metadata: authors: 0: author: Grigoli,Francesco
count: World
docna: 0: docna: An empirical investigation of the nexus
            among money balances, commodity prices and consumer
            goods' prices
docty: Policy Research Working Paper
subtopic: Inflation,Macroeconomic Management,Energy Demand,Energy and Environment,Energy and Mining,Crime and Society,Commodity Risk Management
teratopic: Private Sector Development,Macroeconomics and Economic Growth
abstracts: cdata!: This paper aims to identify the nexus
            between the excess of liquidity in the United States and
            commodity prices over the 1983-2006 period. In particular,
            it assesses whether commodity prices react more powerfully
            than consumer goods' prices to changes in real money
            balances. Within a cointegrated vector autoregressive
            framework, the author investigates whether consumer prices
            and commodity prices react to excess liquidity, and if the
            different price elasticities of supply for goods and
            commodities allow for differences in the dynamic paths of
            price adjustment to a liquidity shock. The results show a
            positive relationship between real money and real commodity
            prices and provide empirical evidence for a stronger
            response of commodity prices with respect to consumer
            goods' prices. This could imply that, if the magnitude
            of the reaction is due the fact that consumer goods'
            prices are slower to react, then their long-run value can be
            predicted with the help of commodity prices. The findings
            support the view that the latter should be considered as a
            valid monetary indicator.
repnme: repnme: An empirical investigation of the nexus
            among money balances, commodity prices and consumer
            goods' prices
display_title: An empirical investigation of the
            nexus among money balances, commodity prices and consumer
            goods' prices
listing_relative_url: /research/2011/01/13576464/empirical-investigation-nexus-among-money-balances-commodity-prices-consumer-goods-prices
topicv3: Energy and Extractives m1326595 507,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Criminal Justice m1326993 1014,Monetary Policy m1327609 444,Commodity and Resource Prices m1503849 3034
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth
no_of_pages: 27
author_keys: 0: author_key: 1110691
model_extractions: WPS5533 Policy Research Working Paper 5533 An Empirical Investigation of the Nexus among Money Balances, Commodity Prices and Consumer Goods’ Prices _Francesco Grigoli_ The World Bank Poverty Reduction and Economic Management Network Public Sector Unit January 2011
Policy Research Working Paper 5533

# **Abstract**

This paper aims to identify the nexus between the excess of liquidity in the United States and commodity prices over the 1983–2006 period. In particular, it assesses whether commodity prices react more powerfully than consumer goods’ prices to changes in real money balances. Within a cointegrated vector autoregressive framework, the author investigates whether consumer prices and commodity prices react to excess liquidity, and if the different price elasticities of supply for goods and commodities allow for differences in the dynamic paths of price adjustment to a liquidity shock. The results show a positive relationship between real money and real commodity prices and provide empirical evidence for a stronger response of commodity prices with respect to consumer goods’ prices. This could imply that, if the magnitude of the reaction is due the fact that consumer goods’ prices are slower to react, then their long-run value can be predicted with the help of commodity prices. The findings support the view that the latter should be considered as a valid monetary indicator.

This paper is a product of the Public Sector Unit, Poverty Reduction and Economic Management Network. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at fgrigoli@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
An Empirical Investigation of the Nexus among Money Balances, Commodity Prices and Consumer Goods’ Prices

# Francesco Grigoli<sup>1</sup>

JEL Classification Code: E31, E40, E50 Keywords: Commodity prices, Cointegration, Inflation, Money

> 1 Permanent address: Department of Economics, University of Insubria, Via Monte Generoso 71, 21100 Varese, Italy. Phone: +39 0332 395501, Fax: +39 0332 395509, fgrigoli@eco.uninsubria.it. Present address: World Bank, 1818 H Street NW, Washington DC, 20043, USA, fgrigoli@worldbank.org.
# **1. Introduction**

In the last four decades, the volatility of commodity prices generated turbulence in the global economy, affecting importing and exporting countries in opposite and vigorous ways. Nonetheless, the attention of the literature to the topic seemed to be proportional to price growth, declining in relatively tranquil periods and rising when the commodities prices were back at high levels. The huge variations of the last decade generated a renewed interest in the topic.

