Measuring Economic Growth in New Zealand (WP 02/14)

Abstract#

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This paper examines New Zealand's ranking in the OECD based on real GDP per capita. The fall in ranking experienced by New Zealand implies that real GDP per capita growth in New Zealand has been relatively poor in comparison to other OECD countries. The paper examines the history of New Zealand’s growth rate and explores the differences between various techniques for measuring average growth rates. The approaches are all shown to be variants of the average annual growth rate but differ in terms of the weighting structure used. Ultimately, the most appropriate technique depends on the underlying data generating process. The implications of data construction techniques for measured growth rates are discussed and differences between the growth rates obtained from different data sources are illustrated. The paper also illustrates the sensitivity of New Zealand growth rates to the sample period chosen.

Acknowledgements#

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The author would like to thank Maryanne Aynsley, Iris Claus, Arthur Grimes, Katy Henderson, Dean Hyslop, Nathan McLellan, Grant Scobie, and David Skilling for their helpful comments and suggestions on various draft versions of the paper.

Disclaimer#

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The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate.

1  Introduction#

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Recently there has been increased interest in New Zealand’s income position relative to other countries, in particular countries in the Organisation for Economic Co-operation and Development (OECD). The increased interest reflects concerns that New Zealand’s relative income position has been falling since the 1950s. For example Growing an Innovative New Zealand(New Zealand Government, 2002) released in February stated that “New Zealand’s relative income declined over much of the post-war period. New Zealand’s real per capita income fell from among the highest in the world in the 1950s, to just under the OECD average in 1970, to 20^th in the OECD by 1999.”

To address such concerns the previous Government (1999-2002) adopted a goal of returning New Zealand’s per capita income to the top half of the OECD.

Our economic objective is to return New Zealand’s per capita income to the top half of the OECD and to maintain that standing. This will require New Zealand’s growth rate to be consistently above the OECD average growth rate for a number of years. That will require sustained growth rates in excess of our historical economic performance.(New Zealand Government, 2002)

While such goals focus on New Zealand’s per capita income, the income measure generally used has been Gross Domestic Product (GDP) per capita.[1] This paper highlights a number of issues that are relevant when measuring economic growth over time and when making international comparisons on the basis of ranking in real GDP per capita.

Section 2 examines New Zealand’s ranking within a group of OECD countries, based on our level of real GDP per capita, when several different data sources are used. This highlights that New Zealand’s ranking is to some extent influenced by the data source used (though all sources are consistent with New Zealand sliding down the ladder over time).

The fall in our ranking implies that New Zealand’s growth rate in real GDP per capita must have been relatively poor over periods of time. This leads to the question of what has been New Zealand’s average growth rate since the 1950s and how does this compare with the experience of other countries? However, prior to addressing this question, there are several issues relating to the construction of average growth rates that are important to highlight if a country’s performance is to be accurately assessed. One of these issues is how to measure average growth over any given period of time. This issue is discussed in Section 3.

Data construction techniques can have important ramifications for the estimated growth rate. The impact of data construction techniques on measured growth rates are discussed in Section 4.

With the issues raised in Sections 3 and 4 borne in mind, Section 5 examines New Zealand’s historical growth performance based on several data sources. Finally, Section 6 concludes by briefly summarising some of the key points.

2  New Zealand’s place on the OECD ladder#

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Figure 1 presents New Zealand’s ranking in the OECD, in terms of real GDP per capita, based on data from three different sources. These different data sources are OECD (2002)[2], Maddison (2001), and Penn World Tables (PWT)[3]. The rankings on which Figure 1 is based are displayed in Table 1.

Figure 1 – New Zealand’s Real GDP per Capita Ranking Amongst OECD Countries

 

Regardless of which data source is used, New Zealand’s ranking has dropped over time. Note that in Figure 1 the values on the vertical axis are displayed in reverse order, ie higher numbers (lower rankings) are below lower numbers (higher rankings). Consequently a negative slope is associated with a worsening in the ranking over time. However, there is a degree of variation in New Zealand’s relative ranking across the different data sources. This implies that data construction and collection techniques can influence the particular ranking that New Zealand attains.[4] It is also interesting to observe that New Zealand’s GDP per capita ranking based on OECD data was substantially higher when 1995 purchasing power parities (PPPs) are used rather than the 1995 exchange rate against the United States dollar.

The OECD datasets used in this paper include the following 26 countries (lowest ranking possible is 26): Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Korea (South), Luxembourg, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, United Kingdom, and the United States.

The Penn World Table (PWT) dataset used in this paper is made up of 25 countries (lowest ranking possible is 25). These are the same as for the OECD datasets with the exclusion of Germany.

The Maddison dataset used in this paper is made up of 24 countries (lowest ranking possible is 24). These are the same as for the OECD datasets with the exclusion of Iceland and Luxembourg.

