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Are Price Adjustments in Spatially Separated Markets Non Linear and/or Asymmetric?

Evidence from Non Parametric Tests on the EU Pork and Poultry Markets

1. Introduction

The analysis of spatial price relationships has been long used in economics to assess the

degree of integration of geographically separated markets. For well-functioning (integrated)

markets spatial arbitrage activities will ensure that price shocks occurring in one market will

elicit responses in other markets; in equilibrium, the price of a homogeneous good in

separated locations will be, at most, equal to transportation costs (weak version of the LOP).

However, when localized markets are not well integrated, profitability opportunities will not

be fully exploited resulting, thus, into efficiency losses (e.g. Ardeni, 1989; Goodwin and

Schroeder, 1991; Asche et al., 1999; Ghosh, 2003).

Recently, research on price transmission between spatially separated food markets has

focused on potential non linearities and asymmetries. Non linear price adjustments have been

associated with the presence of transaction costs (e.g. transportation and freight costs,

spoilage, and risk premium). Such costs may create a band of inactivity (neutral band) of

price differentials within which spatial arbitrage activities are not profitable. Asymmetries of

price transmission are present when the speed of response depends on whether shocks are

positive or negative.

The majority of empirical studies on non linearities and asymmetries of price

adjustments in food markets has employed parametric models like the Threshold

Autoregressive (TAR) and the Threshold Vector Error Correction Model (TVECM)

(e.g.Goodwin and Grennes, 1998; Goodwin and Piggot, 2001; Balcome et al., 2007). Serra et

al. (2006a) and Serra et al. (2006b), however, argued that the parametric models may turn out

to be overly restrictive or unrealistic for two reasons: first, they require assumptions about the

true nature of price adjustments, and second, they rely on constant over time inactivity

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(transaction costs) bands. The non parametric (smoothing) regression techniques, in contrast,

allow the data to determine the shape of the relationship of interest and they dispense with the

assumption of stationary thresholds. Hence, they are more suitable for investigating non

linearities and asymmetries of spatial price adjustments.

Serra et al. (2006a) applied non parametric techniques in their study of spatial price

relationships in four European pork markets (Spain, Germany, Denmark, and France). Serra et

al. (2006b) also used non parametric techniques in their study of spatial price relationships in

four US egg markets (Baltimore, Boston, Dubuque, and New York). The authors of those

earlier works argued that the non parametric analysis provided evidence that deviations from

long-run equilibrium tend to be arbitraged in a non linear and a non symmetric fashion. The

arguments by Serra et al. (2006a) and Serra et al. (2006b), however, were based exclusively

on the visual inspection of the non parametric fits. For the four European pork markets the

non parametric fits had indeed non linear portions which, nevertheless, in all cases were

located at the very extremes of the respective distributions of price differentials; at the

interior, price adjustments appeared to be linear and symmetric.

The non parametric (smoothing) techniques are certainly less restrictive compared to the

parametric ones. However, near the boundary of the observation interval fewer observations

are averaged and the kernel weights become asymmetric. As a result, the accuracy of any

smoothing technique at the extreme parts of the distribution diminishes, and the bias and the

variance of the estimates can be affected (Hrdle, 1989). One, therefore, has to wonder

whether the non linearities and asymmetries reported by Serra et al. (2006a) is a genuine

feature of the price transmissions or just an artifact of the boundary effect.

To shed some light on this issue the present paper employs a non parametric

specification test proposed by Horowitz and Hrdle (1994). Under the null, price adjustments

are linear (and symmetric) while under the alternative they are given by an unknown smooth

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function (allowing, thus, for transaction cost frictions which may result into non linearities

and asymmetries). Serra et al. (2006a) emphasized the need for replication of their findings

through methodological improvements and extensions to other markets and meat products.

This study considers fourteen EU markets and two meats (pork and poultry). Moreover, it

relies on longer time series (for the majority of markets weekly data for the period 1991 to

2006 are available, while the earlier study relied on data for the period 1994 to 2004). In what

follows section 2 presents the analytical framework, section 3 the data and the empirical

results, while section 4 offers conclusions.

2. Analytical Framework

Let itp and jtp be the prices in markets i and j at time t. As in Serra et al. (2006a)

and Serra et al. (2006b) we assume that the adjustment in the price differential in t,

)()( 11 = jtitjtitt ppppY , depends solely on the price differential in 1t ,

).( 111 = jtitt ppX Therefore, with linearity and symmetry, adjustments can be

represented with a simple autoregressive model of price differentials

)1(1 ttt eXY += ,

where 0 < is the speed-of-adjustment parameter and et is a stationary and zero-mean error

term. Given that (1) can be restrictive or unrealistic one may consider the following

relationship between price adjustments and lagged price differentials

)2()( 1 ttt XmY += ,

where m is an unknown smooth function and t is a stationary and zero-mean error. The

regression function of (2) (that is, the conditional expectation of tY given 1tX ) can be

estimated by an appropriate non parametric (smoothing) technique.