In the 1970s, the popular view was that commodity prices were defined as a result of evolution in the relevant commodity market, playing an important role in the stagflation of that decade. However, this idea has been strongly challenged. An increase in the expected inflation rate due, for example, to an increase in money supply, causes agents to shift from money to commodities, provoking a rise in prices. Therefore, increases in the price of oil and other commodities could be the result of an exceedingly expansionary policy, rather than an exogenous inflationary supply shock.

Falling commodity prices in the 1980s and 1990s were not considered as interesting as rising prices, even though oil producers such as Mexico and Russia were experiencing important revenue losses and countries such as Argentina, Brazil and Australia were suffering from low agricultural prices.

After collapsing in the second half of 2008, commodity prices stabilized in early 2009 and subsequently staged a comeback. Such behavior is in contrast with what happened during past recessions. In previous global downturns, prices typically continued to fall into the early phases of recovery or rose at rates far below the increases recorded in recent months. An exception is the price of oil, which recorded meaningful increases early in previous recoveries.

Thus, the recent happenings of quick commodity price increases and higher volatility following the easy monetary stance in the US, matched with similar accommodative policies in the euro area and Japan, led some to infer some causal role for monetary changes in driving commodity prices and ultimately inflation.

Drawing on Dornbusch (1976), the idea of overshooting has been adapted to analyze theoretically the relationship between money, consumer prices and commodity prices by Frankel (1986). The latter argued that tightening monetary policy has relevant effects on commodity prices because they are flexible, whereas other goods’ prices are sticky. Thus, commodity prices overshoot their new equilibrium in the short-run in order to generate an expectation of future appreciation sufficient to offset the higher interest rate.

This paper aims at identifying the nexus between the excess of liquidity in the United States and commodity prices over the 1983-2006 period. In particular, it tests whether the latter react more powerfully than consumer goods’ prices to changes in real money balances.

Within a cointegrated vector autoregressive (VAR) framework, it is investigated whether consumer prices and commodity prices react to excess liquidity in the US, and if the different price elasticities of supply for goods and commodities allow for differences in the dynamic paths of price adjustment to a liquidity shock.

The results show a positive relationship between real money and real commodity prices and provide empirical evidence for a stronger response of commodity prices with respect to consumer goods’ prices. This could imply that, if the magnitude of the reaction is due to the fact that consumer goods’ prices are slower to react, then their long-run value can be predicted with the help of the commodity prices.

The structure of the paper is as follows. In section 2, some contributions on the issue are presented. Section 3 describes the hypothesis to be tested. In section 4 the empirical strategy, tests results and interpretation of the findings are presented. Section 5 ends the paper reporting the conclusions.

2
# **2. A review of the literature**

Before discussing the empirical analysis employed, some of the main contributions on the relationship between monetary policy, consumer prices and commodity prices will be reviewed.

Drawing on Dornbusch’s exchange rate overshooting model, Frankel (1986) provides a theoretical framework to analyze the impact of money supply shocks on commodity prices. He substitutes the price of agricultural goods for the price of foreign exchange and argues that the reason for the overshooting phenomenon is that prices for agricultural and mineral products adjust rapidly, while the price of goods adjusts more slowly. In fact, the hypothesis is that commodities are exchanged in a reactive auction market in which the supply cannot be easily expanded, whereas the consumer goods market enjoys a copious supply.

Frankel illustrates the dynamic starting from a monetary contraction that is expected to be permanent and that would eventually lead to an equal fall of consumer and commodity goods’ prices in the absence of other disturbances. However, given the manufactured price stickiness in the short-run the nominal money supply contraction is a reduction in the real money supply. Such a reduction should be offset by an interest rate rise. Nevertheless, the arbitrage condition implies that, since commodities are storable, the interest rate cannot grow more than the expected rate of increase in the commodity prices plus the storage cost. Therefore, the spot price of commodities must fall today and must do so until the moment in which there is an expectation of future appreciation that is sufficient to offset the higher interest rate.

