Long-Term Trends of Commodity Prices From 1900 to 2011

Abstract

This dissertation aims to check the long-term movements of primary commodity price indexes. The data used in this project is the updated version of the index introduced by Grilli and Yang (1988). This new version covers the period from 1900 to 2011 including four kinds of price with two approaches of algorithm. The regression part applies to two time series model called ARMA and ARIMA models. To ensure the ARIMA models are correctly specified, we employed unit root tests to determine the order of integration of the data. The results suggest that the ARIMA models chosen provide adequate conditional characterisations of the various commodity price indexes. Commodity prices cannot be perfectly forecasted due to the impact of growth and technology.

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Introduction

This dissertation aims to analyse the commodity price indexes for the different periods in the history of worldwide commerce and trade between developed and developing countries. The various periods represent years where those basic commodities were traded and bought for personal and public consumption. The study of commodity price trends demonstrates the flow of supply and demand during those periods which, as this law suggests, affects prices. While the law of supply and demand does not change and remains all throughout the different historical periods, it is also dependent on the way commerce and trade is practiced in those times.

The main focus is on prices of primary commodities from developing countries and manufactured products of developed countries. Quite a number of theories have been studied and related to the PS hypothesis and its effects on economic policies. Some economists provided evidence but these were argued upon by others who noted the gaps in the indexes.

The results of the indexes do not positively show that supply and demand affect the commodity prices; therefore, it is necessary that we examine the indexes that provide evidence for the hypothesis that there is a downward trend in the NBTT despite the fact that the flow and supply of prime commodities is continuous. The downward trend affects economies and economic policies for both developed and developing countries. The factors in the NBTT decline are clearly discussed in the literature.

Evidence from the literature suggests that the distribution of gains from production affected the long-run trends in the NBTT of trading countries, from developing to developed countries, which influenced the distribution of increases from trade between commodity producers in developing countries and consumers in developed countries.

In the data analyses, we explored the price indexes of various economic researchers and international agencies and the declining trend of prices of primary commodities from 1900 to 2011. We paid particular interest to the Grilli and Yang’s (1988) index, which was used in the allocation of growth between producers (the developing countries) and consumers (the industrial countries), although their indexes focused on the period 1900 to 1986. The indexes used had gaps, which point to the two world wars, but were filled up by Grilli and Yang by way of interpolation.

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The renewed interest in the Prebisch-Singer hypothesis is primarily due to two factors. First, Grilli and Yang (1988) introduced new computed commodity price indexes which start from 1900 to 1986. The second factor is that there has been a reassessment of the evidence due to the introduction of new methods in analysing time-series data.

The starting point for Grilli and Yang’s work is their conviction that having high quality price indexes is essential when testing the PS hypothesis. Using their new commodity index, Grilli and Yang re-estimated the time trend model and found a statistically significant long-term decline in the NBTT that supports the Prebisch-Singer hypothesis. According to this hypothesis which came out of independent studies of Rual Prebisch (1950) and Hans Singer (1950), the prices of primary commodities and manufactures have a downward trend over a certain period.

Comparison of the actual and predicted nonfuel commodity terms of trade for the period 1900-96.
Fig. 1 Comparison of the actual and predicted nonfuel commodity terms of trade for the period 1900-96. SOURCE: Lutz (1999).

The PS hypothesis, which predicted the declining trend of commodity terms of trade, is near or almost similar to the actual terms of trade, as shown in figure 1. Grilli and Yang’s (1988) new computation of commodity price indexes triggered the reassessment of the hypothesis evidence.

Over the years, empirical analyses of commodity price trends have proliferated. Few hypotheses in development economics have not attracted as much attention as the PS hypothesis. Spraos (1980) was among those to rekindle academic interest in the empirical validity of the PS hypothesis in the late 1970s.

In an extension of Spraos’ work, Sapsford (1985) found evidence of discontinuous changes in the commodity price data used by Spraos. But Sapsford (1985) found ‘structural instability’ in Spraos’s work, and argued that the latter’s findings were misleading.

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New empirical studies on the PS hypothesis have emerged and so economists continue to debate about it. Cuddington and Urzúa (1999) noted that all these studies appeared to have overlooked the importance of the serial correlation reflected in the price series. The Structural Time Series approach has been proposed by Harvey and others in a number of papers (Harvey and Todd 1983; Franzini and Havey, 1983; Harvey, 1985; Harvey and Durbin, 1986). This approach requires no preliminary assumptions about the properties of the series. Cuddington and Urzúa (1999) re-evaluated the Grilli-Yang index, and focused on the requirement that the error processes in the estimated time trend models be stationary.

Perron (1990) has also examined the (MUV-deflated) Grilli-Yang commodity price index (GYCMPI) for 1900-1983 for the presence of a unit root. Von Hagen (1989) took a different approach from Cuddington and Urzúa (1999). At the same time, the role of commodity prices as foundations of inflation has been referred to significantly and widely in the literature, with many different outcomes.

This dissertation has four parts. The first part explored the literature focusing on the background, concepts and meanings of commodity price indexes in the different periods. The second part lists some information about the data used in this project. The models ARMA and ARIMA comprised the methodology part along with the root tests. The last part is the result of stationarity of each index, fitting model for each index and some forecasts.

The ARMA and ARIMA models appeared in the regression part. An important step was to check the stationarity of the data by applying unit root test. In selecting the appropriate time series model, it is important to correctly capture the time series behaviour of the data. We employed the Akaike and Schwarz information criteria to assist in determining the correct AR and MA lag lengths in our time series models.

The stochastic behaviour of commodity price plays an important role in evaluating commodity-related projects. There are many aspects of commodity price indexes which were analysed, for instance, the variance and skewness, the volatility, the relationship between these indexes with other important economical indexes, and the trend of these indexes during the time periods of commerce and trade. The commodity price index tells us the price elasticity of the various commodities in the different periods, ranging from food to basic needs to raw materials for product manufacturing, etc.

Knowledge of commodity prices and analysing indexes help policy makers institute policies to pre-empt crises and deal with economic crises. Ordinary citizens should also learn to understand commodity price indexes as these are connected with daily life.

Literature review

Rual Prebisch (1950) and Hans Singer (1950) have independently claimed that several factors would combine to construct a worldly decline in the relevant primary commodity prices in terms of manufactured goods. This has been popularly known as the PS hypothesis, the subject of several empirical researches, and has influenced economic policies of developed and developing countries. The policies aimed to differentiate their productive constructions and export bases away from primary commodities towards manufactured goods, thereby evading the terms of trade deterioration Prebisch and Singer (1950) warned about. The factors in the commodities price decline are discussed in the data and methodology sections.

Over the years, researchers have provided empirical analyses of commodity price trend based on the PS hypothesis, but many hypotheses in expansion economics have not drawn as much attention as the PS hypothesis. Most of the empirical arguments about the PS hypothesis have concentrated on the non-stationarity of real commodity prices, which take the form of a non-random trend, a stochastic trend, or with the structural jumps in the trend. The original empirical surveys of Prebisch and the United Nations (1949) reinforced the theory. The evidence collected during the 1950s, 1960s, and 1970s, which has indicated continual upgrading in the quality of available commodity and manufacturing price indexes and more complex econometric techniques have been mingled. John Spraos (1980), Grilli and Yang (1988), Cuddington and Urzúa (1999), and D. Sapsford (1995) have investigated, made their own analyses of the deteriorating trend from the indexes of international agencies, and provided conclusions, albeit, mostly depended on the PS hypothesis.

Spraos (1980) critique of the P-S hypothesis

At the start of his analysis, Spraos (1980) made an intriguing contention about the Prebisch-Singer hypothesis: that economist Prebisch (1950) lacked statistics (or there were gaps in the index) that forced him to depend on index of a particular country, Britain. The prices of traded commodities did not distinguish where the products originated. This is his first contention, only to retract later and then support the theory that there is really such a trend but with exaggerated statistics from Prebisch.

Spraos (1980) argues that Prebisch (1950 as cited in Spraos) only depended on the statistical data of the United Kingdom, and from this he cut two overlapping indexes to cover the periods 1876 to 1880 and 1946 to 1947, showing data improvement for Britain. The Spraos (1980) evidence states that since Britain, a major product manufacturer at that time, was showing “secular improvement” the trend reflected a world-wide NBTT decline. The hypothesis has been greatly criticised because of the gaps in the series. Prebisch argued that his data came from the UN (1949), which proved that his data was not original (Spraos 1980).

Spraos (1980) enumerates four major arguments against Prebisch’s (1950) hypothesis:

  1. The NBTT data for the United Kingdom could not be translated as those from the industrialised world; thus, the opposite could not be considered representative of the terms of trade of primary commodities (Spraos 1980);
  2. Developed countries also produced and exported primary products for industrialised countries, not only those coming from developing countries (Meier & Baldwin 1957; Meier 1958; Van Meerhaeghe 1969; Frank 1976 cited in Spraos, 1980).
  3. The rise in the United Kingdom’s NBTT could be attributed to reduction in transport expenses and not to the decline in the prices by primary producers since exports were valued or priced based on prices quoted for delivery in London, Liverpool (Viner 1953; Baldwin 1955; Ellsworth 1956; Meier & Baldwin 1957; Meier 1958, 1963 as cited in Spraos, 1980).
  4. New manufactured products were exported while the existing ones were upgraded, but these were not clearly stated in the price index of manufactures, which provided an upward bias that vaguely created the impression that NBTT of primary products was declining (Viner 1953; Baldwin 1955, 1966; Ellsworth 1956; Meier & Baldwin 1957 as cited in Spraos, 1980).

Relying on these data, Spraos (1980) argues that while the deteriorating trend can be seen, it is not as large as suggested by the Prebisch’s (1950) series. He further contends that the evidence contrary to the PS hypothesis can be seen on the 1870 to 1938 data, but the declining trend is more doubtful when the period is extended forward. Moreover, index numbers formulated many years back have “conceptual problem errors of measurement” (Spraos 1980, p. 109). The question is whether the available series can plausibly represent for the questionable NBTT or can clarify the plausible conclusions derived from those representations.

Spraos (1980) then provides regressions aimed at testing whether such a trend is reflected in the data and thus support the assumptions acquired by visual analysis of the time series. The analysis is not to provide explanation over the long-term movement of the terms of trade (given that it could produce high R2s), not even to acquire ‘efficient predictors’, nor ‘to seek the best fit on time’ (Spraos 1980, p. 109). He then makes a semi-loglinear regression to show a measure of trend, given that the coefficient of t provides the ‘average rate of change of the regression per unit time given implicitly in the data and the symbol of coefficient clearly tests the hypothesis of deterioration’ (Spraos 1980, p. 109).

