1 | P a g e

Relations between coffee world market price and

retail price in USA:Application of the Vector Error Correction Model

By: Yohannes Mengesha W/Michael (PhD Fellow)

Thursday June 2, 2014

Department of Agri-Economics

Haramaya University

Summary

With reference to monthly coffee price data (Jan. 2006-Apr. 2014) for the world

indicator prices and retail prices in the US, this paper analyzes how the variations

observed at the coffee world market price level pass on the coffee retail price.

Unit root tests of the series under study reveal that all the series are non-

stationary at level and stationary after first difference. The result of Johansen

test indicates the existence of one cointegration relation between the variables and

there is long-term dynamics between coffee retail and world price. Granger causality

test indicates that there is transmission of price signals from the world market to

the local retail market.

Keywords: coffee world market price, coffee retail price in USA, transmission.

1. Background

This paper examines price transmission from the world coffee market to local retail

markets of the US. In the analysis, the study used the monthly coffee price data

(Jan. 2006-Apr. 2014). World indicator prices were collected from the international

coffee organization (ICO)www.ico.org and the retail prices were collected from the

U.S. Bureau of Labor Statistics www.bls.gov.

The world coffee price, namely the ICO Composite Indicator Price is daily and

monthly calculated from different groups prices (Colombian Milds, other Milds,

Brazilian Naturals and Robustas) according to a precise distribution, while the

retail prices are average prices of coffee pack (250 g) collected in representative

cities and shops by agents of U.S. Bureau of Labor Statistics.

The paper observed the transmission of the world coffee price variations to the

retail coffee price and studied the correlation importance between the two prices

series with the help of the Vector Error Correction Model.

All prices are converted in to standard unit (US cents/lb) and currency in order to

make comparison.

2.The model

The price transmission analysis is at world market to consumers in the USA. The

model specification of this study follows the dynamic approach adopted by Baffes and

Gardner (2003) and Krivonos (2004). An autoregressive distributed lag (ARDL) model

includes the lagged value of the domestic price and world price as independent

variables specified as follows:

........................................1

This can be rearranged to yield an error specification

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........................................2

Equation (2) describes the variation of domestic price Pd in terms of its reaction

to fluctuations in the world price Pw and adjustment to own long-term equilibrium. δ

captures the immediate responsiveness of the domestic price to changes in the world

price, and θ is an error-correction term, which measures the speed of adjustment of

Pd to the long-run equilibrium

2.1. Stationarity

Stochastic process is said to be stationary if its mean and variance are constant

over time(do not depend on time or do not change as time changes). Moreover, the

value of the covariance between the two time periods depends only on the lag between

the two time periods and not on the actual time.

In the time series literature, a stochastic process that satisfies such conditions

is known as weakly stationary, or covariance stationary.

Hence, for the ECM to be valid, it needs to be ensured that the time series used in

the estimation is stationary. The stationary properties of the price-time series

(bothlevels and first differences) are tested using the augmented Dickey-Fuller

(ADF) procedure. In each case the hypothesis tested is that the time series follows

stationary processes with the unit root.

Rejecting the null hypothesis allows the time series to be tested as stationary. In

addition, the existence of a long-term cointegration relationship between world

price, and consumer prices is tested in order to check the validity of the error-

correction model.

2.2. Co-integration

If two or more series are integrated together (i.e. in the time series sense) but

some linear combination of them has a lower order of integration, then the series

are said to be co-integrated. A common example is where the individual series are

first-order integrated (I (1)) but some (cointegrating) vector of coefficients

exists to form a stationary linear combination of them.

The purpose of the co-integration test is to determine whether a group of non-

stationary series is co-integrated or not. Tests for co-integration assume that the

co-integrating vector is constant during the period of study. In reality, it is

possible that the long-run relationship between the underlying variables change

(shifts in the co-integrating vector can occur). The reason for this might be

technological progress, economic crises, changes in people’s preferences and

behavior, policy or regime alteration and organizational or institutional

developments. This is especially likely to be the case if the sample period is long.

In simple words, we search for the existence of the number of co-integrated vectors,

r, within Johansen and Juselius’ (1990) framework. Using their technique, we

implement a k-dimensional VAR of the following form:

.............................,,,,,,,,..(3)

Where P is a (2 x 1) vector matrix of the coffee world price prices and retail

price respectively while e are Gaussian residuals. The VAR in Equation 3 can be re-

parameterized into a VECM form as:

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..................,,,,..(4)

Where ∏ is a (2x2) matrix of long-run and adjustment parameters, B is a (2x2)

matrix of the short-run parameters, Ԑ is the vector of residuals and j is the

number of lags. Following Johansen’s procedure, the co-integration relationship

between prices was examined under equation 4, where each price is a function of its

own lagged values and the lagged values of the other price series. The trace and

maximum eigenvalue statistics are used to determine the rank of ∏ and to reach a

conclusion on the number of co-integrating equations, r, in our bivariate VAR

system.

