Deriving Weights for Additivity of Chained Volume Measures in the National Accounts

In current practice in all countries, subaggregate chained volume measures (CVMs) are not weighted and, thus, not additive. However, weights are necessary because without them, nonadditivity permits the nonsensical result that a subaggregate CVM could exceed the aggregate CVM. This paper derives weights to make the sum of weighted subaggregates equal the aggregate (i.e., additivity) and avoid this nonsensical result. The weights are ratios of subaggregate to aggregate chained price deflators that exceed, equal, or fall below 1 depending on relative prices. CVMs in current practice are additive only in the special case of constant relative prices when all weights equal 1. Without weights, they are not additive when relative prices change and, in this case, empirical results show that nonadditivity could significantly distort the sectoral composition of GDP

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

Comparing GDP in Constant and in Chained Prices: Some New Results

This paper's framework for GDP in chained prices yields GDP in constant prices as a special case of constant relative prices, i.e., these GDP measures differ only when relative prices change. The framework has a novel additive procedure, counter to the prevailing view that GDP in chained prices is non-additive. This procedure allows relative prices to change but when they are constant, components in chained and in constant prices are equal, implying consistency with the additivity of GDP in constant prices. Finally, GDP conversion from constant to chained prices removes the fixed base - by making the immediately preceding period the base, i.e., continuous updating - and allows relative prices to change and, thus, removes the base-period dependence and substitution bias of GDP in constant prices

Implementing Weights for Additivity of Chained Volume Measures in the National Accounts

In current practice, subaggregate chained volume measures (CVMs) are neither weighted nor additive. This paper derives and implements "weights" for weighted subaggregate CVMs to be additive (i.e., their sum equals aggregate CVM) because without weights, nonadditivity permits the nonsensical result that a subaggregate CVM could exceed aggregate CVM. The weights are ratios of subaggregate to aggregate chained price deflators that exceed, equal, or fall below 1 depending on relative prices. CVMs in current practice are additive in the special case of constant relative prices when all weights equal 1. If relative prices change, weights do not equal 1 and their use avoids nonadditivity and the above nonsensical result. Empirically, they have widespread implications because CVM is now implemented in over 40 countries. Application to actual GDP data shows significant distortions of GDP composition due to nonadditivity of subaggregate CVMs from ignoring relative price changes. Among this paper's formulas for additive weighted subaggregate CVMs, the one based on Paasche price and Laspeyres quantity indexes is recommended for practical implementation

A Generalized Exactly Additive Decomposition of Aggregate Labor Productivity Growth

Aggregate labor productivity (ALP) growth - i.e., growth of output per unit of labor - may be decomposed into additive contributions due to within-sector productivity growth effect, dynamic structural reallocation effect (Baumol effect), and static structural reallocation effect (Denison effect) of cross-sectional components (e.g., industry or region) of output and labor. This paper implements ALP growth decomposition that is "generalized" to output in constant prices and to output in chained prices (i.e., chained volume measure or CVM) and "exactly additive" since with either output the sum of contributions exactly equals "actual" ALP growth. It compares this "generalized exactly additive" (GEAD) decomposition to the "traditional" (TRAD) ALP growth decomposition devised for output in constant prices. The results show GEAD and TRAD are exactly additive when output is in constant prices but GEAD is exactly additive while TRAD is not when output is in CVM. Also, GEAD components are empirically purer than or analytically superior to those from TRAD. Moreover, considering that contributions to ALP growth can be classified by industry or region each year over many years, GEAD provides a more well-grounded picture over time of industrial or regional transformation than TRAD. Therefore, GEAD should replace TRAD in practice

Computing Additive Chained Volume Measures of GDP Subaggregates

This paper derives formulas for additive "chained volume measures" (CVMs) of GDP subaggregates depending on the underlying GDP quantity index. In turn, this paper explains why the formulas used in current practice yield nonadditive CVMs. This paper's additive formulas have significant practical implications given that nonadditivity prevails in all countries that have adopted the CVM framework for GDP and considering that more countries will be adopting this framework

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

Avoiding Anomalies of GDP in Constant Prices by Conversion to Chained Prices: Accentuating Shifts in Philippine Economic Transformation

Changing the base year (1985) of Philippine GDP in constant prices could change the growth rate and the shares of components even when there is no change in the volume of production, implying that the changes in growth rate and shares are anomalous (i.e., no real basis). This possibility weakens GDP in constant prices as basis for valuing our economy's production and analyzing its growth performance. This paper demonstrates that conversion to chained prices avoids the above anomalies and also shows smaller and shrinking agriculture and industry sectors and enlarging services sector that is now over 50 percent of the Philippine economy than are shown by valuation in constant 1985 prices. In both contributions to level and growth of GDP, chained prices accentuate more than constant 1985 prices the declining importance of agriculture and industry and the rising importance of services in Philippine economic transformation

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,

Consistent GDP Aggregation and Purchasing Power Parity

Consistent aggregation ensures that real GDP level and growth do not change as the existing GDP components are merely rearranged. Otherwise, level or growth changes are spurious. This paper proposes a framework for consistent aggregation where components are converted to "purchasing power parity" (PPP) values that "add up exactly" to the same real GDP regardless of the grouping of components. This PPP framework applies to GDP either in constant prices or in chained prices. PPP is applied to US GDP in chained prices based on the Fisher index to (i) reduce US nonadditivity residuals to zero; (ii) correct misleading contributions to GDP growth computed by the US Bureau of Economic Analysis; and (iii) show that GDP quantity indexes in PPP are consistent in aggregation although the Fisher formula is inconsistent. Moreover, PPP implications on GDP measurement for some areas of economic research (e.g., income inequality and poverty incidence) are discussed