Spraos (1980) then investigates Britain’s representative NBTT for industrialised countries. Some reliable author-economists, like Martin and Thackery (1948 as cited in Spraos) and Kindleberger (1956 as cited in Spraos), also investigated the combined NBTT of industrialised countries and reported that there was no significant trend in their NBTT up to World War II. During the same period, there was no significant trend reported for the US NBTT and for industrial Europe with respect to imported primary products and exported manufactures.

Spraos (1980) produces a table, representing the League of Nations series, which has a compilation of world trade data. The purpose of this table and analysis is to examine whether Prebisch (1950 as cited in Spraos, 1980) gravely misled himself and the economic world by not using an accurate evidence for his hypothesis. By using log regressions of the series on t, the Prebisch series provides ‘an annual rate of change of the relative price of primary products’ which is –0.9 percent, and the League series is –0.6 percent. The analysis presents evidence that there is an exaggeration in Prebisch’s data but this is also present in the League’s series.

According to Spraos (1980, p. 253), Lewis (1952) improved the League’s data by adding ‘the prices of imports and exports of manufactures of the United States and in other ways’. The League’s series shows robustness, and the UN Secretariat added conceptual homogeneity. Based on the data collected by Spraos (1980), Britain’s NBTT as basis for relative price of primary products with respect to manufactures in world-wide trade ‘was not misleading as to direction though it gave an exaggerated impression of the magnitude of deterioration’ (Spraos 1980, p. 113). Britain, which was the leading world trade country at that time, had a large and improved NBTT (Spraos 1980).

Spraos (1980) has made thorough analyses of the deteriorating trend for the 70 years up to World War II and provided a conclusion that indeed there was evidence of the trend in the relative price of primary products. However, there are reservations pointing to the quality of the evidence, although the finality of the conclusion is reached when he examined one by one the main points taken in questioning the inference of the deteriorating trend. He, however, discovered that Prebisch (1950) exaggerated the rate of deterioration – ‘at worse by a factor of more than three’ (Spraos 1980, p.126).

The Grilli and Yang (1988) index

Grilli and Yang (1988) focus on long-term run of prices of primary commodities, and their index has become one of the most sought-after sources on the subject. Their main concern is to analyse the price movements but not to provide economic explanations over this phenomenon. They start with their initial finding that having high quality price indexes is necessary when testing the PS hypothesis. The authors provide data on the prices of nonfuel commodities. They compare the statistical properties between the movements in those commodities and the manufactured products. After this examination, the author-economists further investigate the potential consequence of development on the commodity prices.

Grilli and Yang (1988) modified the United Nations Index in what became known as MUVUN (Manufactured Unit Values, United Nations) based on the Economist Index (EI) and the Lewis Index (WALIl), then used this to analyse 24 nonfuel product prices. They used the 1977-1979 data as weights. The new index – the GYCPI – tells of the movements in different periods of primary commodities. The index filled the two gaps (1914 to 1920 and 1939 to 1947) in the price index by way of their adopted strategy of ‘interpolation,’ utilising product values of the United States and the United Kingdom during the period, as indicators.

Grilli and Yang further re-estimated the time trend model using their new commodity index and found a statistically significant long-term deterioration in the NBTT. Their econometric analysis focused on the likelihood of first-order serial correlation and structural breaks, noting that ‘examination of the residuals of the semi-log time regressions, as well as a priori knowledge of the exogenous factors that may have caused a structural break in the price series, indicated the possibility of breaks at three points in time: 1921, 1932 and 1945’ (Grilli & Yang 1988, p. 10). At this time, we can conclude that the modified index (MUV) is more reliable as Grilli and Yang filled the gaps to provide a complete data for the 1900-1986 deteriorating trend of the NBTT of primary commodities and manufactures between developing and developed countries.

The researchers also developed another index of domestic prices of products made in the United States (example: energy, timber, and metal), as they wanted to avoid the overlapping of goods in the indexes. The index is used to provide a concept of the connection between ‘prices and unit values of exports’ of the different periods and of the logic of the results taken from the interpolation they have created to fill the gaps (Grilli & Yang 1988, p. 5). The two indexes now provide a relative trend growth for the period (1900 to 1986), equivalent to 2.49 percent annually for the MUV (this is shown in figure 1). The USMPI has exhibited 2.48 percent a year. However, the authors argue that the MUV is a bit erratic compared to the USMPI. The MUV has a ‘percentage deviation from trend’ of 6.2 percent for the 1900 to 1986 period, while the USMPI only got 5.1 percent. (Grilli & Yang 1988, p. 5)

 Comparison of the indexes of manufactured goods prices for MUV and USMPI, 1900 to 1986.
Figure 2 Comparison of the indexes of manufactured goods prices for MUV and USMPI, 1900 to 1986. SOURCE: Grilli and Yang (1988).

The two indexes were taken to calculate two collections of relative prices of primary commodities (nonfuel). The first set of commodity prices calculates the beginnings of the purchasing power of those primary commodities which were traded domestically; thus, their prices were also domestic.

Cuddington and Urzúa’s (1999) critique

Cuddington and Urzúa (1999) examined the NBTT downward trend and the Grilli and Yang (1988) index. The authors applied the “time series methods” and discussed the cyclical characteristics of commodity prices using the Beveridge and Nelson (1981) technique. The interest in the cyclical movements in commodity prices is founded on the principle that in policy making the scope, length, and form of the cycles are as important as the current long-term trend.

In examining the NBTT downward trend, Cuddington and Urzua (1999) used the Grilli-Yang commodity price index (GYCPI) which, as mentioned earlier, explored 24 non-fuel commodities as weights and built a new index due to the gaps in the series, as discussed earlier. The GYCPI provided a picture of the significant drop in the NBTT and the other commodity prices examined by their index. Thirlwall and Bergevin (1985) also noticed the drop when they used the United Nations data from 1954 to 1982. Cuddington and Urzúa (199) found the advantage and relevance of Grilli and Yang’s (1988) index as all the other studies ignored the relevance of the serial correlation shown in the price movements.

Moreover, Cuddington and Urzúa (1999) found that the GYCPI was the most logical to use because the other used indexes – the World Bank, UNCTAD and IMF – lacked data as they applied only the periods after the war. On the other hand, the Economist Index (EI) had also been applied with several revisions and its weights are founded on the relevant trade of industrial countries instead of the worldwide import weights. The GYCPI used an annual index of manufactured goods unit values, also called MUV-GY. This series matches with the index of unit values computed by the equivalent United Nations manufactured goods unit values, or MUV-UN, which had gaps. Grilli and Yang filled the gaps through interpolation.

The NBTT sequence taken through deflation of GYCPI by MUV-GY produces the index of real commodity prices used by Cuddington and Urzúa (1999). The series is denoted y(t) in Cuddington and Urzúa’s analysis and considered as good as the others, but they noted that the MUV-GY does not have power on possible changes in the quality of either manufactured goods or primary commodities. This is one of the problems noted in the literature, where quality changes cannot be taken into account in the measures of real commodity prices. Cuddington and Urzúa (1999) have cited Grilli and Yang’s (1988) remarks on the possibility of an “upward bias” borne by manufactured goods prices as they integrate the advantages of technological development that might have improved the goods’ quality (Cuddington & Urzúa, 1999).

All the other studies, excluding Grilli and Yang’s (1988), failed to provide statistical details of the univariate illustrations of the price movements that represented the different years. In other words, all those suppositions had regression difficulties.

Cuddington and Urzúa (1989) considered the price movements as nonstationary. In their analysis of GYCPI, they rebuffed the doctrine of determinism and supported the stochastic trend model using the test methods of Dickey and Fuller (1979), along with the method of Perron (1988). Here, Cuddington and Urzúa (1999) concluded that there was no deterioration in the NBTT for the period from 1900 to 1983. When they focused on the statistical problems caused by non-stationary, they reached a conclusion that there was no significant secular deterioration in the relevant commodity prices. They supported the Grilli and Yang finding that the significant deterioration in commodity prices vanished when the latter considered the TS specification and the large break in the data after 1920 (Cuddington & Urzúa 1989, p. 441). In their examination of the residuals from simple TS and DS models, they concluded that there was a gap in the Grilli-Yang index after 1920, in which Grilli and Yang explained that the data breaks referred to ‘exogenous’ events. The sharp drop in prices after World War II explains the adjustment in commodity supplies and demands following the war. They also quoted Friedman and Schwartz’s theory in the belt-tightening policies of the Federal Reserve in 1920. The literature provides statements that in real terms, commodity prices exhibit invisible or definitely dropping movements, but there are indications of long term drops. Deaton (1999) argues that although the trend is erratic, we also see variance.

Cuddington and Urzúa (1999) concluded that the Prebisch-Singer hypothesis should be applied with changes: that primary commodity prices relative to manufactures had a sharp drop after 1920. It is a one-time drop and there is no continuing downward trend in the prices of primary goods. According to Cuddington & Urzúa (1999, p. 441), it is inappropriate to describe the movement of real primary commodity prices since the turn of the century as one of ‘secular deterioration’. But, indeed, Cuddington and Urzúa recognized that there is a downward trend which supports the other studies, although the disagreement is on the period the trend stopped.

One worrying feature of the Cuddington-Urzúa (1999) paper is their ad hoc methodology for separating structural breaks. It was Cuddington and Urzúa’s examination of the residuals from simple TS and DS specifications that led them to the result that there was a gap in the Grilli-Yang index after 1920. This “data snooping” might not be good because it leads us to choose a point with a high Chow-test value. To be strict, Perron’s statistical test for unit roots in the presence of a shift in the mean needs that the event be exogenous which ensures it is no problem to take it out of the stochastic process when generating the data.

Cuddington and Urzúa (1989, p. 429-430) admitted that ‘in light of its critical importance in our findings below, this sharp drop in prices cries out for some explanation… Presumably, it reflects the adjustment in commodity supplies and demands following the end of the First World War.’ They went on to paraphrase Friedman and Schwartz’s discussion of the belated tightening in Federal Reserve policy in 1920. Unfortunately, the conclusion regarding the trend in commodity prices seems to hinge critically on whatever the break is taken into consideration in the time series analysis.

The DS and TS models

The TS model suggests that ‘all price fluctuations around the deterministic trend line (which has a zero slope here) should be viewed as cyclical; the deterministic trend reflects changes in the permanent component of prices’ (Cuddington & Urzúa 1999, p. 438). The DS model provides a ‘decomposition of price innovations into permanent and cyclical components, with the former being stochastic rather than deterministic’.