Ultimately, it appears there will always be a degree of uncertainty as to New Zealand’s actual GDP per capita ranking for any particular individual year back to 1950 (and prior) due to different data sources or differences in the units in which GDP per capita is expressed providing different rankings. This uncertainty also applies to pinpointing sub-periods where New Zealand’s ranking decline has been the greatest. Three out of the four series for New Zealand’s GDP per capita ranking display substantial falls in the mid-to-late 1970s.[5] For example, the series based on PWT data shows that New Zealand dropped from 7^th in 1975 to 15^th in 1980. Likewise the series based on OECD PPP data shows that New Zealand dropped from 6^th in 1974 to 18^th in 1979. The Maddison series also shows a sizable decline over this period. The entry of Britain into the European Union and the resulting loss of free entry to British markets for dairy products, and the oil price shocks of the 1970s are potential explanations for New Zealand’s relative fall in the real GDP per capita rankings during this period.

Based on the data shown in Table 1, there may be a case for arguing that the mid to late 1960s was also a period in which New Zealand’s ranking fell significantly. For example, in 1966 the Maddison series ranked New Zealand 3rd, whereas in 1970 New Zealand’s ranking had slipped to 9^th. The collapse of wool prices in 1967, due to increased competition from synthetic fibres, coincides with the fall in ranking that occurred during this period.

Other economists have expressed alternative views as to which periods are most significant in New Zealand’s slide down the OECD’s rankings. For example, Brian Easton states that “The economy mainly lost its placing following two major shocks – in the late 1960s when the price of wool collapsed, and the late 1980s when there was a grossly overvalued real exchange rate.”[6] As already discussed, the first of these two explanations is to some extent apparent in the data displayed in Figure 1. The later explanation is not really supported by three of the four series used in this paper, although the PWT series does show that New Zealand’s ranking slipped from 12^th in 1984 to 18^th in 1988. It is clear that dating key periods is itself dependent on the particular data series chosen.

Falls in New Zealand’s ranking within the OECD result from relatively poor growth in real GDP per capita in comparison to other OECD countries over time. Therefore it would be of interest to know what has been New Zealand’s average growth rate since the 1950s and how does this compare with the performance of other OECD countries? As is the case for determining New Zealand’s ranking in the OECD, it is likely that different people will obtain different estimates of New Zealand’s growth rate over a period. These estimates are likely to differ due to: the approach taken to measuring the average growth rate over a period; the real GDP series used; the units in which the series is expressed; and the particular time period used. The next section discusses four possible ways of measuring the average growth rate of real GDP per capita over a period of time.

3  Calculating Growth Rates#

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For a given time series of annual real GDP per capita data, how should the average growth rate for the entire data period, or a particular sub-period of interest, be calculated?[7] There are a number of potential ways of constructing an average growth rate for a particular period. This paper focuses on four alternatives: (a) least squares growth rates; (b) a differenced logarithmic model; (c) the average annual growth rate; and (d) the geometric average growth rate. This section explains the procedures involved in computing growth rates using these alternative techniques. As will be shown, deriving these alternative growth rate estimators algebraically highlights that the different estimates obtained from these methods are all some variant of the average of the annual growth rates. The alternative approaches differ in terms of the averaging technique used on these annual growth rates.

The annual growth rate for a series of T annual observations, say Y₁, Y₂, Y₃, … ,Y_T, is defined as:

(1)    

 

 

where Y_t is the observation for year t.[8]

3.1  Least Squares Growth Rates#

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One common approach to measuring growth rates is the Least Squares or Ordinary Least Squares (OLS) approach. In fact Kakwani (1997) notes that this is the most commonly used procedure for estimating growth rates.

The OLS approach is based on the compound growth formula:

(2)    

 

 

The compound growth formula states that the value of real GDP per capita at time t is equivalent to the value of real GDP per capita at time 1 grown at a constant annual rate r (with compounding occurring annually over t-1 years).

Taking natural logs of (2) gives:

(3)    

 

 

Adding a disturbance term

 

, and letting

 

and

 

yields equation (4):

 

(4)    

 

 

By regressing

 

on t (time) using OLS we obtain an estimate of the slope coefficient (

 

) that provides an estimate of the instantaneous growth rate (

 

). The compound rate of growth can be obtained as follows[9]:

 

(5)    

 

 

It can be shown (see Appendix A.1) that the OLS estimator of

 

can be expressed as:

 

(6)    

 

 

where

 

 

That is,

 

is a weighted average of the

 

’s with the

 

’s serving as weights. As

 

the OLS estimator for

 

approximates a weighted average of the proportional changes in the series of interest (eg, in the case of annual data, a weighted average of the annual growth rates).

 

However, it is worth focusing on the weights. Note that the formula for the weights (

 

) is a quadratic in s. This weighting scheme means that the weights on the annual growth rates first increase with s, until reaching a maximum when

 

, and then decrease symmetrically until

 

.

 

To illustrate the differing weights applied to the (approximations of) the annual growth rates, Figure 2 plots the weights that would apply if one was working with sample of size T=20. When T=20, the weight given to the annual growth rate in the middle of the sample is 5.26 times the weight given to the growth rates at the end points of the sample. In general the ratio of the highest weight used to the lowest weight used is

 

. The ratio of the highest weight to the lowest weight for values of T between 2 and 100 are shown in Figure 3.

