Consistent Level Aggregation and Growth Decomposition of Real GDP

This paper formulates a general framework for consistent level aggregation and growth decomposition of real GDP. However, the focus is on US GDP in chained prices based on the Fisher index since this GDP motivated this paper’s purposes. These are to explain why problematic residuals‒in contributions to US GDP level and growth “not allocated by industry”‒ show up in the existing framework by the Bureau of Economic Analysis and, therefore, to propose an alternative framework for consistent level aggregation and growth decomposition where residuals cannot arise. This paper’s residual-free framework applies to real GDP regardless of the underlying indexes, i.e., to GDP either in chained prices or in constant prices

An Alternative Framework for Sectoral Contributions to GDP Level and Growth: Application to the Philippines

This paper applies relative price weights–where relative price is the ratio of a sector’s GDP deflator to the aggregate GDP deflator–to convert sectoral real GDP to homogeneous units using the economy’s GDP as “numeraire” in an alternative framework for GDP level aggregation and growth decomposition. This alternative and the “traditional” framework–without relative price weights–are compared and applied to Philippine GDP to show that the latter framework is deficient and misleading for its inability to determine the effects on GDP growth of changes and differences in sectoral relative prices that need to be taken into account

A NEW ALGORITHM FOR COMPUTING COMPENSATED INCOME FROM ORDINARY DEMAND FUNCTIONS

This paper proposes a REversible Second-ORder Taylor (RESORT) expansion of the expenditure function to compute compensated income from ordinary demand functions as an alternative to the algorithm proposed by Vartia. These algorithms provide measures of Hicksian welfare changes and Konus-type cost of living indices. RESORT also validates the results by checking the matrix of compensated price effects. obtained through the Slutsky equation, for symmetry and negative semi-definiteness as required by expenditure minimization. In contrast, Vartia's algorithm provides no validation procedure. RESORT is similar to Vartia's algorithm in using price steps. It computes compensated income at each step "forward" from the initial to the terminal prices, and insures that the compensated income computed "backward" is equal to its value computed in the "forward" procedure. Thus, RESORT is "reversible" and guarantees unique values of compensated income for each set of prices and, as a result, also unique measures of welfare changes and cost of living indices. These unique results are not, however, guaranteed by the usual Taylor series expansion for computing compensated income.Research Methods/ Statistical Methods,

Effects of Change in Relative Prices in Existing Decompositions of Aggregate Labor Productivity Growth: A Resolution of the Aggregate Effect

Diewert (2015) reworked Tang and Wang’s (2004) growth decomposition and claimed that: “Thus even if all industry labor productivity levels remain constant and all labor input shares remain constant, economy wide labor productivity growth can change due to changes in industry real output prices (italics added)” (p. 370). However, contrary to his 2015 claim, Diewert (2016) found “puzzling” results from Australian data where the sum of price change effects across industries did not matter much and explained this puzzle by an approximation formula that showed price effects sum to zero with the first-order accuracy. In contrast, this paper derives the exact formula that shows price effects sum to zero, depending on the quantity index underlying the GDP in the definition of aggregate labor productivity. It is shown that Diewert’s formula is an approximation to this paper’s exact formula showing that the aggregate effect of relative price changes is zer

Consistency in Aggregation of GDP Indexes and Uniqueness of Quantity and Price Effects on Growth of GDP and Aggregate Labor Productivity

In traditional decomposition of GDP growth in constant prices, an industry’s contribution consisted only of a quantity effect from GDP growth. Tang and Wang’s (2004, 2014) innovation added a price effect from relative price change. Dumagan (2013a, 2016) showed that Tang and Wang’s quantity and price effects for all industries exactly add up to growth of GDP either in chained or in constant prices, that is, regardless of the GDP index. However, this paper shows that it is only when GDP is in chained prices and the GDP index is consistent-in-aggregation (CIA) that quantity and price effects are invariant with industry regroupings, that is, unique. Therefore, Tang and Wang’s (2004, 2014) growth decompositions in Canada and US—where GDP is in chained prices based on the Fisher index—yield effects that vary with industry regroupings because the Fisher index is not CIA. This variation prevents attributing unique price and quantity effects to industries and, thus, clouds Tang and Wang’s analysis of the role of industries in GDP growth and in aggregate labor productivity growth. This paper also examines price and quantity effects on GDP growth of representative countries with GDP different from that in the US to make the results globally relevant