Sapsford (1985) evidence

Sapsford (1985) criticised Spraos’s (1980) analysis and conclusion of the PS hypothesis regarding NBTT declining trend. Sapsford’s analysis also supports the PS hypothesis, but at the same time, he criticises Sprao’s methodology as having statistical problem. Sapsford’s (1995) methodology drew a simple trend model from the methodology used by Spraos:

NBTTt = a + rt + ut (t = I, …, n)

By using regression methods, Sapsford (1985, p. 782) provides the ‘long-run trend of growth in the NBTT’. He is critical of Spraos’s support of the PS thesis for the pre-World War II period which was acquired by using fitting model (I) by means of the ordinary least-squares (OLS) to two of the series, the United Nations series, which included the 1950 to 1970 period, and the World Bank index (post 1950 period). Sapsford criticised Spraos’s method of trend analysis and estimation, saying that it is only applicable on the premise that the primary constraints of the NBTT’s growth direction remain unchanged during the analysis of the index (Sapsford 1985, p. 782).

Sapsford (1985) found evidence of discontinuous changes in the Spraos’s commodity price data. He observed the structural instability and allowed ‘intercept and slop dummies in 1950,’ allowing him to conclude that there was evidence supporting the PS hypothesis for the pre- and post-World War II periods.

In his study of Spraos’s (1980) analysis, Sapsford took note of the equations provided in a table stating the Cochrane-Orcutt (C-O) counterparts and Spraos’s regressions. The OLS or the C-O equations, made to provide the structural instability in the growth during the pre and postwar periods, results from the data provided by Spraos which created the 1900 to 1970 negative and significant growth rate which supports the PS hypothesis. (Sapsford 1985, p. 783)

Table 1 shows Spraos’s regression analysis. Absolute t values are presented in the figures in parentheses; the single asterisk represents the ‘coefficient which is significantly different from zero at the 5 percent level’. NBTT1 represents the UN series, which is updated to 1980 with data taken from the United Nations Statistical Yearbook (1981 as cited in Sapsford, 1985). The results of the Spraos series support the P-S hypothesis: there is an upward trend before the war and a downward trend after the war, which shows a similar trend during the 1900 period up to the outbreak of the Second World War. However, Sapsford (1985) notices that the UN results provide a different trend. The equation does not show significant alteration in the intercept term but an upward trend after the war. The upward movement also shows that it cannot change the negative trend. The equation further shows that ‘the restriction that the trend growth rate in the UN series and the coefficient of D8 sum to zero in (I.12) is rejected at the 1% level on the usual t test’ (Sapsford 1985, p. 786), which creates evidence to support the PS hypothesis. This further provides a negative trend for both the pre- and post-war periods.

In the final analysis on Spraos’s series, Sapsford (1985) concludes that there is ‘structural instability problems’ in Spraos’s analysis when he provided a re-estimation of Spraos’s own equations from the data provided which showed that there was ‘trendlessness for the period 1900-70’ (Sapsford 1985, p. 787). Although Sapsford recognises his limitations with respect to his analysis and that of Spraos, he continues to conclude that ‘Spraos’s earlier findings were misleading’ (Sapsford 1985, p. 787).

Spraos’s regression analysis of long-run trend in NBTT.
Table 1. Spraos’s regression analysis of long-run trend in NBTT. SOURCE: Sapsford (1985, p. 784).

Data

Grilli and Yang (1988) explored the 24 non-fuel price indexes and the modified index, because they wanted to provide a complete index that would not only examine the post-World War II period but also the periods before the war. The World Bank index started with the 1948 period and beyond while the United Nations index had gaps.

Since it is unfeasible to create a new price index of manufactures that date back from 1900, they used a modified form of the MUVUN (Manufactured Unit Values, United Nations), which they constructed by interpolation to satisfy the continuity, taking both import and export unit value of manufactured goods of the United States and the United Kingdom as indicators. The authors achieved the interpolation by taking average values of the sub-indexes and by using the estimated equation to generalise the values of the MUV index. For the period from 1915 to 1920, the researchers succeeded in conducting interpolation by first order regression of the MUV index with the import and export unit values of manufactures indexes of the United States and the United Kingdom.

Some variable weights reflected the relative significance of the various types of manufactures in international trade. The GYCPI is often referred to and discussed by economic researchers. Additionally, Grilli and Yang (1988) built sub-indexes for agricultural food commodities (GYCPIF), non-food agricultural commodities (GYCPINF), and metals (GYCPIM). The value of the weights relies on each product’s standard price for the period. These data have been used in many different situations in later researches (Bleaney & Greenaway 2001; Kimet et al. 2003).

Important sources used by Pfanffenzeller, Newbold and Rayner (2007) provide more information on the commodity price data, such as the World Bank Development Prospects Group’s CPI, the IMF price tables, and the OECD database. Most of these data can be retrieved through the respective organisations’ websites. Grilli and Yang (1988) have to combine one or two indexes because of the incompleteness of the data. This creates some problems, and a challenge to the researchers, because finding a perfect match in the data is really difficult to do. The GYCPI is displayed in Figure 2.

The GYCPI 1900-2010.
Figure 3. The GYCPI 1900-2010. SOURCE: Grilli & Yang (1988).

Stephan Pfaffenzeller, Paul Newbold, and Anthony Rayner (2007) maintain that the composite index defined by Grilli and Yang (1988) is computed as a weighted average of the commodity prices, which is:

Data

where n=24, ais ‘the appropriate commodity weight,’ and Pi,t is the price of commodity in period t, catalogued to 1977-1979 mean. Cuddington and Wei (1992) suggested that it may be better to use a geometric aggregation to define the index which is expressed as:

GPI

Cuddington and Wei (1992) discussed the specific features of this alternative index in details. ‘Manufacturing unit value index’, referred to in Cuddington and Wei (1992), is taken to reinforce the GYCPI, now termed MUV-G5 index. It is an index for the G5 countries that it is also used by the World Bank, but regarded as unsuitable measure for imports of developing countries, although it is assumed that it can be used as index for imports of developing countries. The MUV is used to measure manufactured products. This is referred to in the MUV 15 index, or the 15 countries.

The indexes are the equivalent to the total of each country’s exports, and the parts are calculated using the SITC tool for exports. In the manufacturing sector, Grilli and Yang (1988) used the OECD Producer Price Index (PPI). The respective countries’ relative weights have different percentages, as shown in table 1.

Table 1. The 15 countries with relative weights comprising the MUV 15.
Country Relative weight (%)
Brazil 2.95
Canada 0.93
China 11.79
France 5.87
Germany 13.29
India 1.77
Italy 6.07
Japan 16.70
Mexico 0.93
South Africa 0.75
Spain 2.30
Thailand 2.51
United Kingdom 3.50
United States 19.68

The MUV5, representing France, Germany, Japan, the United States and the United Kingdom, has another set of data. The World Bank maintains that the time horizon and frequency used in predicting the MUV (15) are the same with the data used in the commodity price prediction.

The MUV 1900 – 2010. 
Figure 4. The MUV 1900 – 2010. SOURCE: Grilli & Yang (1988).

The MUV receives regular updates so that the data coincide with the Global Economic Prospects and other predictions. The World Bank, through its agency the Development Prospects Group, also provides updates. Grilli and Yang (1988) regularly use the 1977-1979 averaging value with 1990 as base year.

Nonfuel commodity prices have lagged behind even during the early 1900s compared to those of manufactures in the United States and the rest of manufactured products coming from industrial countries. These are considered, or noted, in the BYCPI and USMPI series as these showed a negative exponential trend of 0.57 percent a year over the 1900 to 1986 period. On the other hand, the GYCPI and MUV series exhibits a trend decline of 0.59 percent a year over the same period. This is shown in the figure below.

the aggregate trends in the relative prices of primary commodities, 1900-86.
Table 2 shows the aggregate trends in the relative prices of primary commodities, 1900-86. SOURCE: Grilli and Yang (1988).

The GYCPI shows that the purchasing power of nonfuel primary commodities in terms of manufactures dropped since 1900 at an annual rate of 0.63 percent to 0.67 percent when the situation arises that the USMPI or MUV is made to gauge the manufactured goods prices. In including the fuel prices in the index with the use of the GYCPI, the decline fell to 0.52 percent annually. The prices of primary commodities and nonfuel commodities dropped on trend since the period 1900 to 1986.

In checking for the stability of the estimated time coefficients of Grilli and Yang’s (1988) indexes (GYCPI/MUV and GYCPI’’’/MUV regressions), they tested for ‘the possibility of a change in slope’ through regression used by Suits, Mason and Chan (1978 as cited in Grilli and Yang, 1988, p. 10), in order to approximate the time trend of the indexes. Grilli and Yang found ‘no clear break’ that occurred since the 1900 period. World War I made a mark on the cyclical instability in commodity prices which showed in the first forty years covered by the Grilli and Yang series.

Grilli and Yang (1988) also computed the trends in the prices of the three categories of primary commodities relative to those of manufactures, such as for food (GYCPIF), non-food agricultural raw material prices (GYCPINF), and metal (GYCIPIM). They found that the decline in the relative prices was not uniform. The long-term decline showed in the metal and non-food agricultural product prices. In other words, not all producers of nonfuel primary commodities did feel the relative prices fall ‘in the purchasing power of a given volume of their products over the past eighty-six years’ (Grilli & Yang 1988, p. 11).

The commodity price indexes that include the Grilli and Yang (1988), the MUV, GYCPIM are incorporated in a long table shown in Appendix 1.

Methodology

The aim of the research is to investigate the long-term behavior of commodity prices. In order to achieve this aim, several time series analysis models were used.

Unit Root Test

Two characteristics of ‘economic time series’ are known as ‘trending behavior and non-stationarity’ (Grilli & Yang 1988). These two also influence financial time series.

Any inference based on a misspecified model may be misleading unless the model is correctly specified. A necessary first is to determine the order of integration of the data, which may be achieved using a unit root test. Moreover, it will also assure appropriateness of model chosen to make more accurate predictions. Among numerous methods to test unit root, there is a well-known one which is called augmented Dickey-Fuller (ADF) test, popular to be used in more complicated models for time series. The procedures are introduced in the following part. Assume autoregressive model about time series yas below:

(XX)

Unit Root Test

where α is the drift, β is the coefficient associated with the linear deterministic trend and is the lag order.