 

Figure 2 – Weighting Scheme for OLS growth rate estimate (T=20)

 

Figure 3 – Maximum/Minimum Weight Ratio for time series of length T

 

3.2  Log Difference Model Growth Rates#

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As just discussed, the commonly used least square regression approach results in a quadratic weighting scheme. The use of a different model enables us to obtain an estimator based on a simpler weighting scheme. Consider the model:

(7)    

 

 

By noting that this is equivalent to

 

, recursive substitution enables (7) to be rewritten as:

 

(8)    

 

 

Note that the model shown in equation (8) is identical to the model shown in (4) except for the error term[10]. Therefore, the argument (based on manipulating the compound growth formula) that

 

can be interpreted as a growth rate also holds for this model. In the model shown in (8) the error term is described by a moving average process.

 

The OLS estimator of

 

in the model described by equation (7) can be expressed as (see Appendix A.2):

 

(9)    

 

 

So

 

is just an average of the T-1

 

terms, with each

 

term being given an equal weighting of

 

.

 

As was the case in section 2.1, the estimate of the slope coefficient (

 

) provides an estimate of the instantaneous growth rate. The compound rate of growth can be obtained as follows:

 

(10)    

 

 

3.3  The Average Annual Growth Rate#

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Noting that

 

approximates the annual growth rate implies that

 

in equation (9) is approximately equal to the average of the annual growth rates. In fact, using the actual annual growth rates rather than their

 

counterparts gives us another simple way of calculating the annualised rate of growth over a period. This approach is referred to as the “average annual growth rate” (AAGR) approach. The average annual growth rate can therefore be specified as:

 

(11)    

 

 

3.4  Geometric Average Growth Rates#

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Another way of calculating the average growth rate for a period when an annual time series of data (Y₁ to Y_T) is available is to directly utilise the compound growth formula by using the data points Y₁ and Y_T as follows:

(12)    

 

 

solving the expression in (12) for r gives:

(13)    

 

 

Here r is the rate of growth required to grow Y₁ so that it equals Y_T in T-1 years when compounding occurs annually. This approach is referred to as the geometric average approach. The fact that this approach only uses the values of the two endpoints of the series of interest is often considered a weakness. The reason for referring to this approach as the geometric average approach is that it is possible to express 1+r as follows (see appendix A.3 for details):

(14)    

 

 

The expression shown in (14) states that

 

is the geometric average of one plus the annual growth rates obtainable from the data.

 

3.5  The four approaches summarised#

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Sections 3.1 to 3.4 have identified four approaches that can be used to measure the average growth rate over a period or sub-period of interest. Table 2 summarises how these approaches measure the growth rate as a function of the time series observations of the series for which average growth rates are being constructed.

For the time series Y={Y₁, Y₂, Y₃, … , Y_T}

It is possible to show that techniques 2 and 4 are equivalent so that

 

(see Appendix A.4 for details). That is, the average growth rate for a period calculated by the log difference regression technique would be the same as the average growth rate calculated by the geometric average approach. Another point worth noting is that the log difference regression rate is approximately equal to the

 

used in its construction. It was noted that

 

estimated in the log difference regression approximately equals the average annual growth rate and therefore the average annual growth rate is approximately equal to the log difference growth rate (and subsequently the geometric average growth rate).[11] That is:

 

(15)    

 

 

Note: The GDP per Capita series is GDP per head at the price levels and exchange rates of 1995 (US dollars) as published in (OECD 2002). Data was obtained electronically to 3 decimal places and data to this level of accuracy was used in the growth rate calculations.

AAGR, GEO, OLS and LD refer to the growth rate obtained using the Average Annual Growth Rate, Geometric Average, Ordinary Least Squares and Log Difference techniques respectively.

Table 3 illustrates the results obtained by using the four growth rate techniques outlined earlier. Estimates of the average growth rate in New Zealand real GDP per capita over a number of different 10-year windows are computed as well as the average growth rate of the entire period (1970-2000). This means that for each window a sub-series of 11 data points is used. Not surprisingly, the growth rates calculated using the geometric average and log difference techniques are identical and only differ to the average annual growth rates by up to 5 one hundredths of a percent. There is substantial variation between the growth rate computed using the OLS technique and the other three techniques. In some cases the difference between the growth rates obtained using the OLS technique and the average annual growth rate technique is greater than the average annual growth rate value. The quadratic weighting scheme used in the OLS technique results in the OLS growth rates being materially different from the growth rates obtained using the other techniques, even when the rates are calculated over the entire sample.

Figure 4 – A comparison of different growth rate construction techniques (NZ growth rates measured over different 10 year windows)

 

Source: Author’s growth rate calculations based on OECD data as shown in Table 4.

Figure 4 provides an alternative representation of the data in Table 3 and plots the average growth rate in New Zealand’s real GDP per capita for moving 10-year periods as measured using the different growth rate approaches. Thus the first growth rate plotted for each series is for the period 1970 to 1980, the second for the period 1971 to 1981 and so on. Figure 4 again highlights that the growth rate estimates for a particular period can vary significantly depending on the technique used, with the OLS growth rate at times differing substantially from the rates obtained using other approaches.