2.3. Granger causality tests

One of the main uses of VAR models is forecasting. The structure of the VAR model

provides information about the forecasting ability of a variable or a group of

variables. The Grangercausality test helps us to measure whether one variable can be

used to forecast the other.

Therefore, the paper implements a complete dynamic Granger Engle VECM test of the

following form (as indicated in Reziti and Panagopoulos, 2008):

∆P = µ +

1

1

n

i β ∆P +

2

1

n

i β ∆P + ᴨ Z + e ,,,,,,,,,,,,,,,,,,,,,,

(5)

∆P = µ +

1

1

n

i β ∆P +

2

1

n

i β ∆P + ᴨ Z + e

,,,,,,,,,,,,,,,,,,,,,,(5’)

Where Z and ᴨ Z are adjustment or error correction terms whereas ᴨ and ᴨ are

their respective coefficients and the β are short-run coefficients.

The set of hypotheses and options which are now available are as follows:

(a) ᴨ 0 and ᴨ 0 (a feedback long-run relationship between the two variables)

(b) ᴨ = 0 and ᴨ 0 (price of retail price causes world price in the long-run)

(c) ᴨ 0 and ᴨ = 0 (world price causes price of retail coffee in the long-run)

For testing the three alternative options, a weak exogeneity test is implemented

according to Johansen’s (1992) methodology.

2.4. Symmetry/asymmetry of price transmission

Asymmetric price transmission is tested to check whether price increases are passed

through to the other price as rapidly as price decreases with the help of an

asymmetric ECM. In general, as indicated in Minot (2011), the Error Correction

Model, including many lags, can be presented as shown by equation 5. That is;

∆P = µ +

1

1

n

i β ∆P +

2

1

n

i β ∆P + ᴨ Z + e ....................(7)

Given the above equation, the procedure of testing for asymmetry price transmission

requires the creation of dummy variable from the error correction term, Z for

positive and negative adjustments to shocks. Splitting the error correction term

into positive and negative components (i.e. positive and negative deviations from

the long-term equilibrium as Z and Z ) makes it possible to test for asymmetric

price transmission according to Meyer and Von Cramon Taubadel, (2004). Hence, the

equation of for symmetry analysis can be stated as:

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∆P = µ +

1

1

n

i β ∆P +

2

1

n

i β ∆P + ᴨ Z + ᴨ Z + e ...... (7)

Where Z measures the movement towards equilibrium by the cofee retail price when

there is a negative shock to world price (or a decrease in world price) and Z

measures the movement viseversa.

3. Results

3.1. Stationarity

The results of the stationarity tests conducted for the price

variables are reported in Table 1 and 2 for the world indicator

price and consumer prices in USA respectively.

As can be seen from the tables below, the ADF test statistics in absolute value is

1.171 for the world indicator price and 0.828 for the consumer price.These values

are less than the critical values at 1%,5% and also 10%.

This tells us that both prices are unit root processes(i.e. they are nonstationary

processes). Thus, the ADF test does not reject the null hypothesis that

the price series follow a unit root process.

Table 1: Stationarity of world prices

Dickey-Fuller test for unit root Number of obs = 99

---------- Interpolated Dickey-Fuller ---------

Test 1% Critical 5% Critical 10% Critical

Statistic Value Value Value

------------------------------------------------------------------------------

Z(t) -1.171 -3.511 -2.891 -2.580

------------------------------------------------------------------------------

MacKinnon approximate p-value for Z(t) = 0.6858

.

Table 2: Stationarity of retail prices

Dickey-Fuller test for unit root Number of obs = 99

---------- Interpolated Dickey-Fuller ---------

Test 1% Critical 5% Critical 10% Critical

Statistic Value Value Value

------------------------------------------------------------------------------

Z(t) -0.828 -3.511 -2.891 -2.580

------------------------------------------------------------------------------

MacKinnon approximate p-value for Z(t) = 0.8109

Since the prices are found to be nonstationary at levels, we generated the first

differences of each prices and have run the Dickey-Fuller test once again to check

whether the unit root problems are resolved.