The augmented Dickey–Fuller test is on the basis of statistic related with the significance of negative coefficient γ. The null hypothesis is that the data in question has a unit root. This may be expressed as:

H0: gamma = 0 in equation no. (XX)

The alternative hypothesis is expressed as:

H1: gamma < 1 in equation no. (XX).

The ADF test is calculated using:

(XX1)

The ADF test

In (XX1) gamma hat and SE (gamma hat are obtained from OLS estimation of equation (XX).

DFτ is smaller than the critical value related at a given confidence level, null hypothesis gamma = 0 will be rejected, implying that there is no evidence of a unit root in the data of interest. In addition, before calculating DF statistics, lag order should also be determined. If the lag order k is incorrectly specified for equation (XX) then inference about the presence of a unit root based on tests constructed as (XX1) may be invalid.

The delta coefficients in (XX) have to be correctly determined. One approach is to begin with a high order for k and to test down until the kth lag coefficient is significant. However, most serious disadvantage is that higher lag order seems to be preferable by this method without considering appropriateness and complexity of the model.

Therefore, there is also another feasible approach to measure relative quality of model with certain lag order by trading off complexity and goodness of the model, such as Akaike information criterion (AIC) or Bayesian information criterion (BIC). In this project, Akaike information criterion (AIC) will be applied to estimate lag order k, which can be represented by the following equation:

(XX2)

Unit Root Test

where is lag order and is maximized likelihood of statistical model. It can be seen that AIC offers a relative estimate of complexity increase by lag orderand information lost by likelihood L, which provides the assumption that AIC is more appropriate.

In addition, EViews has been chosen as the statistic software for this project. EViews can easily give the result whether the data has unit root. If the data rejects the null hypothesis, it means the data does not have a unit root. If EViews accepts the null hypothesis, it indicates that the data itself is nonstationary. When the data does not have this property, we can also test if its first order difference has stationarity. Once we have the result about the stationarity of the data, we can do the regression model. For the stationary data we will apply ARMA model, and ARIMA model will be used for the nonstationary data.

ARMA model

ARMA is acronym for autoregressive moving average model, which was first defined by Peter (1952) to aid in mathematical analysis, particularly econometrics. Hannan and Deistler (1988) also gave their expertise, using the Box-Jenkins method. ARMA can be used to describe a stationary time series, and to predict future values, using a time series of two parts, ‘the autoregressive and the moving average’ (Grilli & Yang 1988). This is represented in the symbol AR(p) , and calculated using the formula:

ARMA model

The formula has the following representations:

ARMA model

as coefficients, can be considered constant, while εrepresents the random variable. Considering moving-average model, the one with order q, noted by MA(q), can be written as:

ARMA model

where

ARMA model

are white noise error terms,

ARMA model

are the corresponding coefficients of error terms and μ is drift part.

RMA(p, q), has the following equation.

ARMA model

Equivalently, ARMA model can also be specified by lag operator L. By these simplifying notations, the alternative AR(p) model is given by

ARMA model

and the alternative MA(q) model is given by

ARMA model

Thus, Box and Reinsel (1994) used a different method to estimate ARMA coefficients that allows ARMA to be similar expression as polynomial. Thus the ARMA(p,q) model could be expressed in

ARMA model

When suitable values of and are estimated, generally, ARMA models can be fitted by least squares regression to estimated coefficients in ARMA. ARMA and must have an appropriate data which can be taken from autocorrelation functions. AIC can be used to finding and as recommended by Brockwell & Davis (2009).

ARIMA

ARIMA is acronym for ‘autoregressive integrated moving average,’ considered an additional tool for ARMA. The difference between these two similar models is that ARIMA model is employed in some situations when data do not show stationary property, while an initial differencing method can be used to eliminate the nonstationarity. This is also referred to as ARIMA(p,d,q) model, wherein represents the autoregressive order; for the integrated order; and for the ‘moving average order’ of ARIMA. ARIMA models come from the general ARMA model which is expressed in the following formula:

ARIMA

where indicates the lag operator, the mi are the autoregressive parameters of the model, the nare the parameters appearing in the moving average part and the εi  denote error terms. The term εis considered a random and independent variable, taken from a ‘normal distribution’.

Assume now that the polynomial

the polynomial has a unitary root of multiplicity which means that it can be rewritten as:

the polynomial

Doing the change of parameters with p = p’ – d will lead an ARIMA(p,d,q) model to such a formula:

ARIMA

Results

The stationarity of the data

The stationarity of GYCPI/MUV for the period 1900 – 1986

The result for examining the stationarity of GYCPI/MUV is illustrated in table 2. From this table, EViews gives the probability 0.1125 and t-statistic value for Augmented Dickey-Fuller test statistic with -3.095835 which is larger than 10% level. This indicates that there is no significance evidence against the null hypothesis of a unit root. This evidence suggests that there is a unit root in the level of GYCPI/MUV series.

Given the apparent unit root in the level of GYCPI/MUV, we will look at its first difference, denoted as D(GYCPI/MUV). Table 3 shows the result of checking stationarity of D(GYCPI/MUV). This evidence suggests that there is no unit root in the first difference of GYCPI/MUV series. This is consistent with the view that this series is I(1).

The stationarity of GYCPICW/MUV

The GYCPI/MUV and GYCPICW/MUV 1900-2010
Figure 5. The GYCPI/MUV and GYCPICW/MUV 1900-2010.

The result in examining the stationarity of GYCPICW/MUV is illustrated in table 6. From this table we can see EViews gives the probability 0.2128 and t-statistic value for Augmented Dickey-Fuller test statistic with -2.766571 which is larger than 10% level. There is no evidence against the null of a unit root in GYCPICW/MUV. The evidence is consistent with the view that the data are non-stationary.

Again, given the apparent unit root in the level of GYCPICW/MUV, we will look at its first difference, denoted as D(GYCPICW/MUV). Table 7 shows the result of checking stationarity of D(GYCPICW/MUV). The evidence suggests that there is no unit root in the first difference of GYCPICW/MUV. This is consistent with the view that this series is I(1).

The stationarity of GYCPIM/MUV

The GYCPIM and GYCPIMCW/MUV 1900-2010.
Figure 6. The GYCPIM and GYCPIMCW/MUV 1900-2010.

The result for examining the stationarity of GYCPIM/MUV is shown in the table 10. From this table we can see EViews gives the probability 0.4088 and t-statistic value for Augmented Dickey-Fuller test statistic with -2.339955 which is larger than 10% level. There is no evidence against the null of a unit root in GYCPIM/MUV. The evidence is consistent with the view that the data are non stationary.

Given the evidence of a unit root in the level of GYCPIM/MUV, we will look at its first difference, denoted as D(GYCPIM/MUV). Table 11 shows the result of checking stationarity of D(GYCPIM/MUV). The evidence suggests that there is no unit root in the first difference of GYCPIM/MUV. This is consistent with the view that this series is I(1).

The stationarity of GYCPIMCW/MUV

The result for examining the stationarity of GYCPIMCW/MUV is shown in table 14. EViews gives the probability 0.1549 and t-statistic value for Augmented Dickey-Fuller test statistic with – 2.937905 which is larger than 10% level. There is no evidence against the null of a unit root in GYCPIMCW/MUV. The evidence is consistent with the view that the data are non-stationary.

The evidence suggests that there is a unit root in the level of GYCPIMCW/MUV. If there is no evidence of a unit root in the first difference of the series this would be consistent with the view that this series is I(1). Table 15 shows the result of checking stationarity of D(GYCPIMCW/MUV). The evidence suggests that there is no unit root in the first difference of GYCPIMCW/MUV. This is consistent with the view that this series is I(1).

The stationarity of GYCPINF/MUV

The result for examining the stationarity of GYCPINF/MUV is shown in the table 18. From this table, EViews gives the probability 0.0370 and t-statistic value for Augmented Dickey-Fuller test statistic with -3.571039 which is less than 5% level. There is no evidence of a unit root in the level of GYCPINF/MUV.

The stationarity of GYCPINFCW/MUV

The result for examining the stationarity of GYCPINFCW/MUV is shown in the table 21. From this table we can see EViews gives the probability 0.0214 and t-statistic value for Augmented Dickey-Fuller test statistic with -3.777520 which is less than 5% level. There is no evidence of a unit root in the level of GYCPINFCW/MUV.

GYCPINF and GYCPINFCW/MUV 1900-2010.
Figure 7. GYCPINF and GYCPINFCW/MUV 1900-2010.

The stationarity of GYCPIF/MUV

The result for examining the stationarity of GYCPIF/MUV is shown in the table 24. From this table we can see EViews gives the probability 0.0151 and t-statistic value for Augmented Dickey-Fuller test statistic with -3.901358 which is less than 5% level. There is no evidence of a unit root in the level of GYCPIF/MUV.

The GYCPIF and GYCPIFCW/MUV 1900-2010.
Figure 8. The GYCPIF and GYCPIFCW/MUV 1900-2010.

The stationarity of GYCPIFCW/MUV

The result for examining the stationarity of GYCPIFCW/MUV is shown in table 27. The result of 0.1211 can be taken from EViews and t-statistic value for Augmented Dickey-Fuller test statistic with -3.060341 which is a bit larger than 10% level. There is no evidence against the null of a unit root in GYCPIFCW/MUV. The evidence is consistent with the view that the data are non stationary.

Given the evidence of a unit root in the level of GYCPIFCW/MUV, we have to look at its first difference, denoted as D(GYCPIFCW/MUV). Table 28 shows the result of checking stationarity of D(GYCPIFCW/MUV). The evidence suggests that there is no unit root in the first difference of GYCPIFCW/MUV. This is consistent with the view that this series is I(1).

It is accepted among the storage model theorists that agricultural prices should be stationary. With an i.i.d. supply and a deterministic demand function, the storage model seeks to show how commodity storage induces price auto-correlation. Actually, under Prebish-Singer hypothesis, there exist some literatures having focused on stationarity of price. The primary reason why this phenomenon happened was the low income elasticity of commodity demand and the high prices caused by manufacturers’ market power. Policy also has effects on the price stationarity. It should be emphasized that there is obvious randomness regarding the existence of trends in agricultural commodities. Moreover, trends do not seem to sustain for very long time given the assumption of existence of trends. Since it is unknown that whether prices have trend, and whether price shocks are consistent, one reasonable solution at the level of producer and national may be extending commodity production, and this would probably diminish the risks connected with the existence of shocks and price volatility.