Effects of Relative Prices on Contributions to the Level and Growth of Real GDP

Existing procedures for GDP in chained or in constant prices ignore relative prices – ratios of industry GDP deflators to the economy’s GDP deflator – and, consequently, yield economically misleading results by understating (overstating) level contributions of industries with above (below) average relative prices, at the same time understating (overstating) growth contributions of industries with rising (falling) relative prices. These are illustrated by US GDP in chained prices and Philippine GDP in constant prices. However, the above misleading results could be mitigated by this paper’s general formulas for level and growth contributions applied to the same GDP. While allowing for differences and changes in relative prices, these general formulas encompass existing formulas as special cases of constant relative prices. In principle, relative prices convert real GDP of industries to the same (i.e., homogeneous) units so that they can be added to equal (i.e., additive) aggregate real GDP. Without relative prices – and, therefore, no homogeneity and no additivity – industry contributions to the level and growth of aggregate real GDP are questionable

Modifying the “Generalized Exactly Additive Decomposition” Decomposition”of GDP and Aggregate Labor Productivity Growth in Practice for Consistency with Theory

The generalized exactly additive decomposition (GEAD) of GDP and aggregate labor productivity (ALP) growth, originated by Tang and Wang (2004), is gaining attention in the literature and acceptance in practice. This paper shows, however, that the original GEAD is not always consistent with the “theory” that aggregate GDP growth is pure quantity growth and ALP growth depends only on productivity and labor share changes. This paper modifies the original GEAD for consistency, subject to certain requirement, depending on the GDP quantity index that in current practice is either (1) chained Laspeyres, (2) direct Laspeyres, or (3) chained Fisher. GEAD employs relative price to obtain contributions that exactly add up to GDP or ALP growth. Sector contributions equal pure growth effect plus price change effect (PCE) to GDP growth and with-in sector productivity growth effect plus inter-sectoral reallocation effect to ALP growth. When relative prices change, a sector’s PCE could be positive, zero, or negative but this paper shows that consistency with the above theory requires the Sum of PCE = 0 for all sectors. That is, there are no residual price effects. However, the original GEAD yields Sum of PCE = 0 only if the GDP quantity index is chained Laspeyres and, therefore, this paper modifies GEAD for theoretical consistency if the index is direct Laspeyres or chained Fisher. The findings are globally relevant because these three indexes underpin GDP in all countries in current practice

Measuring Hicksian Welfare Changes From Marshallian Demand Functions

A.E. Res. 91-10A problem persists in measuring the welfare effects of simultaneous price and income changes because the Hicksian compensating variation (CV) and equivalent variation (EV), while unique, are based on unobservable (Hicksian) demand functions, and observable (Marshallian) demand functions do not necessarily yield a unique Marshallian consumer's surplus (CS). This paper proposes a solution by a Taylor series expansion of the expenditure function to approximate CV and EV by way of the Slutsky equation to transform Hicksian price effects into Marshallian price and income effects. The procedure is contrasted with McKenzie's money metric (MM) measure derived from a Taylor series expansion of the indirect utility function. MM requires a crucial assumption about the marginal utility of income to monetize changes in utility levels. No such assumption is required by the proposed procedure because the expenditure function is measured in money units. The expenditure approach can be used to approximate EV and CV while the MM is an approximation to EV. The EV and CV approximations are shown to be very accurate in numerical examples of two prices and income changing simultaneously, and are generally more accurate than MM

Rational Choices and Welfare Changes in Philippine Family Energy Demand: Evidence from Family Income and Expenditure Surveys

This study found Philippine family demands for (1) electricity, (2) gas and liquid fuels, (3) solid fuels, (4) food, and (5) others—based on Family Income and Expenditure Surveys (FIES) in 2009, 2012, and 2015—are rational (i.e., expenditure minimizing). Specifically, all own-price elasticities are negative (downward sloping demand curves). Cross-price elasticities between (1), (2), and (3) are positive (substitutes) while cross-price elasticities of (1), (2), and (3) with (4) or (5) are mostly negative (generally complements). Income elasticities are positive (normal goods), except for (3), comprising “fuelwood, charcoal, and biomass residues” that are consumed less at higher incomes (inferior goods). These elasticities yield a Hicks-Slutsky substitution matrix that is symmetric and negative semi-definite—the necessary and sufficient conditions for expenditure minimization—a finding unprecedented in a Philippine demand study. These results validate computing compensating variation (CV) and equivalent variation (EV) that are changes in compensated incomes for restoring welfare after prices change. During 2009-2015, the overall Consumer Price Index increased 3.08 percent annually to which energy price increases contributed 0.23 percentage points, about equal to mid-point CV and EV estimates of welfare losses ranging 0.18 to 0.30 percent of 2009 total expenditures. However, improved household energy end-use efficiency by “waste” reduction compensated the above welfare losses even without increasing total expenditures or investing in efficiency improvements