3.6  Choice of Method#

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Section 3.5 highlighted that growth rates obtained from the OLS approach sometimes differed substantially to those obtained from the other 3 methods. Given this, what is the most appropriate way of calculating a growth rate? This depends on the data generating process underlying the data being used. In the case that the log of GDP per capita is stationary around a deterministic trend and hence does not contain a unit root, then it is appropriate to use the OLS approach. On the other hand when the log of GDP per capita is integrated of order one (I(1)) the log difference approach is more appropriate.[12] As the log difference approach provides the same results as the geometric average approach, and is approximately equal to the average annual growth approach, there is little in it when choosing between these three approaches.

The average annual growth rate approach involves a weighting structure (standard arithmetic weights) that makes it intuitively simple. The geometric average approach (and consequently log difference approach) is also quite intuitive and has the advantage that if one takes the value of real GDP per capita at the start of the sample period of interest and grow it at the geometric average growth rate for the appropriate number of years, the value obtained will be that of the final value of real GDP per capita in the sample period of interest. In general this will not be the case when the other growth rate approaches are used.

As shown in Table 4, the natural log of all the New Zealand real GDP per capita series used in this paper are integrated of order 1 (I(1)). What this means is, that with New Zealand data at least, the use of the OLS approach to calculate an average growth rate should be avoided and one of the other 3 approaches used. Due to its simplicity, when growth rates are computed in the rest of this paper the average annual growth rate has been used.

Both a constant and trend were included in the Augmented Dickey-Fuller (ADF) tests when conducted on levels data. Numbers in brackets in the second and third columns indicate number of lags used in these tests. The lag lengths were determined using the Schwarz criterion.

* signifies a unit root null is rejected at the 5% significance level

** signifies a unit root null is rejected at the 1% significance level

4  Data Construction Techniques and Measured Growth Rates#

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Section 3 examined different techniques to estimate an average growth rate over a particular period. Figure 4 highlighted that when these different techniques were applied to a common data series, the OLS approach could result in average growth estimates that looked quite different to those obtained from the other approaches. That is, the choice of average growth rate estimation technique can be quite important. Another factor that must be borne in mind is what dataset to use when calculating average growth rates over a period. For example, there exist several potential series for New Zealand’s real GDP per capita and these series differ in the length of their coverage and how real GDP per capita has been measured[13].

This section illustrates the differences in New Zealand’s growth rate in real GDP per capita when different data sets are used. Six data sets are used in this illustration. Their details are shown in Table 5.

The New Zealand series described in this table are presented in Appendix B.

For each of these series New Zealand’s average growth rate over every possible ten-year window has been calculated using the average annual growth rate (AAGR) approach outlined in Section 3. As the series are of different lengths the number of possible windows for each series also differs. Figure 5 shows the average growth rate for each ten-year period plotted against the window endpoint.[16] This means that a value for, say, 1990 represents the average growth rate over the period 1980 to 1990. Likewise, a value for 1970 represents the average growth rate over the period 1960 to 1970. Figure 5 illustrates the variation between the average growth rate for a ten-year period when different data sets are used.

One feature of Figure 5 is that there appears to be more variability in the growth rates obtained using different data sets earlier on in the sample. This is particularly the case if one omits the preliminary Penn World Table data that is yet to be finalised. However, it is worth pointing out that as the graph displays the average growth rate for a ten-year period even small differences would result in material differences in real GDP per capita over time. For example, even when we exclude the preliminary Penn World Table data, the average growth rate for the period ending 1992 (ie 1982 to 1992) differs between data sources by up to a bit under 0.5% per annum. If actual performance was to differ by this much then real GDP per capita would have increased by nearly 5% more over the ten year period when comparing performance for this period under the highest and lowest growth estimates.

Figure 5 – A comparison of New Zealand’s growth rates obtained from different data sets (NZ growth rates measured over different 10 year windows)

 

Note: The average annual growth rate method was used to obtain the average growth rates presented in this figure.

Figure 6 – A comparison of New Zealand’s growth rates obtained from different data sets (NZ growth rates measured over different 10 year windows)

 

Note: The average annual growth rate method was used to obtain the average growth rates presented in this figure.

Vertical axis displays annual average growth rate (%)

Horizontal axis displays year of window endpoint

Figure 6 illustrates the growth rates for each series shown in Figure 5 separately (using consistent scales). Casual observation of the Maddison and PWT plots in Figure 6 could suggest a downward trend over time in New Zealand’s average growth rate. However such a conclusion is likely to be misleading due to changes over time in the way in which real GDP for New Zealand has been measured.

4.1  Changes in the way New Zealand real GDP is measured#

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Over time there have been efforts to improve the way real GDP is measured. Unfortunately, however, these improvements mean that real GDP series constructed on a consistent basis and covering a long historical time period are not available. Consequently long time series of annual GDP data either tend to include data constructed in several different ways or require a considerable proportion of the series to be based on estimated rather than measured values.