The regression

To get the regression model for each index, we should check the values of all the parameters first. For those indexes with stationary property, ARMA will be used for regression and for those indexes without stationary property, ARIMA will be implied. ARMA model needs two parameters p and q to be determined and ARIMA model needs three parameters p, d and q to be determined. There are some criteria which can be chosen to determine the parameter values. The Akaike information criterion (AIC) (Akaike, 1974) and Schwarz information criterion (SIC) (Schwarz, 1978) are two objective measurements to check the goodness of fitting for a model which takes those considerations into account. The order consistent of a criterionis described to be the criterion is minimized at the true order with a probability which approaches agreement as the sample size increases. The AIC procedure has however been criticized because of the inconsistence and tends over fitting models. Shibata (1976) demonstrated this for autoregressive models, Geweke and Meese (1981) for regression models, and Hannan (1982) for ARMA model.

The ARIMA model of GYCPI/MUV

The result of choosing parameters of ARIMA for GYCPI/MUV is shown in the table 4. The least AIC appears in ARIMA(1,1,1) with value 7.81. Table 5 gives the regression result for GYCPI/MUV. As we can see, the probabilities of C, AR(1) and MA(1) are all below 5%. This result means this ARIMA(1,1,1) fits GYCPI/MUV very well. Denotes GYCPI/MUV as ‘C’, then we have the following regression formula:

The ARIMA model of GYCPI/MUV

The ARIMA model of GYCPICW/MUV

The result of choosing parameters of ARIMA for GYCPICW/MUV is shown in the table 8. The least AIC appears in ARIMA(1,2,2) with value 7.09. Table 9 gives the regression result for GYCPICW/MUV. As we can see, the probabilities of AR(1) and MA(2) are both below 5%. This result indicates that this ARIMA(1,2,2)  model fitsGYCPICW/MUV well. Denotes GYCPICW/MUV as ‘CW’, then we have the following regression formula:

The ARIMA model of GYCPICW/MUV

The ARIMA model of GYCPIM/MUV

The result of choosing parameters of ARIMA for GYCPIM/MUV is shown in table 12. The minimum AIC appears in ARIMA(0, 2, 3) with value 8.81. Table 13 gives the regression result for GYCPIM/MUV. As we can see, the probabilities of MA(1), MA(2) and MA(3) are all below 5% which means this ARIMA(0, 2, 3) fits GYCPIM/MUV very well. Denotes GYCPIM/MUV as ‘CM’, then we have the following regression formula:

The ARIMA model of GYCPIM/MUV

The ARIMA model of GYCPIMCW/MUV

The result of choosing parameters of ARIMA for GYCPIMCW/MUV is shown in the table 16. The minimum AIC appears in ARIMA(1, 2, 2) with value 8.09. Table 17 gives the regression result for GYCPIMCW/MUV. As we can see, the probabilities of AR(1) and MA(2) are both above 5%. This result means the ARIMA(1, 2, 2) model does not fit GYCPIMCW/MUV very well. Denotes GYCPIMCW/MUV as ‘CMW’, then we have the following regression formula:

The ARIMA model of GYCPIMCW/MUV

The ARMA model of GYCPINF/MUV

The result of choosing parameters of ARIMA for GYCPINF/MUV is shown in the table 19. The minimum AIC appears in ARMA (2, 2) with value 8.12. Table 20 gives the regression result for GYCPINF/MUV. As we can see, the probabilities of AR(1),AR(2), MA(1) and MA(2) are all below 5%. This result strongly means the ARMA (2, 2) modelfitsGYCPINF/MUV very well. This result means this ARMA (2, 2) fits GYCPINF/MUV very well. Denotes GYCPINF/MUV as ‘CN’, then we have the following regression formula:

The ARMA model of GYCPINF/MUV

The ARMA model of GYCPINFCW/MUV

The result of choosing parameters of ARIMA for GYCPINFCW/MUV is shown in the table 22. The minimum AIC appears in ARMA (1, 2) with value 7.43. Table 23 gives the regression result for GYCPINFCW/MUV. As we can see, the probabilities of AR(1), and MA(2) are all below 5%. This result tells us that the ARMA (1, 2) model fits GYCPINFCW/MUV very well. This result means this ARMA (1, 2) fits GYCPINFCW/MUV very well. Denotes GYCPINFCW/MUV as ‘CNW’, then we have the following regression formula:

The ARMA model of GYCPINFCW/MUV

The ARMA model of GYCPIF/MUV

The result of choosing parameters of ARIMA for GYCPIF/MUV is shown in the table 25. The minimum AIC appears in ARMA (1, 2) with value 8.24. Table 26 gives the regression result for GYCPIF/MUV. As we can see, the probabilities of AR(1) and MA(2) are all below 5%. This result indicates that this ARMA (1, 2) model fitsGYCPIF/MUV well. Denotes GYCPINF/MUV as ‘CF’, then we have the following regression formula:

The ARMA model of GYCPIF/MUV

The ARIMA model of GYCPIFCW/MUV

The result of choosing parameters of ARIMA for GYCPIFCW/MUV is shown in the table 29. The minimum AIC appears in ARIMA (0, 2, 3) with value 7.45. Table 30 gives the regression result for GYCPIFCW/MUV. As we can see, the probabilities of MA(1), MA(2) and MA(3) are all below 5% which means this ARIMA (0, 2, 3) fits GYCPIFCW/MUV very well. Denotes GYCPIFCW/MUV as ‘CFW’, then we have the following regression formula:

The ARIMA model of GYCPIFCW/MUV

The Q-stat values suggest that these models are free from neglected serial correlation and therefore can be used to produce potentially valid forecasts for the various series.

The forecast of commodity price index

The result of static forecast for every commodity price index is given is figures 1 to 8. From the result, it is easy to find that the forecast interval of geometric weights is lower than the forecast interval of arithmetic weights for each kind of index. It means that using geometric weights will make the data easier to forecast. However, we found in the literature that the decline in the relative prices of primary commodities cannot be ascertained because of the lack of long-term factor productivity growth in developing countries, the source of agricultural and mining products. Productivity growth impacts on real export prices (Grilli & Yang 1988, p. 35).

Conclusion

The research is based on examining the long-term trends of commodity price indexes. This study investigates the stationary property of each commodity price index. The period of the sample is from 1900 to 2011and includes four kinds of commodity price indexes with respect to two different weights algorithms. This study reviewed the theories and empirical studies of the various economists’ arguments on the long-term movements of commodity prices, especially on the declining trend of nonfuel commodity prices from 1900 to 2011.

In a bid to reach the main objective, many statistical methods were applied. First, augmented Dickey–Fuller test was chosen to be the method to test the stationarity of the data. There are several reasons that ADF is our choice. One reason is that this test is used by Eviews which is the statistic software chosen in this project. Stationary testing uses arithmetic weights that can ‘bring’ more stationarity.

After unit root testing, EViews was again used to complete the estimation. For those indexes with stationary property, ARMA was used for regression and for those indexes without stationary property, ARIMA was implied. To determine the lag lengths of ARMA and ARIMA models, Akaike information criterion was used.

Through the estimation of ARMA and ARIMA models, we managed to get several regression models for commodity price indexes. The Q-stat values suggest that these models can do the forecast for future values. The results presented in this thesis are important because we found that empirical evidence on the prices of exported and imported goods, particularly nonfuel primary commodity prices between developed and developing countries needs to be presented and strengthened. This was presented in the literature review and strengthened in the methodology. This study provided a glimpse of the economies of the past through prices of primary commodities and how economists relate prices with economic policies.

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Appendix 1

The following are data and tables taken from the Grilli and Yang (1988) indexes, and shown with their 1977-1999 averages. The acronyms have corresponding data information, as explained in the literature; in particular, the CYCPIM represents the metals index; the CYCPINP for the non-food products; and the CYCPIF for the agricultural food products.