Over the last three decades the role of commodity prices in setting monetary policy has been faced by many researchers. On the one hand, it has been argued that commodity prices may be an earlier indicator of the current state of the economy because, as assumed by Frenkel (1986) these prices are usually set in continuous auction markets with efficient information (see Olivera, 1970; Garner, 1989; Marquis and Cunningham, 1990; Cody and Mills, 1991). Thus, some policymakers became advocates of using commodity prices as a leading indicator of inflation and endorsed policy proposals using commodity prices as a guide to adjust short run money growth target ranges (see Garner, 1989). A rise in commodity prices may indicate to policymakers that the economy is growing too rapidly and hence inflation is inclined to rise. In such a case, the monetary authority may observe the rising commodity prices and respond by raising interest rates to tighten money supply.

On the other hand, the counterargument is that commodity prices cannot be used effectively in formulating monetary policy because they are subject to large, market-specific shocks, which may not have macroeconomic implications (see Marquis and Cunningham, 1990; Cody and Mills, 1991). However, many others (see Bessler, 1984; Pindyck and Rotemberg, 1990; Hua, 1998) argue that commodity price movements are the result of monetary or macroeconomic changes and that the causality should run from macroeconomic/monetary variables to commodity prices. Barsky and Kilian (2002) offer another important contribution. They argue that monetary expansions and contractions could generate stagflation of important magnitudes, by providing evidence about the role of monetary fluctuations in determining the prices of oil and, in particular, the prices of industrial commodities that preceded the 1973 oil price increase. Bernanke et al. (1997) investigate the relationship between the oil price shocks, US monetary policy and the business cycle. They assert that a relevant part of the effect of oil price shocks on the economy comes from tighter monetary policy resulting from the change in oil prices and not from the change in oil prices _per se_ .

3
Another piece of literature analyzes the impact of the commodity price evolutions on the behavior of monetary policy and its informational role for formulating it. Awokuse and Yang (2003) argue that commodity price indicators contain important information about the future movements of macroeconomic variables. Bhar and Hamori (2008) assess the information content of commodity prices for monetary policy. Using a cross correlation approach between economic activity and commodity futures prices, they affirm that commodity prices can serve as suitable information for monetary policy.

Fuhrer and Moore (1992) investigate the relationships between asset prices and inflation in a Keynesian model in which monetary policy controls inflation by manipulating the federal funds rate. They find that the indicator properties of asset prices are quite sensitive to the monetary policy rule. Hamori (2007) empirically analyzes the relationship between the commodity prices index and macroeconomic variables in Japan, arguing that the former and the general price level are closely related, with movements in commodity prices leading movements in the general price level. However, he specifies that the commodity price index was found to be valid as a leading indicator of the consumer price index before the zero interest policy was introduced, as afterwards the relationship ceased to exist.

Other studies, such as Surrey (1989), Boughton and Branson (1990, 1991), and Browne and Cronin (2007), investigate empirically the potential importance of monetary conditions on the relationship between commodity prices and consumer goods’ prices. However, they all use different empirical techniques or different specifications from the one employed in this paper.

# **3. A Model of Price Dynamics**

This section presents the theoretical framework through which the investigation aims to answer the following research question: do commodity prices react more strongly than consumer goods’ prices?

As mentioned, the commodity price overshooting theory was advanced by Frankel (1986). The essence of this theoretical framework is that the short-term reaction to an expansionary monetary policy produces an overshoot of the commodity prices and a more delayed reaction in the consumer goods market. In the long-run, consumer prices adjust to the new equilibrium. However, Frenkel’s theory is fundamentally based on the assumption that commodity prices react more strongly in the short-run than the consumer goods’ prices.

In order to test the hypothesis it is allowed for a two-good economy, and commodities and consumer goods with prices �<sup>���</sup> and �<sup>���</sup> , respectively. The substantial difference between these two goods is that consumer prices are decided in a market with a supply that adjusts to the changes in demand, while the commodity prices are decided in a market restricted in supply and with high transaction costs, due to transportation expenses. Therefore, consumer goods’ prices are sticky, whereas commodity prices are not.