Aas anticipated, testing the same hypothesis for first differences

allowed the rejection of the unit root hypothesis at 1% level of

significance for both types of coffee prices (Table 3 & 4).

Table 3: Stationarity of world prices after first differnecing

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Dickey-Fuller test for unit root Number of obs = 98

---------- Interpolated Dickey-Fuller ---------

Test 1% Critical 5% Critical 10% Critical

Statistic Value Value Value

------------------------------------------------------------------------------

Z(t) -6.577 -3.513 -2.892 -2.581

------------------------------------------------------------------------------

MacKinnon approximate p-value for Z(t) = 0.0000

Table 4: Stationarity of retail prices after first differnecing

Dickey-Fuller test for unit root Number of obs = 98

---------- Interpolated Dickey-Fuller ---------

Test 1% Critical 5% Critical 10% Critical

Statistic Value Value Value

------------------------------------------------------------------------------

Z(t) -10.854 -3.513 -2.892 -2.581

------------------------------------------------------------------------------

MacKinnon approximate p-value for Z(t) = 0.0000

.

The above results lead to the conclusion that price differentials

can be used in the ECM.

3.2. Cointegration between prices

Turning to the long term cointegration between the consumer and

world prices, the Johansen (1991) cointegration test is applied..

However, before testing for cointegration, the number of lags to include in the

model was specified using the lag Selection-order criteria (LR, FPE, AIC, HQIC and

SBIC) as presented in the Table 5 below.

Table 5: Lag Selection-order criteria

Sample: 5 - 100 Number of obs = 96

+---------------------------------------------------------------------------+

|lag | LL LR df p FPE AIC HQIC SBIC |

|----+----------------------------------------------------------------------|

| 0 | -1052.58 1.2e+07 21.9704 21.992 22.0238 |

| 1 | -712.767 679.62 4 0.000 10922.7 14.9743 15.0391 15.1346 |

| 2 | -703.352 18.83* 4 0.001 9758.94 14.8615 14.9695* 15.1286* |

| 3 | -698.968 8.7679 4 0.067 9684.39* 14.8535* 15.0047 15.2275 |

| 4 | -696.157 5.622 4 0.229 9933.09 14.8783 15.0726 15.3591 |

+---------------------------------------------------------------------------+

Endogenous: indicatorprice consumerprice

Exogenous: _cons

As three of the five criteria (LR, HQIC and SBIC) suggested that two lags should be

used in the estimation of the co-integration equation, the Johansen tests for

cointegration was computed to determine the number of co-integration equations.

Table 6 provides information about the sample, the trend specification, and the

number of lags to be included in the model.

Table 6: Johansen tests for cointegration

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Trend: constant Number of obs = 98

Sample: 3 - 100 Lags = 2

-------------------------------------------------------------------------------

5%

maximum trace critical

rank parms LL eigenvalue statistic value

0 6 -729.54913 . 26.1143 15.41

1 9 -717.84739 0.21244 2.7108* 3.76

2 10 -716.49199 0.02728

-------------------------------------------------------------------------------

5%

maximum max critical

rank parms LL eigenvalue statistic value

0 6 -729.54913 . 23.4035 14.07

1 9 -717.84739 0.21244 2.7108 3.76

2 10 -716.49199 0.02728

-------------------------------------------------------------------------------

As can be seen in the above Table, both the trace and maximum statistic at r = 0,

26.1143 and 23.4035, exceed their respective critical values of 15.41 and 14.07.

Both trace and max tests are telling the same dicision and it is double confirmed

that the variables are cointegrated, which allows us to reject the null hypothesis

of no cointegrating equations.

The resuls also indicate that the two prices have a considerable long-run

relationship and are moving together in the long run. Hence as we can be sure that

there is atleast one cointegratibg equation in our model, we can now use the Vector

Error Correction Model (VECM). The “*” by the trace statistic at r = 1 indicates

that this is the value of r selected by Johansen’s multiple-trace test procedure.

3.3. Analysis of causality between the two price series

Once the presence co-integration between the two price series is ensured, the

question of which price causes the other was answered by this test of causlity,

analyzed using Engel Granger - Vector Error Correction Model. The estimation result

is presented in table 7.

Table 7 shows that, in our estimation of the VECM, there are two types of parameters

of interest; including the adjustment and the short-run coefficients. The

coefficient on price of coffee retail price, in the co-integrating equation is

statistically significant, as are the adjustment parameter shown in table 7. The

adjustment parameter on price of retail price (ie D_consumer)has coefficient of -

.9177752 and P-value of 0.0000 implying that it is significant at 1% level of

significance.