=========================== Table 1 ===========================

Year MUV GYCPI GYCPIM GYCPINF GYCPIF GYCPICW GYCPIMCW GYCPINFCW GYCPIFCW
1900 14.607 19.309 27.778 21.31 15.587 12.866 20.064 11.049 12.014
1901 13.858 18.236 27.522 19.292 14.716 12.008 18.485 10.366 11.232
1902 13.483 18.145 25.518 19.268 15.209 11.878 17.268 10.433 11.22
1903 13.483 19.006 26.668 22.86 14.634 12.173 18.672 11.424 10.938
1904 13.858 20.586 27.526 24.45 16.444 13.07 18.835 11.337 12.459
1905 13.858 21.621 29.15 26.226 16.924 13.624 20.898 11.693 12.793
1906 14.607 21.61 31.726 27.547 15.422 13.759 23.904 12.519 12.057
1907 15.356 22.757 36.699 25.967 16.672 14.089 25.435 12.42 12.386
1908 14.232 20.427 24.245 22.291 18.276 13.526 17.797 11.501 13.41
1909 14.232 21.554 20.822 28.973 18.143 13.787 16.623 12.837 13.443
1910 14.232 22.63 21.026 32.924 18.088 14.224 16.781 13.504 13.834
1911 14.232 21.909 19.923 28.122 19.498 14.773 16.731 12.863 15.195
1912 14.607 22.64 23.176 28.166 19.739 15.611 19.731 13.338 15.642
1913 14.607 20.461 23.134 25.44 17.149 14.592 19.151 13.488 13.893
1914 13.858 20.21 19.291 22.239 19.509 14.642 16.272 13.231 14.878
1915 14.232 24.468 31.321 24.388 22.292 17.723 23.26 15.839 17.158
1916 17.603 31.933 50.327 30.897 26.497 22.237 34.085 21.671 19.614
1917 20.974 39.396 45.271 40.257 37.074 27.255 34.109 30.256 24.07
1918 25.468 42.028 35.121 42.841 43.861 30.731 30.419 35.787 28.595
1919 26.966 39.208 30.853 43.292 39.902 31.15 25.861 34.477 31.464
1920 28.839 41.951 29.684 39.641 47.052 29.631 24.672 32.652 29.968
1921 24.345 21.356 20.219 21.605 21.602 16.904 16.433 18.896 16.145
1922 21.723 21.91 19.919 24.771 21.147 17.176 17.097 19.401 16.195
1923 21.723 26.407 24.587 29.989 25.234 19.615 20.316 22.481 18.128
1924 21.723 26.521 25.066 28.365 26.086 20.319 20.534 20.843 19.996
1925 22.097 29.381 26.315 36.778 26.637 22.112 22.075 24.005 21.243
1926 20.974 25.758 25.962 28.691 24.25 20.117 21.822 20.045 19.628
1927 19.85 25.143 24.028 26.823 24.677 19.759 20.124 19.904 19.57
1928 19.85 24.423 23.585 25.393 24.217 19.97 20.015 19.89 19.995
1929 19.101 23.266 25.21 22.332 23.098 19.114 21.143 18.161 18.975
1930 18.727 18.277 21.655 16.949 17.838 15.085 16.727 15.769 14.272
1931 15.356 13.61 18.479 12.308 12.675 11.002 12.894 10.13 10.888
1932 12.734 10.797 16.883 8.958 9.734 8.787 10.734 7.722 8.779
1933 14.232 12.591 18.388 12.357 10.833 10.243 13.292 10.291 9.393
1934 16.854 15.763 18.591 16.427 14.522 12.825 14.813 13.623 11.88
1935 16.479 17.294 18.383 16.229 17.465 13.654 15.178 13.27 13.382
1936 16.479 18.418 18.677 18.348 18.369 14.543 15.299 14.632 14.263
1937 16.854 21.361 20.931 20.366 21.988 17.127 18.064 16.84 16.976
1938 17.603 16.552 18.474 16.198 16.105 13.481 15.153 14.173 12.663
1939 16.105 16.019 19.188 17.499 14.267 13.062 16.027 14.749 11.513
1940 17.603 17.237 18.932 20.547 15.063 14.122 16.023 17.897 12.058
1941 18.727 20.093 18.452 24.844 18.288 17.032 16.131 22.107 15.237
1942 21.723 23.073 18.039 27.716 22.419 19.593 16.107 24.761 18.594
1943 24.345 24.283 18.132 29.094 23.905 20.605 16.35 26.568 19.583
1944 27.715 25.243 18.132 30.786 24.816 21.278 16.35 28.627 20.01
1945 28.464 25.832 18.232 30.112 26.186 21.504 16.584 27.149 20.843
1946 28.839 31.232 19.485 32.688 34.314 25.501 18.361 29.72 26.293
1947 34.831 40.389 24.709 37.349 46.952 33.426 23.146 33.635 37.532
1948 35.581 38.722 27.98 40.934 41.107 33.168 26.122 37.349 33.79
1949 33.333 35.845 26.479 35.727 38.93 30.331 24.901 30.596 32.192
1950 30.337 39.263 27.767 45.06 40.13 32.653 26.036 36.674 33.175
1951 35.955 48.093 32.466 58.702 47.929 39.647 30.557 48.526 39.031
1952 36.704 40.508 31.825 45.983 40.623 35.287 29.973 41.726 34.241
1953 35.206 37.897 32.214 40.839 38.289 33.477 29.985 36.948 33.041
1954 34.457 38.565 33.066 39.797 39.738 34.216 30.543 35.714 34.752
1955 34.831 38.233 38.267 42.537 36.107 34.213 34.695 38.528 32.116
1956 36.33 39.895 40.977 41.517 38.747 36.664 36.931 38.421 35.741
1957 36.704 40.108 35.376 42.372 40.525 36.585 32.541 39.059 36.79
1958 36.33 36.231 32.546 38.647 36.235 33.525 30.069 36.057 33.498
1959 36.33 37.113 35.379 40.667 35.926 34.707 32.675 37.072 34.256
1960 37.079 37.327 36.781 41.799 35.305 35.045 33.763 39.222 33.548
1961 37.453 36.466 35.242 40.424 34.917 34.053 32.738 38.153 32.604
1962 37.453 36.486 34.734 39.893 35.377 33.719 32.65 37.11 32.495
1963 37.453 41.419 34.747 39.084 44.723 36.693 33.158 36.075 38.236
1964 38.202 41.046 37.62 39.782 42.774 38.251 36.349 37.174 39.441
1965 38.951 38.119 40.499 39.99 36.429 35.758 39.095 38.326 33.569
1966 39.7 37.935 40.568 37.445 37.325 35.297 38.953 35.37 34.154
1967 39.7 36.846 41.509 33.813 36.83 34.425 39.874 32.214 33.921
1968 39.326 37.431 43.914 34.62 36.718 35.211 42.213 33.233 34.167
1969 40.449 39.761 47.712 37.459 38.322 37.805 45.324 36.109 36.468
1970 42.697 42.201 53.5 36.438 41.381 40.194 49.763 35.596 39.833
1971 45.318 42.324 50.293 37.638 42.051 40.034 46.982 37.038 39.504
1972 48.689 46.625 49.613 43.823 47.037 43.607 46.895 42.538 43.119
1973 58.801 69.472 55.72 69.054 74.123 63.951 53.118 66.967 66.38
1974 71.161 102.41 79.813 74.718 123.33 84.803 77.415 73.73 93.6
1975 79.026 85.156 76.09 65.807 97.598 73.494 74.452 65.02 77.757
1976 78.652 83.11 81.408 78.946 85.707 80.105 79.964 77.76 81.336
1977 86.517 93.125 87.752 90.681 96.064 92.193 87.316 90.251 94.823
1978 98.876 93.627 91.149 94.173 94.159 93.426 90.943 94.141 93.89
1979 114.61 113.25 121.1 115.15 109.78 112.388 120.204 114.786 108.827
1980 125.47 138.83 144.72 126.49 142.99 128.818 138.845 125.138 127.547
1981 119.1 117.94 124.21 108.87 120.38 113.227 123.156 108.409 112.583
1982 115.73 96.784 110.54 96.727 92.364 94.597 108.241 95.845 89.976
1983 110.49 102.78 118.37 103.15 97.566 100.094 114.464 102.299 94.814
1984 108.61 103.54 112.81 105.29 99.686 100.297 108.995 104.256 95.783
1985 109.59 91.268 105.59 90.49 87.022 88.034 100.879 89.379 83.608
1986 130.3 88.358 105.34 86.026 84.013 84.122 97.014 84.284 80.253
1987 142.9 95.215 108.047 118.203 79.694 90.567 103.931 117.07 76.295
1988 153.3 116.574 155.777 124.23 100.101 109.537 142.006 121.927 95.511
1989 152.925 118.705 151.529 129.335 102.826 108.972 140.342 127.158 93.027
1990 166.647 113.918 135.879 139.309 94.255 102.306 124.454 135.078 83.691
1991 165.558 103.689 111.752 130.249 87.945 94.312 102.724 125.237 79.734
1992 171.841 101.897 111.151 122.767 88.58 91.564 102.345 117.187 78.179
1993 170.123 99.068 95.373 115.683 92.048 89.73 88.804 111.072 81.015
1994 170.123 114.839 115.39 132.639 105.858 109.502 107.21 130.351 101.148
1995 171.841 128.768 138.508 154.315 112.983 121.763 126.433 151.673 107.908
1996 168.075 123.471 118.752 146.121 113.797 115.837 112.093 142.603 105.637
1997 168.634 120.882 122.247 142.559 109.72 115.79 112.656 138.579 106.891
1998 167.617 106.333 99.364 125.907 98.909 101.75 94.276 119.959 96.139
1999 165.445 93.311 97.679 115.649 80.85 87.322 92.105 108.425 77.115
2000 161.945 92.753 107.338 112.766 78.136 84.939 99.488 107.261 71.907
2001 157.179 88.68 95.077 106.41 77.842 79.425 88.17 100.669 68.292
2002 155.212 92.114 90.655 112.585 82.463 83.803 84.233 107.987 73.805
2003 166.853 98.879 99.672 127.848 84.297 90.456 93.482 125.158 76.22
2004 178.361 112.819 141.579 133.11 93.477 103.338 135.162 129.683 84.674
2005 178.361 121.482 167.96 132.433 101.025 111.463 154.674 128.023 93.612
2006 181.215 153.017 282.602 144.449 115.317 131.615 242.454 138.424 105.344
2007 189.732 177.004 311.703 180.202 131.828 154.51 282.438 170.109 121.205
2008 202.444 194.575 290.844 173.006 174.086 174.555 271.662 165.591 155.269
2009 191.039 163.481 219.018 150.592 151.882 151.037 203.246 143.264 140.833
2010 195.844 204.535 306.068 196.923 175.441 189.339 280.874 190.159 166.297
2011 211.988 254.44 367.429 234.367 227.799 235.046 334.232 225.341 214.155

Table 2. GYCPI/MUV.

Null Hypothesis: GYCPI has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.095835 0.1125
Test critical values: 1% level -4.042819
5% level -3.450807
10% level -3.150766
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPI)
Method: Least Squares
Sample (adjusted): 1901 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPI(-1) -0.195600 0.063182 -3.095835 0.0025
C 27.52129 9.543479 2.883779 0.0047
@TREND(1900) -0.122498 0.057506 -2.130167 0.0354
R-squared 0.083957 Mean dependent var -0.109589
Adjusted R-squared 0.066993 S.D. dependent var 12.12960
S.E. of regression 11.71626 Akaike info criterion 7.786488
Sum squared resid 14825.25 Schwarz criterion 7.859718
Log likelihood -429.1501 Hannan-Quinn criter. 7.816195
F-statistic 4.949177 Durbin-Watson stat 1.747009
Prob(F-statistic) 0.008779

Table 3. The Difference of GYCPI/MUV.

Null Hypothesis: D(GYCPI) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -10.05153 0.0000
Test critical values: 1% level -4.043609
5% level -3.451184
10% level -3.150986
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPI,2)
Method: Least Squares
Sample (adjusted): 1902 2011
Variable Coefficient Std. Error t-Statistic Prob.
D(GYCPI(-1)) -0.978227 0.097321 -10.05153 0.0000
C -1.200261 2.391399 -0.501908 0.6168
@TREND(1900) 0.019480 0.036890 0.528052 0.5986
R-squared 0.485765 Mean dependent var 0.147147
Adjusted R-squared 0.476153 S.D. dependent var 16.96536
S.E. of regression 12.27907 Akaike info criterion 7.880563
Sum squared resid 16132.98 Schwarz criterion 7.954212
Log likelihood -430.4310 Hannan-Quinn criter. 7.910436
F-statistic 50.53796 Durbin-Watson stat 1.978445
Prob(F-statistic) 0.000000

Table 4. AICs for different p and q of D (GYCPI/MUV).

p 0 0 0 1 1 1 2 2 3
q 1 2 3 0 1 2 0 1 0
AIC 7.86 7.82 7.83 7.86 7.81 7.82 7.85 7.82 7.88

Table 5. ARIMA model for GYCPI/MUV.