Statistics New Zealand released upgraded national accounts at the end of 2000 and in mid 2001. These introduced a number of important changes, including moving from a fixed weight to a chain linked calculation of constant price (real) data, the adoption of the international accounting standard, System of National Accounts 1993 (SNA93), and the Australia New Zealand Standard Industrial Classification (ANZSIC). Real GDP figures back as far as the June quarter of 1987 are available on this consistent basis. These new SNA93 chain linked series are now New Zealand’s official data series and replace the previous official series that was based on a different accounting standard called System of National Accounts 1968 (SNA68). The previous official series was also a fixed weight rather than chain weighted series (more details of what this means are provided below). The previous official fixed weight series was available from September 1977.[17] What this means is that real GDP series that provide estimates of New Zealand’s real GDP for time intervals that include 1977 are likely to include data that is constructed in several different ways. When this is the case, estimates of economic performance for different sub periods are probably not strictly comparable and unfortunately there is no easy way around this.

4.2  Different approaches to constructing real GDP series (Chain versus Fixed weights) and their influence on growth rates#

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Annual GDP series measure the total value of goods and services produced in an economy over a 12-month period. Nominal GDP series simply sum over all possible goods and services the total value of each type of good or service produced in the 12 months. For each good or service, the total value is the number of units of the good or service produced, multiplied by the price of a unit of that good or service for that year. An increase in nominal GDP from one year to the next can therefore be attributed to an increase in prices, an increase in the volume of goods and services produced, or most probably, some combination of these two. For example, if in year 2 all prices are 10% higher than they were in year 1, and the same quantity (volume) of each good or service is produced, then nominal GDP will be 10% higher. If these goods and services must be shared amongst the same number of people in each year, is the country better off? The answer is no as in aggregate people have the same quantity of goods and services available for consumption.

Real GDP series overcome this problem by removing the impact of price changes. Consequently, changes in real GDP reflect changes in the volume or quantity of goods and services produced. Such a series is commonly referred to as being expressed in constant prices or real terms. There are several approaches to doing this, with the approaches differing in the choice of which year’s prices are used in the construction of the index.[18] As is illustrated below, the choice of which year’s prices are used has implications for the growth rates that can be obtained from the series. This section begins by considering the difference between two types of volume indexes (the Laspeyres and Paasche indexes).

A Laspeyres index calculates the total value of GDP holding prices constant at their first year levels. Table 6 presents a theoretical example of real GDP in the first and second year constructed using the Laspeyres method (note the total value of each commodity for each year utilises the first year’s prices). In the example, real GDP has grown by 18.1%.

Source: Statistics New Zealand (1998) - with very minor amendments

A Paasche index calculates the total value of GDP holding prices constant at their second (or last) year levels. Table 7 presents a theoretical example of real GDP in the first and second year using the Paasche method (note the total value of each commodity for each year utilises the last (second) year’s prices). In the example, real GDP has grown by 15.4%.

Source: Statistics New Zealand(1998) - with very minor amendments

Clearly the growth rate is dependent on which approach (Laspeyres or Paasche) is used. The result that the growth rate of the Laspeyres index is greater than the growth rate shown by the Paasche index is not just due to the construction of the example[19]. The reason why Laspeyres indexes tend to exhibit higher growth than Paasche indexes is due to the substitution effect that occurs when relative price changes occur. People tend to purchase more of goods that have become relatively cheaper and less of goods that have become relatively more expensive. Consequently goods that have become relatively cheaper tend to have faster growth (in terms of numbers of units produced and consumed) and goods that have become relatively more expensive tend to have slower growth. By using first year prices (before the relative price changes), the Laspeyres approach gives a higher weight to fast growing commodities and a smaller weight to slow growing commodities.

In terms of what drives differences in the growth rates obtained from the two approaches, Statistics New Zealand (1998) states “What matters is the extent to which the pattern of relative prices (ie the ratio of the price of one commodity to another) changes over time and not the general rate of inflation. If all prices were to increase at the same rate the two volume indices would be equal, but if some prices go up faster than others, and especially if some go down while others go up, the two volume indices will diverge. The more variation there is in the price changes, the more the volume indexes will diverge.”

Things become even more complex when one is interested in constructing values for real GDP over more than 2 periods. There are two general approaches. The first is known as the fixed weight index approach and uses the prices of just one period. Real GDP for each period in the series is calculated by multiplying the price of each commodity (in the chosen base year) by the quantity of the commodity produced in the year for which real GDP is being calculated. Until recently, this is the approach that Statistics New Zealand used and when using this approach 1991/1992 was chosen as the base year’s prices to be used. For each year, the quantity of a particular commodity produced was multiplied by that commodity’s 1991/1992 price. Summing this product over all commodities gave a value for real GDP expressed in 1991/1992 prices. Consequently, the values of real GDP prior to 1991/1992 are constructed using the Paasche index approach (as the 1991/1992 prices being used relate to a later period than the quantities of commodities produced). On the other hand, values of real GDP for years after 1991/1992 utilise the Laspeyres index approach. As a Laspeyres index tends to register higher growth rates than a Paasche index, this means that it is likely that growth prior to 1991/92 (based on a Paasche index) would be understated to growth post 1991/1992 (based on a Laspeyres index).