The rationale for this assumption can be found in the current scenario where many low-cost producers (especially in developing countries) are generating additional supply of consumer goods, while commodity supply is constrained by natural factors. Furthermore, the speed of the adjustment depends on the fact that participants in the commodity markets are usually more equally informed than their consumer goods’ counterparts.

Graphically, the two markets can be represented as in Figure 1.

[Figure 1 about here] 4
<!-- Start of picture text --> p CPI<br>t<br>poom por<br>t+1<br><!-- End of picture text --> <!-- Start of picture text --> p = Apo! +(1—-A)ypo? 0<A<1<br>(1 + He) De-1<br>poom<br>t<br>Pr = ApeeM + (1 — Avery<br>t+1 t<br>Pesa = Apert + (1 —A)p eri<br>ApeoM + (1 —A)pEPL = ApELM + (1 — A) ErT<br>Pei pe ope = Oty) pee"<br>pei — p£P! = [AC — a) [p£TM — (1 + wpe")<br>t<br>(ppeTM)<br>t+1((1+ ,)pfol)<br>C2<br><!-- End of picture text -->
<!-- Start of picture text --> X<br>y"<br>m"<br>X,= bm<br>lp<br>AP<br>CRB — CPI<br>D,<br>i I<br>Xt<br>Il r<p Dp<br>rxp a (1 = ap)<br>r<br>p-r<br><!-- End of picture text -->
In order to perform an I(1) analysis, a nominal to real transformation has been performed. Since nominal GDP and nominal money supply show clear features of I(2) processes, they have been considered in real terms. Likewise, some transformations have been done on price indexes. On the one hand, inflation has been considered instead of the CPI index (typically I(2)); on the other hand, the difference between the CRB index and the CPI index has been taken (real commodity prices hereafter).

Real money, real GDP, inflation and real commodity prices have been taken in logs. The interest rates have been transformed into quarterly rates. Table 1 presents some descriptive statistics of the variables considered<sup>2</sup> .

# [Table1 about here]

The unit root properties of the series are tentatively investigated using two unit root tests. The first unit root test performed is the Augmented Dickey-Fuller (ADF) test, for which stationarity serves as the null hypothesis. However, it should be noted that the ADF test could fail to distinguish between a unit root and a near unit root process and it can happen that indicates that a series contains a unit root when it does not (Perron 1989). Thus, a second unit root test is adopted, namely the Kwiatkowsk, Phillips, Schmidt and Shin (KPSS) test, for which the null hypothesis is non-stationarity.

[Table 2 about here] As shown in Table 2, the results from both the tests employed confirm that all the variables in the system are integrated of order one at 5% significance level. Nonetheless, it should be remembered that such tests are not reliable in the presence of breaks or shifts in the series.

Figure 2 and 3 show the graphs of the series in levels and first differences.

[Figure 2 about here]

[Figure 3 about here] A graphical inspection of the data reveals that the assumption of constant mean does not seem appropriate for the level of the variables, whereas it does much more so for the differenced series. The assumption of constant variance seems to be approximately satisfied for the differences, even though some variability can be observed in most of the series. In order to account for the biggest departures from assumptions, three permanent blip dummies have been added to the model in correspondence of the biggest residuals. The first one takes the value one during the fourth quarter of 1984, when Ronald Reagan was re-elected as President of the US. The second one controls for the dramatic slump in inflation during the

> 2 Note that for both the CPI and CRB index the value 100 is given to the first quarter of 1983.

7
second quarter of 2006, probably due to an unexpected plunge in energy prices. The last dummy controls for the economic impacts of the terrorists attack of September 11, 2001.

Moreover, it is worth noting that the graph of the real money shows two breaks in trend. A constant increase in the variable is observed from the beginning of the sample until 1987. A period of approximately zero growth follows and lasts until 1995, when it starts increasing as fast as in the first period. Thus, the slope of the two growing trends seems to be roughly the same. Even though the introduction of two breaks has been attempted, it turned out more satisfactory to allow for trends in the levels. This should have the effect of averaging out the aforementioned breaks. Moreover, since it is not possible to know _a priori_ whether these trends cancel out in the cointegrating relations, the chosen specification allows these to be trend-stationary and have non-zero intercepts.

