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Mismeasuring long-run growth: The bias from spliced national accounts

As demonstrated by the dramatic upward revision of Nigeria’s GDP for 2013, the choice of a benchmark year matters when computing GDP statistics. This column explains how the replacement of benchmark years creates an inconsistency between new and old national accounts series, and how different ways of resolving this inconsistency yield very different estimates of historical GDP levels and growth rates. When used to evaluate the relative historical performance of Spain and France, the interpolation procedure for splicing national accounts produces more plausible results than the conventional ‘retropolation’ approach.

In April it was made public that Nigeria’s GDP figures for 2013 had been revised upwards by 89%, as the base year for its calculation was brought forward from 1990 to 2010 (Financial Times, 7 April 2014). As a result, Nigeria became the largest economy in sub-Saharan Africa. Though spectacular, this is not an exceptional case. Ghana (2010), Argentina (1993), and Italy (1987) also experienced dramatic upward revisions of their GDP. How should this revision affect GDP time series and, consequently, the country’s relative position? Should the existing historical series be re-scaled in the same proportion?

Official national accounts are only constructed in a homogeneous way for short periods, and are usually available from mid-20th century onwards, but often only for the latest decades. Thus, when a homogeneous long-run GDP series is required, various sets of national accounts using different benchmark years and often constructed with dissimilar methodologies need to be spliced. The alternative choice of splicing procedures to derive a single GDP series may result in substantial differences in levels and growth rates and, hence, in significant biases in the assessment of economic performance over time. Angus Maddison (1991) addressed the issue of inadequate splicing while researching Italy’s long-term economic performance. Unfortunately, Maddison’s warning about a serious risk of mismeasuring growth over the long run did not receive much attention.

Benchmark years in GDP statistics

National accounts rely on complete information on quantities and prices in order to compute GDP for a single benchmark year, which is then extrapolated forward on the basis of limited information for a sample of goods and services. To allow for changes in relative prices and, thus, to avoid that forward projections of the current benchmark become unrepresentative, national accountants periodically replace the current benchmark with a new and closer GDP benchmark. The new benchmark is constructed, in part, with different sources and computation methods. Often far from negligible differences in the new benchmark year between ‘new’ and ‘old’ national accounts stem from statistical (sources and estimation procedures) and conceptual (definitions and classifications) bases. Once a new benchmark has been introduced, newly available statistical evidence would not be taken on board to avoid a discontinuity in the existing series. Thus, the coverage of new economic activities partly explains the discrepancy between the new and old series. As a result, a problem of consistency between the new and old national account series emerges.

Is there a solution to this inconsistency problem? The obvious option would be computing GDP for the years covered by the old benchmark with the same sources and procedures employed in the construction of the new benchmark. However, this option is beyond the resources of an independent researcher. The challenge is, then, establishing the extent to which conceptual and technical innovations in the new benchmark series hint at a measurement error in the old benchmark series. In particular, whether the discrepancy in the overlapping year between the new benchmark (in which GDP is estimated with ‘complete’ information) and the old benchmark series (in which reduced information on quantities and prices is used to project forward the ‘complete’ information estimate from its initial year) results from a measurement error in the old benchmark’s initial year estimate.

The ‘retropolation’ approach

A simple solution, widely used by national accountants (and implicitly accepted in international comparisons), is the ‘backward projection’, or ‘retropolation’, approach, that accepts the reference level provided by the most recent benchmark estimate (YT) and re-scales the earlier benchmark series (Xt) with the ratio between the new and the old series for the year (T) at which the two series overlap (YT/XT).

Underlying this procedure is the implicit assumption of an error level in the old benchmark’s series whose relative size is constant over time (de la Fuente 2014). In other words, no error is assumed to exist in the old series’ rates of variation that are, hence, retained in the spliced series YRt. Official national accountants have favoured this procedure of linking national accounts series on the grounds that it preserves the earlier benchmark’s rates of variation.