One issue that arises with fixed weight series is that the growth rates between consecutive years are sensitive to the choice of base year chosen. “In general, moving the base year forward in time will tend to reduce growth rates previously recorded so that they have to be revised downwards. History is rewritten.” (Statistics New Zealand, 1998) Statistics New Zealand (1998) provides an illustration of this by comparing annual growth rates for total real gross domestic expenditure when 1991/92 prices were used with the growth rates when 1982/83 prices are used.[20] Table 8 reproduces a table summarising the results. As can be seen from the table the differences in annual growth rates are quite substantial.

Source: Based on Table C from Statistics New Zealand (1998)

The second general approach to obtaining real GDP values for multiple years is known as the annual chain-linked approach and this method updates the price weights used every year. For the period 1987 to 2000, the chain-linked real GDP series is derived by calculating the (percentage) change between 1987 and 1988 using 1987 prices to value the quantities in 1987 and 1988. The change between 1988 and 1989 is calculated using 1988 prices to value the quantities in 1988 and 1989 and so on. To obtain a series of real GDP figures based on 1995 prices the following approach is used. For each year a measure of the total change between the year of interest and the year 1995 is obtained by multiplying together the annual changes between consecutive years. For years prior to 1995, the value of 1995 real GDP (which will equal the nominal GDP for 1995 as 1995 prices are being used) is divided by the by the appropriate total change figure. For years post 1995 the 1995 value for real GDP is multiplied by this amount.[21]

Note that the above approach to obtaining a chain-linked series is known as a Laspeyres chain linked approach as for each pair of years the prices of the earlier year are used. If the latest year’s prices were used for each pair the resulting index would be a Paasche chain index.

If relative prices change monotonically using chain weights instead of fixed weights tend to result in a growth rate somewhere between that of a fixed Laspeyres or fixed Paasche index. As outlined above, Statistics New Zealand has upgraded New Zealand’s National Accounts by moving from fixed to (Laspeyres) chain weights. Theoretically this should increase growth rates prior to 1991/92 as a chain Laspeyres index will produce higher growth rates than a fixed Paasche. The upgrade would also theoretically reduce growth rates after 1991/1992 as a chained Laspeyres index will result in lower growth rates than a fixed Laspeyres index.

Experimental work by Statistics New Zealand based on real (expenditure based) GDP series showed that when moving from a fixed weight method to a Laspeyres chain weighted method for constructing real GDP series the differences in (annual) growth rates are less than 0.3 percentage points although the annual growth rate between the 1994 and 1995 March years was as high as 0.6 percentage points (see Statistics New Zealand (1998) for more details).[22]

The key point to be taken from this section is that there are a number of measurement issues associated with measuring real GDP and consequently with measuring the growth in real GDP per capita. As a result there probably does not exist a definitive or ‘true’ calculated value for the historical rate of growth in a particular period. Different approaches to measuring or constructing real GDP series have resulted in the various series for real GDP per capita that are available not being identical. Therefore, the average growth rate for a period of interest will tend to vary across series.

5  Measured New Zealand growth rates over time#

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One point that should be noted when considering New Zealand’s average growth rate over a particular sub-period is that the growth rate can be quite sensitive to the endpoints (or time period) chosen. Table 9 shows New Zealand’s growth rate based on OECD data for a number of different length sub-periods. To illustrate the sensitivity of the average growth rate for a period, consider the average growth rate for the period 1988 to 1994 (a 6 year window with window endpoint 1994). The average growth rate for this sub-period is 0.63 percent. Compare this to the growth rate for the period 1987 to 1993. The average growth rate for this period was -0.10 percent per annum. These growth rates differ significantly yet the start and end of the six year period under consideration differ by only one year.

Growth Rates calculated using average annual change method.

Example: the growth rates with window endpoint 1999 and window length 8 is calculated using real GDP data for the years 1991 through to 1999.

Bold figures show the highest average growth rate for each window length. For example if one focuses on growth rates for sub periods that are 7 years long, the highest growth rate for any period of this length was 2.5% and this relates to the period 1992 to 1999.

Alternatively, this same point can be illustrated when the endpoint is fixed and the length of the sub-period differs by a single year. For example the average growth rate for the period 1991 to 1997 was 2.30 percent. Extending this period back just one year results in a growth rate for the period 1990 to 1997 of 1.32 percent. This is nearly a whole percentage point lower. These differences are a result of the variability of the annual growth rates. Due to this variability it is often desirable to measure trend growth, which loosely put implies measuring growth rates between two years that are similarly placed during the growth cycle, for example, peak to peak. The objective of this paper is, however, to document New Zealand’s historical growth performance over time and not to determine New Zealand’s trend (or potential) growth rate.

Table 10 gives the ranking of the New Zealand growth rate for each cell in Table 9 within the 26 OECD countries included in the OECD dataset used for this paper. For each possible sub-period shown in the table, the average growth rates of the other 25 OECD countries have been calculated and New Zealand’s ranking within these growth rates computed. As Table 10 shows New Zealand’s growth rate for most sub-periods has been towards the bottom of the OECD (lowest possible ranking is 26). Periods where performance has been in the top half are rare and not sustained for long periods of time.