# **4.3. Lag Length Selection and Residual Analysis**

Table 3 shows that the Schwartz criterion (SC) suggests ��1 and the Hannan-Quinn (HQ) criterion suggests ��2. However, when imposing ��1 the other misspecifications tests become much worse, implying that the SC might have penalized too much. The LM tests in the last two columns show the left-over residual autocorrelation in each VAR(�� model and seem to accept the absence of autocorrelation for the VAR with 2 lags.

# [Table 3 about here]

Table 4 presents the results of the multivariate residual analysis. In particular the null hypothesis of no autocorrelation is rejected at both the first and the second lag. Given the relatively small sample, it is not advisable to rely on the asymptotic properties of the estimator, thus the normality assumption turns out to be relevant and it is safely accepted. Lastly the null hypothesis of no ARCH effects is accepted at both lags.

# [Table 4 about here]

Table 5 shows the results of the univariate residual analysis. The output of the ARCH and Normality tests reflect the good results of the multivariate analysis. The skewness and kurtosis statistics are close to the normal distribution values, suggesting that by inserting the three blip dummies the biggest outliers should have been controlled for.

# [Table 5 about here]

Overall, both the multivariate and univariate tests suggest that the residuals are well behaved and therefore that the model is well specified.

# **4.4. Rank Determination**

The cointegration rank is determined according to Johansen (1996) LR Trace test. When the sample is small, the asymptotic distributions are generally poor approximations to the true distributions. To secure a correct test size one can apply the small sample Bartlett 8
corrections developed in Johansen (2002). The asymptotic distribution of the rank test statistic differs depending on the deterministic components in the model and on almost any type of dummy variable<sup>3</sup> . Therefore, the safest procedure is to simulate the new critical values. Table 6 presents the Trace test results with the Bartlett corrections and the simulated critical values.

# [Table 6 about here]

The choice of the cointegration rank is not clearly defined, in fact the Trace test Bartlett corrected suggests that ��3 is accepted only at 10% significance level. Looking at the significance of the α coefficients of the third cointegration vector in Table 7 it seems that information regarding the real GDP and the real commodity prices would be neglected by choosing ��2.

# [Table 7 about here]

A graphical inspection of the cointegrating relations in Figure 4 reveals some symptom of I(2)ness. The first two cointegration relationships look fairly stationary, but the third one presents some indication of cyclical swings. However, it should be observed that the lower panel ��� _′_ ���� corrected for short-run effects of each graph is similar to the upper panel _′_ ��� ���, confirming that the I(2) problem could have been limited (see appendix for a formal I(2) rank test).

# [Figure 4 about here]

Moreover, an examination of the characteristic roots shows that the largest unrestricted root for ��2 is 0.90 and for ��3 is 0.78 (pretty far from the unit circle). This seems to confirm the presence of three common stochastic trends. Figure 5 shows the roots of the companion matrix for ��3.

[Figure 5 about here]

# **4.5. Recursive Tests**

The graphs of the recursively calculated fluctuation tests in Figure 6 show that the X- form of �̂� and �̂� are in the rejection region at the beginning of 1995, when the recursion starts. The test statistics remain at a fairly high level until approximately 1998. The recursive graphs of the �̂� suggest that the parameter of the second cointegration relation are considerably constant over the sample period. The overall test in the lower right-hand side

> 3 An exception to this are the centered seasonal dummies, which, by construction, sum to zero over time, and hence do not change the asymptotic distribution of the rank tests.

9
panel picks up the non-constancy at the beginning of the recursions. However, it should be noted that the R-form looks stable in all �̂, meaning that the instability is only in the short-run coefficients. In general, the eigenvalue fluctuation tests provide a fair picture.

[Figure 6 about here] The Max test of β Constancy is always lower than one and shows a slightly higher volatility after 2003. Figure 7 confirms what is suggested by the eigenvalue fluctuation tests, namely that the changes in the eigenvalues are due to changes in α.