On the other hand, the adjustment parameter on coffee world price (ie

D_indicator)has coefficient of .0883406 and P-value of 0.235, implying that it is

not significant. This indicates that we have one way of causality that price of

world price causes price of retail price.

Table 7: Vector error-correction model

Sample: 4 - 100 No. of obs = 97

AIC = 15.07402

Log likelihood = -722.0899 HQIC = 15.17061

Det(Sigma_ml) = 10023.6 SBIC = 15.31291

Equation Parms RMSE R-sq chi2 P>chi2

----------------------------------------------------------------

D_consumerpric~1 4 13.3894 0.6266 156.0706 0.0000

D_indicatorpri~1 4 7.80229 0.2058 24.0956 0.0001

----------------------------------------------------------------

------------------------------------------------------------------------------

7 | P a g e

| Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

D_consumer~1 |

_ce1 |

L1. | -.9177752 .1277475 -7.18 0.000 -1.168156 -.6673947

|

consumerpr~1 |

LD. | -.1791781 .0896892 -2.00 0.046 -.3549656 -.0033906

|

indicatorp~1 |

LD. | -.8254287 .1827206 -4.52 0.000 -1.183554 -.4673029

|

_cons | .0180914 1.360501 0.01 0.989 -2.648442 2.684625

-------------+----------------------------------------------------------------

D_indicato~1 |

_ce1 |

L1. | .0883406 .0744411 1.19 0.235 -.0575613 .2342425

|

consumerpr~1 |

LD. | -.0657955 .0522637 -1.26 0.208 -.1682306 .0366395

|

indicatorp~1 |

LD. | -.3920219 .1064751 -3.68 0.000 -.6007092 -.1833346

|

_cons | .1879521 .7927922 0.24 0.813 -1.365892 1.741796

------------------------------------------------------------------------------

Cointegrating equations

Equation Parms chi2 P>chi2

-------------------------------------------

_ce1 1 16.19943 0.0001

-------------------------------------------

3.4. Symmetry/asymmetry of price transmission between the two price series

Existence of symmetry price transmission refers to the situation that the magnitude

of the effect of increase in price of world price (on retail price of coffee) is

equal to that of the fall in world price.

The empirical result of the analysis indicates that there exists symmetry in price

transmission between the two price series, as shown in table 8. This was analyzed in

such a way that coefficients of the adjustment parameters of the co-integrating

equation in our VECM estimation were decomposed into positive and negative

adjustments thereby comparison of extent of variation between the two adjustments

was made using joint F-statistic.

The analysis was carried out taking retail price as dependent variable whereas world

prices are taken as independent variable.

Table 8: Variance ratio test

------------------------------------------------------------------------------

Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]

---------+--------------------------------------------------------------------

adju~lus | 46 12.51517 1.473856 9.996175 9.546677 15.48367

adju~nus | 53 -11.40706 1.330922 9.689255 -14.07775 -8.73637

---------+--------------------------------------------------------------------

combined | 99 -.2916778 1.555387 15.47591 -3.378293 2.794937

------------------------------------------------------------------------------

ratio = sd(adjustplus) / sd(adjustminus) f = 1.0644

Ho: ratio = 1 degrees of freedom = 45, 52

Ha: ratio < 1 Ha: ratio != 1 Ha: ratio > 1

Pr(F < f) = 0.5881 2*Pr(F > f) = 0.8239 Pr(F > f) = 0.4119

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Table 8 presents estimation result for the comparative analysis. In the table it is

shown that standard standard error and deviation of the positive adjustments are

1.473856 and 9.996175 respectively, with 46 observations; whereas that of the

negative adjustments are 1.330922 and 9.689255 respectively, having 53 observations.

The result of estimation of the F-statistic was found to be 1.0644, implying that

there is symmetric price transmission.

4. Conclusion

Using cointegration analysis and an error-correction model (ECM), this paper

examines price transmission from the world coffee market to local retail markets of

the US. The consumer price and world indicator prices are the two major time-series

prices on which the analysis centres. Each price series is based on monthly prices

that extend from January 2006 to April 2014.

Unit root tests of the series under study reveal that all the series are non-

stationary at level and stationary after first difference. The result of Johansen

test indicates the existence of one cointegration relation between the variables and

there is long-term dynamics between coffee retail and world price. Granger causality

test indicates that there is transmission of price signals from the world market to

the local retail market.