Possible rankings range from 1 (highest growth rate for the period in the OECD) to 26 (lowest growth rate for the period in the OECD). Bold cells show New Zealand’s highest ranking in each column.

* indicates that the growth rate ranking is sufficiently high to be categorised as being in the top half of the OECD.

Bearing in mind the sensitivity of NZ growth rates to the sample period, the results shown in Tables 9 and 10 may highlight signs of improved performance by the NZ economy over the last decade. In Table 9, the decade with the highest growth rate out of any decade long period in the table was the most recent decade ending in 2000. However, while this period also resulted in New Zealand’s highest growth ranking out of all decade long periods, the rate of growth achieved was still insufficient to register New Zealand in the top half of OECD growth rates.

It should be noted that exactly the same growth rates are obtained when using OECD data from publications such as National Accounts of OECD Countries (OECD, 2002) regardless of whether real GDP per capita is converted into a common currency using exchange rates or PPPs. This is because the OECD converts all the observations in a country’s real GDP per capita series (expressed in the country’s national currency) using the exchange rate or PPP rate for a single year.[23] A transformation that involves either multiplying or dividing all observations in a series by some constant has no impact on the growth rate of the transformed series.

Tables equivalent to Tables 9 and 10 based on the PWT, Maddison and Haugh’s calibrated real GDP data sources are provided in Appendix D. Nuxoll (1994) raises a concern that data construction techniques used in constructing series such as those contained in the PWTs may have inadvertently introduced a spurious correlation between growth rates and income. Nuxoll argues that (based on what he calls the Gerschenkron proposition) any income index using fixed prices to measure growth rates would tend to understate the growth rates for less developed countries and overstate the growth rates for more developed countries relative to the national income accounts.

The PWT draw heavily on the work of the International Comparison Project (ICP). The ICP estimates real expenditure in a large number of countries based on what are termed “international prices”. International prices are constructed using the Geary-Khamis formula for international prices.[24] This results in the international price of a good depending little on the prices in low-income countries, countries with small populations or low or relatively small demand for the good.

The ICP only produces expenditure estimates of real GDP for a few years and consequently to construct the annual series that appear in the PWT, Summers and Heston extrapolate estimates for real consumption, investment, government spending and net foreign balance for a large number of years. These estimates are based on international prices. “The estimates for real consumption, investment, government spending, and net foreign balance were combined with the growth rates for the same series in existing World Bank national-accounts data. This amounts to assuming that these series measured in terms of international prices grow at the same rate as these series measured in domestic prices. The result is a series of estimates for each year, all measured in terms of international dollars.” (Nuxoll, 1994)

Consequently, real total GDP measures from the PWT and national accounts estimates differ because of the price weights used. The PWT use international prices whereas national accounts uses domestic prices. If this results in the share in GDP of consumption, investment, government or net foreign balance differing between the PWT and the national accounts, the growth rates obtained from the different sources will differ.

Nuxoll (1994) notes that international prices are a synthetic set of average prices across countries, so they are not drawn directly from one country. He also states that prices in Hungary are the closest to the international prices used in the ICP and PWTs. Nuxoll’s research ultimately finds that “Current versions of the Penn World Table do not systematically distort the data, because of the very high level of aggregation. Nonetheless, the growth rates in Penn World Tables do differ from national accounts.” (Nuxoll, 1994). Nuxoll goes on to argue that the use of real GDP series measured in domestic prices is more reliable than using series expressed in international prices, because domestic prices characterise the trade-offs faced by people in the country. An awareness of the sorts of problems associated with the use of different price weights is, however, still desirable for empirical work.

6  Conclusion#

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This paper has examined issues associated with measuring economic growth and the international ranking of countries by real GDP per capita. Section 2 illustrated that New Zealand’s international ranking depends to some extent on the data source used. While each data source produced a picture of a falling ranking over time, different data sources do influence the timing of falls and consequently may support different theories as to the major events contributing to such falls.

Section 3 examined the differences between various approaches to measuring the average growth rate over a period. The weighting system underlying growth rates estimated by OLS can lead to results that differ significantly from other techniques. The OLS technique is not appropriate when the log of real GDP per capita series contains a unit root. All the New Zealand series used in this paper contained a unit root, suggesting that the use of the OLS approach is inappropriate when using New Zealand data. At the very least it is important that people disclose the technique used in constructing a growth rate.

Section 4 focused on the impact of different data construction techniques on measured growth rates. It highlighted that knowledge of how data has been constructed is important as data construction can potentially have important implications for the measurement of real GDP and its associated growth rates. Changes in construction techniques over time do hinder the consistency of growth rate measures across time for New Zealand. This is also likely to be the case for most other countries, making international comparisons difficult. Large amounts of effort and resources have been expended in trying to make the construction of GDP measures as consistent as possible across countries. While this effort is extremely valuable, rankings of countries should still be treated with caution. This is particularly so when GDP per capita is being used as a proxy for living standards across countries.

