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2018 | OriginalPaper | Buchkapitel

Relating Postal Activity to the Business Cycle by Linear Regression with Integral Equations

verfasst von : Katalin K. Clendenin, Soiliou D. Namoro, Edward S. Pearsall

Erschienen in: New Business and Regulatory Strategies in the Postal Sector

Verlag: Springer International Publishing

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Abstract

We relate the cyclical components of USPS volumes and revenues per piece to a coincident indicator of the business cycle. The relationships are represented as linear integral equations and fit employing specialized algebraic methods. Our technique yields OLS estimates in the form of continuous coefficient functions spanning three years. In general, we find that USPS volumes and revenues respond to business conditions as expected but with diverse timings. However, our fits do not explain a high percentage of the variation in the cyclical component of any postal time series. Overall, U.S. postal activity does not appear to be strongly related to the business cycle.

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Vorheriges Kapitel E-Government: A Curse or an Opportunity for Posts?

Nächstes Kapitel To What Extent Has E-Substitution Impacted the Demand for Letters and Which Factors Are Constraining Its Advance

In a recent exigent rate case U.S. Postal Service (USPS) witnesses used their econometric demand model to estimate volume and revenue losses due to the great recession. See PRC-LR-R2013-11/1 and 2.

The HP filter is the most commonly used technique for this purpose. However, it is not without its detractors including, notably, Hamilton (2017). For our purposes the most relevant criticism is that the HP filter may not correctly separate trend and cycle when there are discontinuous changes in the series. Fortunately, our method and findings do not depend critically upon the accuracy of the separations.

An alternative, but unlikely, explanation for these results is that the HP filter has failed to sufficiently separate the trend and cyclical components of our postal time series.

To account for different possible timings, a conventional single-equation linear model would have to be specified with many explanatory variables defined as leading, concurrent and lagging values of the indicator. However, applying OLS to fit such a model with monthly data does not produce useable estimates of the coefficients because the explanatory variables are nearly co-linear.

This section employs algebraic methods for treating linear integral equations described in greater detail in Pearsall (2018).

The row vector function f(t)^′ is the transpose of f(t).

One-variable real-valued functions are represented as MacLauren’s and Taylor’s series using powers vectors. Alternative choices were tested with results described briefly in Sect. 8.

Since the elements of f(u) are independent, the matrix and vectors of the linear integral equation are related by a system of independent linear equations: XCβ + e = y.

These sub-ranges correspond to the range [0, 1] of the variable v of the linear integral equation. However, it is possible to make the local fits over ranges that differ from v ∈ [0, 1].

The estimator has the well-known properties of an OLS estimator.

The data bank maintained by the Federal Reserve Bank of St. Louis (FRED) is the most important of these sources. Other sources are Macroeconomic Advisors, Stock-Watson and the Economic Cycle Research Institute (ECRI).

Most of the observations were compiled from Same Period Last Year (SPLY) values reported in the APRs for the following year. The only APRs missing from the PRC’s files were for FYs 1992, 1993, 2007 and 2008. The observations for FY 1992 are interpolations made from quarterly Revenue, Pieces and Weight (RPW) reports, the data for 1993 were recovered from SPLYs, and the FY 2007 and 2008 reports were supplied by USPS.

There are two major reallocations needed to obtain series according to consistent definitions. Prior to 1989 Government mail (except Penalty mail) was reallocated to other classes and, more recently, several reclassifications of small packages and parcel services as competitive were undone using quarterly RPWs to estimate the reallocations.

The time series we use to represent business conditions are already seasonally adjusted.

The seasonal adjustments were performed using a Eurostat program called DEMETRA.

See Hamilton (2017).

To be complete, an econometric model of demand for any category of USPS mail must explain both volume and revenue per piece because both are endogenous. See Pearsall (2011 and 2012) and Bzhilyanskaya, Cigno, and Pearsall (2015).

The prominent “blip” in Vol.APR.Total occurs at the time that USPS transitioned from using 13 4-week accounting periods to 12 monthly accounting periods.

This is done to avoid displaying the endpoints of the estimated function which are poorly supported.

The tables and graphs for these cases and others are available on request from one of the authors at espearsall@verizon.net.

Bzhilyanskaya, L. Y., Cigno, M. M., & Pearsall, E. S. (2015). A branching AIDS model for estimating U.S. postal price elasticities. In M. A. Crew & T. J. Brennan (Eds.), Postal and delivery innovation in the digital economy. Cham, Switzerland: Springer.

Hamilton, J. D. (2017). Why you should never use the Hodrick-Prescott filter. Manuscript available from the author at jhamilton@ucsd.edu

Pearsall, E. S. (2011 and 2012). An econometric model of the demand for U.S. Postal Services with price elasticities and forecasts to GFY 2015. Documentation prepared for the PRC, January 11, 2011, estimates and forecasts revised February 2012.

Pearsall, E. S. (2018). Algebraic methods for linear integral equations. Manuscript available from the author at espearsall@verizon.net

U.S. Postal Service. (various years since 2009). Econometric demand equations for market dominant products. Filed with the PRC annually in January.

Titel: Relating Postal Activity to the Business Cycle by Linear Regression with Integral Equations
verfasst von: Katalin K. Clendenin
Soiliou D. Namoro
Edward S. Pearsall
Verlag: Springer International Publishing
Buch: New Business and Regulatory Strategies in the Postal Sector
Print ISBN: 978-3-030-02936-4

Electronic ISBN: 978-3-030-02937-1

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-030-02937-1_19