Dependent Variable: D(GY_CPI_MUV)
Sample (adjusted): 1902 2011
Included observations: 110 after adjustments
Convergence achieved after 9 iterations
MA Backcast: 1901
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) -0.689852 0.333427 -2.068975 0.0409
MA(1) 0.785183 0.286085 2.744577 0.0071
R-squared 0.017220 Mean dependent var -0.105147
Adjusted R-squared 0.008121 S.D. dependent var 12.18503
S.E. of regression 12.13545 Akaike info criterion 7.808153
Sum squared resid 15905.07 Schwarz criterion 7.897253
Log likelihood -429.6484 Hannan-Quinn criter. 7.868069
Durbin-Watson stat 2.093991
Inverted AR Roots -.69
Inverted MA Roots -.79

Table 6. GYCPICW/MUV.

Null Hypothesis: GYCPICW has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.766571 0.2128
Test critical values: 1% level -4.042819
5% level -3.450807
10% level -3.150766
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPICW)
Method: Least Squares
Sample (adjusted): 1901 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPICW(-1) -0.155681 0.056272 -2.766571 0.0067
C 15.71208 6.056226 2.594369 0.0108
@TREND(1900) -0.032982 0.029836 -1.105444 0.2714
R-squared 0.067813 Mean dependent var 0.205369
Adjusted R-squared 0.050550 S.D. dependent var 8.720614
S.E. of regression 8.497340 Akaike info criterion 7.144039
Sum squared resid 7798.117 Schwarz criterion 7.217269
Log likelihood -393.4941 Hannan-Quinn criter. 7.173746
F-statistic 3.928300 Durbin-Watson stat 1.665835
Prob(F-statistic) 0.022551

Table 7. The Difference of GYCPICW/MUV.

Null Hypothesis: D(GYCPICW) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.757282 0.0000
Test critical values: 1% level -4.044415
5% level -3.451568
10% level -3.151211
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPICW,2)
Method: Least Squares
Sample (adjusted): 1903 2011
Variable Coefficient Std. Error t-Statistic Prob.
D(GYCPICW(-1)) -1.157016 0.132120 -8.757282 0.0000
D(GYCPICW(-1),2) 0.258271 0.097177 2.657752 0.0091
C -0.407022 1.704311 -0.238819 0.8117
@TREND(1900) 0.010269 0.026181 0.392228 0.6957
R-squared 0.486009 Mean dependent var 0.116998
Adjusted R-squared 0.471323 S.D. dependent var 11.82555
S.E. of regression 8.598380 Akaike info criterion 7.177032
Sum squared resid 7762.875 Schwarz criterion 7.275797
Log likelihood -387.1482 Hannan-Quinn criter. 7.217085
F-statistic 33.09452 Durbin-Watson stat 1.979725

Table 8. AICs for different p and q of D (D(GYCPICW/MUV).

p 0 0 0 1 1 1 2 2 3
q 1 2 3 0 1 2 0 1 0
AIC 7.21 7.22 7.28 7.67 7.23 7.09 7.49 7.26 7.45

Table 9. ARIMA model for GYCPICW/MUV.

Dependent Variable: D(D(GY_CPICW_MUV))
Method: Least Squares
Included observations: 109 after adjustments
Convergence achieved after 18 iterations
MA Backcast: 1901 1902
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) -0.929016 0.036188 -25.67184 0.0000
MA(2) -0.956655 0.019783 -48.35677 0.0000
R-squared 0.446327 Mean dependent var 0.116998
Adjusted R-squared 0.441152 S.D. dependent var 11.82555
S.E. of regression 8.840324 Akaike info criterion 7.094702
Sum squared resid 8362.193 Schwarz criterion 7.164085
Log likelihood -391.2013 Hannan-Quinn criter. 7.234729
Durbin-Watson stat 1.867566
Inverted AR Roots -.93
Inverted MA Roots .98 -.98

Table 10. GYCPIM/MUV.

Null Hypothesis: GYCPIM has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 2 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.339955 0.4088
Test critical values: 1% level -4.044415
5% level -3.451568
10% level -3.151211
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIM)
Method: Least Squares
Sample (adjusted): 1903 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPIM(-1) -0.141522 0.060481 -2.339955 0.0212
C 18.29999 10.32147 1.773002 0.0792
@TREND(1900) -0.046580 0.075574 -0.616355 0.5390
R-squared 0.199355 Mean dependent var -0.146194
Adjusted R-squared 0.168561 S.D. dependent var 20.50837
S.E. of regression 18.70021 Akaike info criterion 8.739732
Sum squared resid 36368.57 Schwarz criterion 8.863189
Log likelihood -471.3154 Hannan-Quinn criter. 8.789799
F-statistic 6.473820 Durbin-Watson stat 1.952630
Prob(F-statistic) 0.000108

Table 11. The Difference of GYCPIM/MUV.

Null Hypothesis: D(GYCPIM) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -9.298631 0.0000
Test critical values: 1% level -3.491345
5% level -2.888157
10% level -2.581041
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIM,2)
Method: Least Squares
Sample (adjusted): 1903 2011
Variable Coefficient Std. Error t-Statistic Prob.
D(GYCPIM(-1)) -1.104360 0.118766 -9.298631 0.0000
D(GYCPIM(-1),2) 0.347167 0.093064 3.730404 0.0003
C -0.292469 1.833485 -0.159516 0.8736
R-squared 0.475260 Mean dependent var 0.242049
S.D. dependent var 26.16133 S.E. of regression 19.12894
Akaike info criterion 8.767419 Sum squared resid 38787.14
Schwarz criterion 8.841493 Log likelihood -474.8243
Hannan-Quinn criter. 8.797459 F-statistic 48.00235
Durbin-Watson stat 1.992121

Table 12. AICs for different p and q of D (D (GYCPIM/MUV)).

p 0 0 0 1 1 1 2 2 3
q 1 2 3 0 1 2 0 1 0
AIC 8.90 8.84 8.81 9.33 8.87 8.90 9.36 8.87 8.91

Table 13. ARIMA model for GYCPIM/MUV.

Dependent Variable: D(D(GY_CPIM_MUV))
Method: Least Squares
Included observations: 110 after adjustments
Convergence achieved after 22 iterations
MA Backcast: 1899 1901
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) -0.833848 0.093320 -8.935336 0.0000
MA(2) -0.418596 0.119828 -3.493308 0.0007
MA(3) 0.270634 0.094614 2.860400 0.0051
R-squared 0.448898 Mean dependent var 0.078299
Adjusted R-squared 0.438597 S.D. dependent var 26.09762
S.E. of regression 19.55412 Akaike info criterion 8.811143
Sum squared resid 40912.90 Schwarz criterion 8.884792
Log likelihood -481.6129 Hannan-Quinn criter. 8.841016
Durbin-Watson stat 1.868662
Inverted MA Roots .98 .46 -.60

Table 14. GYCPIMCW/MUV.

Null Hypothesis: GYCPIMCW has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.937905 0.1549
Test critical values: 1% level -4.043609
5% level -3.451184
10% level -3.150986
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIMCW)
Method: Least Squares
Sample (adjusted): 1902 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPIMCW(-1) -0.164049 0.055839 -2.937905 0.0041
D(GYCPIMCW(-1)) 0.256517 0.098513 2.603891 0.0105
C 17.59959 7.204686 2.442798 0.0162
@TREND(1900) -0.026262 0.046530 -0.564402 0.5737
S.E. of regression 13.40749 Akaike info criterion 8.065191
Sum squared resid 19054.66 Schwarz criterion 8.163390
Log likelihood -439.5855 Hannan-Quinn criter. 8.105021
Durbin-Watson stat 1.908410

Table 15. The Difference of GYCPIMCW/MUV.

Null Hypothesis: D(GYCPIMCW) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.432720 0.0000
Test critical values: 1% level -4.044415
5% level -3.451568
10% level -3.151211
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIMCW,2)
Method: Least Squares
Sample (adjusted): 1903 2011
Variable Coefficient Std. Error t-Statistic Prob.
D(GYCPIMCW(-1)) -1.061999 0.125938 -8.432720 0.0000
D(GYCPIMCW(-1),2) 0.254000 0.097587 2.602791 0.0106
C -2.378029 2.702874 -0.879815 0.3810
@TREND(1900) 0.044907 0.041559 1.080564 0.2824
S.E. of regression 13.57534 Akaike info criterion 8.090394
Sum squared resid 19350.44 Schwarz criterion 8.189159
Log likelihood -436.9265 Hannan-Quinn criter. 8.130447
Durbin-Watson stat 2.036146

Table 16. AICs for different p and q of D (D(GYCPIMCW/MUV)).

p 0 0 0 1 1 1 2 2 3
q 1 2 3 0 1 2 0 1 0
AIC 8.15 8.13 8.10 8.57 8.12 8.09 8.46 8.10 8.36

Table 17. ARIMA model for GYCPIMCW/MUV.

Dependent Variable: D(D(GY_CPIMCW_MUV))
Sample (adjusted): 1903 2011
Included observations: 109 after adjustments
Convergence achieved after 13 iterations
MA Backcast: 1901 1902
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) -0.925973 0.037566 -24.64909 0.0000
MA(2) -0.953414 0.020263 -47.05292 0.0000
R-squared 0.404810 Mean dependent var 0.179492
Adjusted R-squared 0.399248 S.D. dependent var 18.13454
S.E. of regression 14.05576 Akaike info criterion 8.092120
Sum squared resid 21139.39 Schwarz criterion 8.191502
Log likelihood -441.7455 Hannan-Quinn criter. 8.162146
Durbin-Watson stat 1.726598
Inverted AR Roots -.93
Inverted MA Roots .98 -.98

Table 18. GYCPINF/MUV.

Null Hypothesis: GYCPINF has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.571039 0.0370
Test critical values: 1% level -4.042819
5% level -3.450807
10% level -3.150766
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Method: Least Squares
Sample (adjusted): 1901 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPINF(-1) -0.227749 0.063777 -3.571039 0.0005
C 36.24696 10.82242 3.349248 0.0011
@TREND(1900) -0.189976 0.071506 -2.656777 0.0091
R-squared 0.106412 Mean dependent var -0.318308
Adjusted R-squared 0.089864 S.D. dependent var 15.20003
S.E. of regression 14.50099 Akaike info criterion 8.212965
Sum squared resid 22710.09 Schwarz criterion 8.286196
Log likelihood -452.8196 Hannan-Quinn criter. 8.242673
F-statistic 6.430537 Durbin-Watson stat 1.778004
Prob(F-statistic) 0.002298

Table 19. AICs for different p and q of GYCPINF/MUV.

p 1 1 1 1 2 2 2 3 3 4
q 1 2 3 4 1 2 3 1 2 1
AIC 8.27 8.22 8.24 8.16 8.27 8.12 8.21 8.13 8.13 8.15

Table 20. ARMA model for GYCPINF/MUV.