[Table 7 about here]

# **4.6. Long-Run Exclusion**

The Π matrix gives tentative evidence of long-run exclusion for the variables in the system. If a variable is excludable, the coefficients in the columns must be insignificant. From the PI matrix there are no clear signs that any of the variables can be excluded from the cointegration relations.

A formal LR-test for variable exclusion has been performed. Based on the results in Table 8, it is not possible to exclude any variable at 10% significance level for ��3. However, the real commodity prices seem to be a border-line case.

[Table 8 about here]

# **4.7. Weak Exogeneity and Pure Adjustment**

The Π matrix gives preliminary evidence of weak exogeneity. If a variable is weakly exogenous, the coefficients in the rows must be insignificant; in other words, it represents a pushing force. The only variable that seems not to react to any other variables is the real money.

The formal LR-test for weak exogeneity in Table 9 shows that both real GDP and real money are weakly exogenous at 10% significance level, even though the joint exogeneity is rejected. It has been decided to carry out the analysis including them in the system in order to analyze their impact in the Γ matrix.

[Table 9 about here] Another LR-test is carried out to test for unit vector in the α matrix. In other words, it tests whether the cumulated disturbances from the i<sup>th</sup> variable do not enter the common trends (pure adjustment hypothesis). At 10% significance level Table 10 shows that the null hypothesis cannot be rejected for the long term interest rate and the real commodity prices. Thus, these can be considered pulling forces.

10
# [Table 10 about here]

# **4.8. Identification and Interpretation of the Results**

The identifications process starts from the long-run relationships. It is carried out by imposing ��1 non-testable<sup>4</sup> just-identifying restrictions on each beta vector of the unrestricted reduced VAR model with rank ��3, with no changes to the likelihood function with respect to the under identified model. Table 11 presents the estimation results that seem to suggest that the first beta vector is describing a money demand relationship with an unconventional sign on the inflation variable. The second cointegrating relationship illustrates the expected correlation between real output, real money, real commodity prices and a trend. Finally, the third stationary vector is expressing a relationship between inflation and the interest rate spread.

# [Table 11 about here]

The over-identified structure is modeled imposing restrictions accordingly to the t- value of the β vectors’ coefficients of the just-identified structure. This is accepted with a fairly large p-value of 0.642 (meaning that the stationarity of the long-run relations cannot be jointly rejected).

Table 12 permits the detection of the pulling forces for each cointegration relation. The money demand relationship is corrected by changes in inflation, whereas the real commodity prices are the only equilibrium correcting force for the second cointegrating relation. Lastly, deviations from the inflation expectations relationship are corrected by inflation itself.

# [Table 12 about here]

The short-run identification has been carried out by removing all the non-significant variables from each equation of the cointegrated VAR<sup>5</sup> . The parsimonious structure cannot be rejected with a p-value of 0.257 and is broadly consistent with the classification into pushing and pulling forces<sup>6</sup> .

The equation for the interesting variable is reported in Table 13.

# [Table 13 about here]

From the inspection of the Ώ matrix in Table 14, it is evident that some residuals are highly correlated (positively between real GDP and real money, negatively between inflation

> 4 Since we have imposed ��1 restrictions, there are zero degrees of freedom, thus restrictions cannot be tested.

> 5 Centered seasonal dummies have been left in the equations for each variable, even if insignificant.

> 6 The equilibrium correcting role of the real commodity prices for the second cointegrating relationship confirmed.

11
and real GDP, negatively between inflation and real money and positively between the two interest rates) and this would suggest a simultaneous specification of the model. Nonetheless, such analysis has not been pursued because of the problems in determining the direction of the causation between the mentioned variables.

# [Table 14 about here]

Overall, the results confirm the existence of the hypothesized long-run equilibrium relationship between real money and real commodity prices, with an effect from real output. Moreover, there is evidence that the real commodity prices are the only equilibrium correcting variable.

It can be concluded that in order to restore the long-run equilibrium when there is a real excess (lack) of liquidity, the real commodity prices need to increase (decrease). Such increase (decrease) can be achieved through an increase (decrease) in the commodity prices stronger (smaller) than the increase (decrease) in the consumer goods’ prices, generating a larger spread between the two as in Figure 8.