Usually the most recent benchmark provides a higher GDP level for the overlapping year, as its coverage of economic activities is wider. Thus, the backwards projection of the new benchmark GDP level with the available growth rates – computed at the previous benchmark’s relative prices – implies a systematic upwards revision of GDP levels for earlier years. This one-sided upward revision effect on the levels of spliced GDP series is hardly noticeable when discrepancies between the new and old benchmarks are small for the overlapping year and the considered time span is short. However, as the time horizon expands and earlier series are re-scaled again and again to match newer ones, the gap tends to deepen significantly.

The interpolation approach

An alternative to the backward projection linkage is provided by the interpolation procedure that accepts the levels computed directly for each benchmark year as the best possible estimates, on the grounds that they have been obtained with ‘complete’ information on quantities and prices, and distributes the gap or difference between the ‘new’ and ‘old’ benchmark series in the overlapping year T at a growing rate.

Contrary to the retropolation approach, the interpolation procedure assumes that the error is generated between the years 0 and T. Consequently, it modifies the annual rate of variation between benchmarks (usually upwards) while keeping unaltered the initial level – that of the old benchmark. As a result, the initial level will be probably lower than the one derived from the retropolation approach.

Choosing between the two approaches

The choice of linkage procedure makes a significant difference for GDP levels and growth rates. When the levels for earlier years are re-scaled upwards with the retropolation procedure, the country in question becomes retrospectively richer. Alternatively, interpolating each original benchmark tends to raise the economy’s rate of growth and, hence, implies a lower initial GDP level. Which method is preferable? A practical answer may be derived by analysing the experience of Spain – a country that went through a process of deep structural change during the second half of the 20th century.

Figure 1 presents the GDP levels resulting from splicing national accounts through non-linear interpolation relative to the levels derived through extrapolation. It can be noticed how the over-exaggeration of GDP levels cumulates over time when the extrapolation method is used.

Figure 1. Ratio of spliced interpolated series to retropolated series, 1954–2013 (GDP at current prices)

Differences between the results of the interpolation and retropolation procedures appear much more dramatic when placed in a long-run perspective, that is, when the spliced national accounts are projected backwards into the 19th century with volume indices taken from historical accounts series. This is due to the fact that most countries grew at a slower pace before 1950, so a country’s per capita GDP level by mid-20th century determines its earlier relative position in country rankings.

Thus, the choice of splicing procedure can result in far from negligible differences in the relative position of a country in terms of per capita income over the long run. As an illustration I present Spain’s relative position to France derived with retropolation and interpolation splicing methods (Figure 2).

According to the retropolation splicing procedure, by mid-19th century, real per capita GDP in Spain would have been similar, if not superior, to that of France. If, alternatively, the interpolation splicing procedure were used, Spain’s real per capita GDP would have been 80% of that of France. When the period 1850–1913 is considered, Spain would match France’s real income per head, according to the retropolated series, and reach only four-fifths if the interpolated series are employed. These proportions hardly alter if the period under comparison is extended to 1935. It can be concluded that whatever the measurement error embodied in the interpolation procedure may be, its results appear far more plausible than those resulting from the conventional retropolation approach.

Figure 2. Spain’s real per capita GDP (France = 1), alternative splicing results (2011 EKS $)

Concluding remarks

The bottom line is that splicing national accounts must be handled with extreme care, especially when countries have experienced intense growth and deep structural change, as there is a risk of biasing their income levels upwards and, consequently, their growth rates downwards. A systematic revision of national-accounts splicing in fast-growing countries over the last half-century using the interpolation approach would most probably reduce their initial per capita GDP levels while raising their growth – with the result of a more intense and widespread catching-up to the core countries.


de la Fuente Moreno, A (2014), “A Mixed Splicing Procedure for Economic Time Series”, Estadística Española, 56(183): 107–121.

Maddison, A (1991), “A Revised Estimate of Italian Economic Growth 1861–1989”, Banca Nazionale del Lavoro Quarterly Review, 177: 225–241.

Prados de la Escosura, L (2014), “Mismeasuring Long Run Growth. The Bias from Spliced National Accounts”, CEPR Discussion Paper 10137. 

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