Dependent Variable: GY_CPINF_MUV
Method: Least Squares
Sample (adjusted): 1902 2011
Included observations: 110 after adjustments
Convergence achieved after 25 iterations
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) 1.571076 0.107501 14.61448 0.0000
AR(2) -0.574739 0.106609 -5.391115 0.0000
MA(1) -0.668659 0.123406 -5.418364 0.0000
MA(2) -0.304041 0.120056 -2.532490 0.0128
R-squared 0.848573 Mean dependent var 113.2865
Adjusted R-squared 0.844287 S.D. dependent var 36.03817
S.E. of regression 14.22083 Akaike info criterion 8.122979
Sum squared resid 21436.59 Schwarz criterion 8.221178
Log likelihood -446.0638 Hannan-Quinn criter. 8.222809
Durbin-Watson stat 2.033904
Inverted AR Roots .99 .58
Inverted MA Roots .98 -.31

Table 21. GYCPINFCW/MUV.

Null Hypothesis: GYCPINFCW has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.777520 0.0214
Test critical values: 1% level -4.042819
5% level -3.450807
10% level -3.150766
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPINF_CW)
Method: Least Squares
Sample (adjusted): 1901 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPINF_CW(-1) -0.231438 0.061267 -3.777520 0.0003
C 23.75098 6.481054 3.664678 0.0004
@TREND(1900) -0.039512 0.031016 -1.273938 0.2054
R-squared 0.116715 Mean dependent var 0.276190
Adjusted R-squared 0.100358 S.D. dependent var 10.42580
S.E. of regression 9.888812 Akaike info criterion 7.447340
Sum squared resid 10561.17 Schwarz criterion 7.520571
Log likelihood -410.3274 Hannan-Quinn criter. 7.477048
F-statistic 7.135422 Durbin-Watson stat 1.745378
Prob(F-statistic) 0.001229

Table 22. AICs for different p and q of GYCPINFCW/MUV.

p 1 1 1 1 2 2 2 3 3 4
q 1 2 3 4 1 2 3 1 2 1
AIC 7.43 7.43 7.45 7.46 7.43 7.45 7.46 7.46 7.48 7.48

Table 23. ARMA model for GYCPINFCW/MUV.

Dependent Variable: GY_CPINFCW_MUV
Sample (adjusted): 1901 2011
Included observations: 111 after adjustments
Convergence achieved after 8 iterations
MA Backcast: 1899 1900
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) 0.999349 0.006609 151.2178 0.0000
MA(2) -0.361353 0.091232 -3.960790 0.0001
R-squared 0.624115 Mean dependent var 92.14567
Adjusted R-squared 0.620666 S.D. dependent var 16.27652
S.E. of regression 10.02472 Akaike info criterion 7.425838
Sum squared resid 10953.95 Schwarz criterion 7.514659
Log likelihood -412.3540 Hannan-Quinn criter. 7.485643
Durbin-Watson stat 1.985436
Inverted AR Roots 1.00
Inverted MA Roots .60 -.60
Dependent Variable: GY_CPINFCW_MUV
Method: Least Squares
Date: 11/24/13 Time: 22:04
Sample (adjusted): 1901 2011
Included observations: 111 after adjustments
Convergence achieved after 8 iterations
MA Backcast: 1899 1900
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) 0.999349 0.006609 151.2178 0.0000
MA(2) -0.361353 0.091232 -3.960790 0.0001
R-squared 0.624115 Mean dependent var 92.14567
Adjusted R-squared 0.620666 S.D. dependent var 16.27652
S.E. of regression 10.02472 Akaike info criterion 7.465838
Sum squared resid 10953.95 Schwarz criterion 7.514659
Log likelihood -412.3540 Hannan-Quinn criter. 7.485643
Durbin-Watson stat 1.985436
Inverted AR Roots 1.00
Inverted MA Roots .60 -.60
Dependent Variable: GY_CPINFCW_MUV
Method: Least Squares
Date: 11/24/13 Time: 22:04
Sample (adjusted): 1901 2011
Included observations: 111 after adjustments
Convergence achieved after 8 iterations
MA Backcast: 1899 1900
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) 0.999349 0.006609 151.2178 0.0000
MA(2) -0.361353 0.091232 -3.960790 0.0001
R-squared 0.624115 Mean dependent var 92.14567
Adjusted R-squared 0.620666 S.D. dependent var 16.27652
S.E. of regression 10.02472 Akaike info criterion 7.465838
Sum squared resid 10953.95 Schwarz criterion 7.514659
Log likelihood -412.3540 Hannan-Quinn criter. 7.485643
Durbin-Watson stat 1.985436
Inverted AR Roots 1.00
Inverted MA Roots .60 -.60

Table 24. GYCPIF/MUV.

Null Hypothesis: GYCPIF has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.901358 0.0151
Test critical values: 1% level -4.042819
5% level -3.450807
10% level -3.150766
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIF)
Method: Least Squares
Sample (adjusted): 1901 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPIF(-1) -0.256780 0.065818 -3.901358 0.0002
C 34.20464 9.282767 3.684746 0.0004
@TREND(1900) -0.151951 0.059011 -2.574954 0.0114
S.E. of regression 14.42287 Akaike info criterion 8.202162
Sum squared resid 22466.07 Schwarz criterion 8.275393
Log likelihood -452.2200 Hannan-Quinn criter. 8.231870
Durbin-Watson stat 1.886512

Table 25. AICs for different p and q of GYCPIF/MUV.

p 1 1 1 1 2 2 2 3 3 4
q 1 2 3 4 1 2 3 1 2 1
AIC 8.26 8.23 8.26 8.27 8.26 8.27 8.27 8.28 8.26 8.30

Table 26. ARMA model for GYCPIF/MUV.

Dependent Variable: GY_CPIF_MUV
Sample (adjusted): 1901 2011
Included observations: 111 after adjustments
Convergence achieved after 7 iterations
MA Backcast: 1899 1900
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) 0.993852 0.009760 101.8259 0.0000
MA(2) -0.289425 0.093547 -3.093910 0.0025
R-squared 0.738724 Mean dependent var 100.0482
Adjusted R-squared 0.736327 S.D. dependent var 28.85984
S.E. of regression 14.81926 Akaike info criterion 8.227586
Sum squared resid 23937.54 Schwarz criterion 8.296407
Log likelihood -455.7410 Hannan-Quinn criter. 8.267391
Durbin-Watson stat 2.184502
Inverted AR Roots .99
Inverted MA Roots .54 -.54

Table 27. GYCPIFCW/MUV.

Null Hypothesis: GYCPIFCW has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.060341 0.1211
Test critical values: 1% level -4.042819
5% level -3.450807
10% level -3.150766
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIFCW)
Method: Least Squares
Sample (adjusted): 1901 2011
Variable Coefficient Std. Error t-Statistic Prob.
GYCPIFCW(-1) -0.171670 0.056095 -3.060341 0.0028
C 17.15696 5.988389 2.865037 0.0050
@TREND(1900) -0.045881 0.033934 -1.352041 0.1792
R-squared 0.080300 Mean dependent var 0.169135
Adjusted R-squared 0.063268 S.D. dependent var 10.16203
S.E. of regression 9.835307 Akaike info criterion 7.436489
Sum squared resid 10447.19 Schwarz criterion 7.509720
Log likelihood -409.7252 Hannan-Quinn criter. 7.466197
F-statistic 4.714792 Durbin-Watson stat 1.775727
Prob(F-statistic) 0.010887

Table 28. The Difference of GYCPIFCW/MUV.

Null Hypothesis: D(GYCPIFCW) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic – based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -9.838473 0.0000
Test critical values: 1% level -4.044415
5% level -3.451568
10% level -3.151211
*MacKinnon (1996) one-sided p-values.
Dependent Variable: D(GYCPIFCW,2)
Method: Least Squares
Sample (adjusted): 1903 2011
Included observations: 109 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(GYCPIFCW(-1)) -1.299384 0.132072 -9.838473 0.0000
D(GYCPIFCW(-1),2) 0.325313 0.093995 3.460946 0.0008
C -0.212066 1.951645 -0.108660 0.9137
@TREND(1900) 0.006124 0.029978 0.204272 0.8385
S.E. of regression 9.845976 Akaike info criterion 7.448010
Sum squared resid 10179.04 Schwarz criterion 7.546775
Log likelihood -401.9165 Hannan-Quinn criter. 7.488063
Durbin-Watson stat 1.942876

Table 29. AICs for different p and q of D (D(GYCPIFCW/MUV)).

p 0 0 0 1 1 1 2 2 3
q 1 2 3 0 1 2 0 1 0
AIC 7.51 7.53 7.45 8.05 7.54 7.50 7.77 7.46 7.70

Table 30. ARIMA model for GYCPIFCW/MUV.

Dependent Variable: D(D(GY_CPIFCW_MUV))
Method: Least Squares
Included observations: 110 after adjustments
Convergence achieved after 28 iterations
MA Backcast: 1899 1901
Variable Coefficient Std. Error t-Statistic Prob.
MA(1) -0.941109 0.093079 -10.11087 0.0000
MA(2) -0.351437 0.125074 -2.809838 0.0059
MA(3) 0.311449 0.093576 3.328305 0.0012
R-squared 0.523177 Mean dependent var 0.157335
Adjusted R-squared 0.514264 S.D. dependent var 14.18832
S.E. of regression 9.888511 Akaike info criterion 7.447518
Sum squared resid 10462.74 Schwarz criterion 7.521168
Log likelihood -406.6135 Hannan-Quinn criter. 7.477391
Durbin-Watson stat 1.973607
Inverted MA Roots .97 .55 -.58

Figures 1 – 9 (Forecasts)

Forecast of GYCPI/MUV.
Figure 9. Forecast of GYCPI/MUV.
Forecast of GYCPICW/MUV.
Figure 10. Forecast of GYCPICW/MUV.
Forecast of GYCPIM/MUV.
Figure 11. Forecast of GYCPIM/MUV.
Forecast of GYCPIMCW/MUV.
Figure 12. Forecast of GYCPIMCW/MUV.
Forecast of GYCPINF/MUV.
Figure 13. Forecast of GYCPINF/MUV.
Forecast of GYCPINFCW/MUV.
Figure 14. Forecast of GYCPINFCW/MUV.
Forecast of GYCPIF/MUV.
Figure 15. Forecast of GYCPIF/MUV.
Forecast of GYCPIFCW/MUV.
Figure 16. Forecast of GYCPIFCW/MUV.
Long-Term Trends of Commodity Prices From 1900 to 2011
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