is treated as one aggregated input and the total amount of capital as another. Resources are not disaggregated into input variables measuring the amount of labour used to produce the first output, the amount of labour used to produce the second output, the amount of labour used to produce the third output and so on, for both labour and capital. It is shown that such intra-input aggregation causes downward bias in reported technical efficiency scores, with variations in bias unrelated to true technical efficiency. Therefore, with few exceptions, any technical efficiency comparisons among DMUs are invalid. The presence of intra-input aggregation bias is demonstrated mathematically, simulation is used to exhibit its severity, and the exceptions that permit intra-input aggregation without causing bias are identified. It is concluded that, for multiple-input, multiple-output DEA applications, inputs must be disaggregated into the amounts used to produce each output in order to validly report technical efficiency, unless one of the exceptions is present.     

TESTING UNCOVERED INTEREST PARITY: A CONTINUOUS‐TIME APPROACH*

Nowadays researchers can choose the sampling frequency of exchange rates and interest rates. If the degree of overlap is large relative to the sample size, standard GMM asymptotic theory provides unreliable inferences in uncovered interest parity (UIP) regression tests. We specify a continuous‐time model for exchange rates and forward premia robust to temporal aggregation, unlike existing discrete‐time models. We test the UIP restrictions on the continuous‐time model parameters and propose a novel specification test that compares estimators at different frequencies. Our results based on correctly specified models provide little support for UIP at both short and long horizons.     

Introduction to judgment aggregation

This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals' judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.     

Solutions For Some Dynamic Problems With Uncertainty Aversion

In a discounted expected-utility problem, tomorrow's utilities are aggregated across tomorrow's states by the expectation operator. In our problems, this aggregation is accomplished by a Choquet integral of the form ∫ u d P ^α, where α specifies uncertainty aversion. We solve all finite-state problems by either a closed form or a finite-dimensional iteration, and show that uncertainty aversion reduces the perceived return on investment, thereby decreasing the saving rate given elastic preferences and increasing the saving rate given inelastic preferences.
JEL Classification Numbers: C61, D81, D9.     

An Equilibrium Approach to the Aggregation of Beliefs

This paper presents a new answer to the old question of how to aggregate individual beliefs. We construct a model which allows agents to take arbitrage opportunities against the aggregated belief by making contingent claims against the states, and the aggregator (market maker) regulates the probability of states. When all claims from the agents are mutually covered for every realization of the state, an aggregation of individual beliefs is thus obtained. We prove the existence and uniqueness of the equilibrium aggregation, and also show that the aggregate belief lies in the convex hull of individual beliefs. This model allows us to address some important problems such as how individual agent’s attitude toward risk and wealth endowment affect the outcome of the aggregation process, and whether the aggregate belief satisfies the well-known properties like equal treatment.     

Understanding and forecasting aggregate and disaggregate price dynamics

There are doubts regarding the empirical benefits of forecast aggregation. Theoretical research clearly supports forecast aggregation but conflicting results exist in the empirical literature. We search the literature for empirical regularities. One important issue often cited is estimation error and papers which are unsupportive of forecast aggregation often have short spans of data. A second empirical regularity is that researchers frequently use a relatively small number of disaggregates. Our work finds that the greatest benefits to aggregation are realised when a large number of disaggregates are used. This is a natural consequence of the theoretical results. A second critical issue in forecast aggregation is model selection. We suggest a simple guide to model choice based on the empirical properties of the data. In this regard, the extent of comovements between the constituent series determines model choice.