Section 5 illustrated that New Zealand’s average growth rate for a period can be very sensitive to the endpoints used. This needs to be borne in mind when statements are made comparing the average growth rate for one period to another. To be credible, the analysis behind such statements needs to consider whether the comparison changes significantly when relatively minor changes are made to the time periods for which the growth rates are being compared. The tables included in section 5 and the appendices provide an accessible documentation of New Zealand’s historical growth performance as suggested by several different real GDP per capita series.

References#

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Buckle, Robert A., David Haugh, and Peter Thomson (2001) "Calm after the storm?: Supply-side contributions to New Zealand's GDP volatility decline." Treasury Working Paper 01/33.

Easton, Brian (2002) "Of roast pork - Treasury debates the economy." Listener, 9 March 2002.

Geary, R. C. (1958) "A note on the comparison of exchange rates and purchasing power between countries." Journal of the Royal Statistical Society, Series A 121(1): 97-99.

Haugh, David (2001) "Calibration of a chain volume production GDP database." New Zealand Treasury, September.

Kakwani, Nanak (1997) "Growth rates of per-capita income and aggregate welfare: An international comparison." The Review of Economics and Statistics 79(2): 201-211

Khamis, Salem H. (1967) "Some problems relating to the international comparability and fluctuations of production volume indicators." Bulletin of the International Statistics Institute 42(2): 213-230.

Maddison, Angus (2001) “The World Economy, A Millennial Perspective”, OECD Development Centre, Paris.

New Zealand Government (2002) "Growing an innovative New Zealand." http://www.executive.govt.nz/minister/clark/innovate/index.html>

Nuxoll, Daniel A. (1994) "Differences in relative prices and international differences in growth rates." American Economic Review 84: 1423-1436.

OECD (2002) “National Accounts of OECD Countries – Main Aggregates”, OECD, Paris.

Statistics New Zealand (1998) "Chain volume measures in the New Zealand national accounts." Wellington, Statistics New Zealand, October.

Appendix A#

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A.1 Weighting Scheme of the OLS Growth Rate Estimator#

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As explained in Section 3.1 one way of estimating a growth rate is to estimate the model:

 

 

 

The OLS estimator for

 

can be written as:

 

(A.1.1)    

 

 

where

 

and

 

 

Now

 

which implies:

 

(A.1.2)    

 

 

We can therefore rewrite (A.1.1) as:

(A.1.3)    

 

 

by noting that

 

due to (A.1.2) and

 

 

The next step is to note that:

 

 

note that the last term in a bracket cancels with the first term in the following bracket so:

 

 

 

substituting this into (A.1.3) gives:

 

(A.1.4)    

 

 

where

 

, ie a set of weights.

 

Using the definition of

 

we get:

 

(A.1.5)    

 

 

By making use of

 

and

 

it can be shown that:

 

(A.1.6)    

 

where

 

 

Therefore:

(A.1.7)    

 

 

A.2 Obtaining the growth rate estimator in a log-difference model#

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The OLS estimator for the model

 

can be found as follows:

 

(A.2.1)    

 

 

Therefore:

(A.2.2)    

 

 

Differentiating with respect to

 

gives:

 

(A.2.3)    

 

 

Minimisation requires setting (A.2.3) to zero. Therefore:

(A.2.4)    

 

 

Thus:

(A.2.5)    

 

 

and so:

(A.2.6)    

 

 

A.3 The geometric Average Growth Rate#

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Solving the compound growth formula for the growth rate r is one possible way of calculating the average annual growth rate over a period. Outlined below is why this solution for r is known as a geometric average growth rate. We begin with the compound growth rate formula:

(A.3.1)    

 

 

which can be rewritten as:

(A.3.2)    

 

 

This is equivalent to:

(A.3.3)    

 

as

 

 

Note: the numerator in each fraction cancels with the denominator in the following fraction, except at the endpoints.

Therefore by adding and subtracting

 

to the numerator:

 

(A.3.4)    

 

 

so that:

(A.3.5)    

 

 

(A.3.6)    

 

 

A.4 Proof that Log Difference Regression and Geometric Growth Rates are Equal#

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The log difference regression estimate of the growth rate can be found using the following expression:

(A.4.1)    

 

 

now

 

as

 

 

and

 

(by using the rules

 

and

 

). Consequently (A.4.1) can be rewritten as:

 

(A.4.2)    

 

 

which can be simplified further to:

(A.4.3)    

 

 

Noting that

 

and observing that the numerator in each fraction cancels with the denominator in the following fraction, except at the endpoints, we get:

 

(A.4.4)    

 

 

Appendix B – New Zealand real GDP per capita series#

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Appendix C – New Zealand average annual change growth rates from different data sources#

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Appendix D – New Zealand growth rates and growth rate rankings from alternative data sources#

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Possible rankings range from 1 (highest growth rate for the period in the OECD) to 25 (lowest growth rate for the period in the OECD).

* indicates that the growth rate ranking is sufficiently high to be categorised as being in the top half of the OECD.

Appendix D – New Zealand growth rates and growth rate rankings from alternative data sources (continued)#

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Possible rankings range from 1 (highest growth rate for the period in the OECD) to 24 (lowest growth rate for the period in the OECD).

* indicates that the growth rate ranking is sufficiently high to be categorised as being in the top half of the OECD.