# [Figure 8 about here]

The Moving Average (MA) representation of the data for ��3 corresponds to ����3 common trends. Since ����1 �2 just-identifying restrictions are imposed on each vector, estimates are not unique and the likelihood function is unchanged. However, the space spanned by � _┴_ and � _┴_ is uniquely determined, so that the estimated long-run impact matrix C is unique<sup>7</sup> . The normalization has been placed on the variables with the highest residual standard errors, namely real GDP, real money and real commodity prices.

The cumulated empirical shocks to the real GDP have had significant and high negative effects on the real commodity prices. The inverse is true, but the impact is much more moderate. The cumulated shocks to real money have had positive effects on inflation, as well as the cumulated shocks to short-term interest rate on long-term term one and vice versa. Moreover, the cumulated shocks to long term interest rate have had positive effects on inflation. Likewise, the cumulated shocks to inflation have had similar positive effects on both the interest rates. Finally, the cumulated shocks to all the variables have had a positive effect on themselves. It seems that the long-term interest rate is purely adjusting (consistently to the previous findings).

In order to impose the over-identifying restrictions on α, joint weak exogeneity for real money and real GDP is tested keeping fixed the restrictions on the β vectors. Since the hypothesis turns out to be rejected at 10% significance level, a zero row in α is imposed only for the real money, for which the null hypothesis cannot be rejected with a p-value of 0.505. The C matrix of the over-identified MA representation is broadly consistent with the results obtained for the just-identified structure.

As a robustness check, the CRB has been replaced with the Conference Board’s Sensitive Materials Index (SENSI). This comprises raw materials and metals but excludes food and energy. The results remain broadly the same as before.

> 7 As when imposing just-identifying restrictions on the cointegrating relationships, the PI matrix was uniquely determined, albeit � and β vectors were not.

12
# **5. Conclusions**

Commodity prices are currently seen as one or the main source of current inflationary pressures and there seems to exist, as discussed by Frenkel (2006), a linkage between increases in commodity prices in commodity exporting countries and monetary policy changes in advanced industrial economies. This, as suggested, would defy the common knowledge that changes in commodity prices are solely impacted by developments occurring in the commodity markets.

The aim of the paper is to identify the nexus between the excess of liquidity in the US and commodity prices over the period 1983-2006 within a cointegrated VAR framework and in particular at testing whether the commodity prices react more powerfully than the consumer goods’ prices to changes in real money balances.

The results provide empirical evidence on the magnitude of the reaction of commodity and consumer goods’ prices to an increase in real money. In particular, a long-run equilibrium relationship between real money and real commodity prices has been found, with an effect from real output. The two variables of interest show positive and significant correlation.

Moreover, real money seems to be a weakly exogenous variable and therefore is a pushing force (away from the equilibrium), whereas real commodity prices are the only equilibrium correcting variable to such cointegration relationship, or pulling force.

Therefore, in order to restore the long-run equilibrium when there is a real excess (lack) of liquidity, the real commodity prices need to increase (decrease). Such increase (decrease) can be achieved through an increase (decrease) in the commodity prices stronger (smaller) than the increase (decrease) in the consumer goods’ prices, generating a larger spread between the two.

The results have important policy implications. More specifically, if the magnitude of the reaction is due to the fact that consumer goods’ prices are slower to react, then their longrun value can be predicted with the help of the commodity prices. In other words, the extent of the rise in the commodity prices acts to predict subsequent changes in the price of the other goods, namely the consumer goods, whose price is initially unchanged.

Moreover, the results also support the idea that monetary policy cannot only focus on the core CPI and ignore developments in the commodity market. In fact, if commodity prices are very high it might be the case that monetary policy is loose; therefore they should be taken into account as a useful monetary indicator. This conclusion is particularly relevant to those countries that are adopting an inflation targeting regime which target is the CPI.

# **Acknowledgments**

I wish to thank Katarina Juselius, Morten Tabor and Paolo Paruolo for their kind support in carrying out the econometric analysis. A special thank to Paolo Paruolo for providing me with important comments. Note that all mistakes and opinions expressed in the paper belong to the author only.

# **References**

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