For the problem at hand one wishes to test the hypotheses:

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)()/(:)3(

)/(:

111

110

=

=

ttt

ttt

XmXYEH

XXYEH ,

where under the null price adjustments are linear and symmetric and under the alternative

they are non linear and asymmetric. Horowitz and Hrdle (1994) developed the non

parametric HH test to select between a parametric Single Index Model (SIM) (probit or logit)

and a semiparametric one. That test can be also used to assess whether the functional of

interest is linear or non linear.1 The HH test statistic is computed as

)4())()((2

1

PNPPT

t

ttYYYYXwhHH

=

= ,

whereP

Y

andNP

Y

are the parametric and the non parametric estimate, respectively, of the

regression function; h is the bandwidth parameter used for estimatingNP

Y

, T is the number of

observations, and w is function which trims 5 percent of the extreme values of the

conditioning variable to improve the tests power. In (4), the first difference term measures

the deviation of the parametric fit from the true realizations, while the second difference term

measures the distance between the regression values obtained under the null and the

alternative. The residuals of the parametric fit are blown up by large differences between the

parametric and the non parametric fit. Therefore, for the null hypothesis to be true, the

residuals of the parametric must be small enough to accommodate large differences in the two

alternative fits (Hrdle et al., 1999). The HH test statistic is distributed asymptotically as

( )0,1N . The test is one-sided as the statistic diverges to + under the alternative

hypothesis against which it is consistent. The non parametric regression function has been

estimated here using the Nadaraya-Watson estimator, defined as

1 Delgado and Miles (1997) applied the HH test to verify whether the demand for food in Spain is consistent with

PIGLOG preferences (linearity of budget shares in the logarithm of income).

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)5(

)(

)(

)()(

2

1

2

1

=

=

==T

t

t

T

t

t

t

NP

h

xXK

Yh

xXK

xmxY ,

whereKis an appropriate kernel smoother (Hrdle, 1989).

3. Data and Empirical Results

The data for the present study have been obtained from the European Commission. For

10 out of the 14 countries considered, prices are available from the first week of 1991 to the

last week of 2006. Exceptions are Austria, Finland, and Sweden for which the earliest

observations go back to the first week of 1995 and Portugal (only for poultry) where the

earliest observation goes back to the first week of 1993. For both pork and poultry Germany

has been selected as the benchmark country because it is a central EU market and, thus, it is

expected to lead the price formation process.2 All non parametric estimations have been

carried out using the Quartic Kernel, while the bandwidth parameters have been selected

using cross-validation (Hrdle, 1989).

3.1 Price Transmission in the Pork Markets

Prior to the parametric and the non parametric estimation of the regression fits all price

differentials (e.g. 1 1, 1,2,...,13it GEt p p i = ) have been subjected to ADF tests for unit roots in

order to avoid potential spurious regressions. Table 1 presents the ADF test results. In all

cases, the null of unit root is strongly rejected by the data. Figures A.1 to A.13 in the

Appendix present the parametric and the non parametric regression fits. 3 For all countries but

the Netherlands the non linear portions of the non parametric fits are generally located at the

very lower end of the respective price differential distributions in 1t . Also, for most cases,

2 The same benchmark has been used by Serra et al. (2006a), as well. Note that direct trade between two markets

is not necessary for transmission of price shocks. The reason is that the two markets can be integrated though

third markets (e.g. two exporters that do not trade with each other but export to the same country) (Barrett andLi, 2002).3 The dashed lines represent the parametric and solid lines the non parametric fits.

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the parametric fits are almost indistinguishable from the non parametric ones over the parts of

the distributions where the overwhelming majority of observations lie.

Table 2 presents the HH test results. The null hypothesis (linearity and symmetry of

price adjustments) is rejected at the 5 percent level only for the Netherlands. For countries

where the null cannot be rejected, the parametric approach yields more efficient estimates

than the non parametric one. Here, the parameter of interest is the speed-of -adjustment. Table

3 presents the parametric estimates of along with the respective t-statistics. The estimates

have the theoretically expected sign (high price differential in 1t works towards a reduction

in the price differential during the next period) and they are statistically significant at any

reasonable level. They are, however, generally quite low. Indeed, the highest-speed-of

adjustment coefficient is 0.23 (Austria) and the lowest 0.017 (Greece) suggesting that the

drive to equilibrium price differentials may take considerable amount of time. It is

remarkable, that even for Denmark which has a common border and intense trade of with

Germany the speed-of-adjustment coefficient is only 0.026. For the Netherlands, price

differentials in the range 20 to 40 appear to be corrected faster than those in the range 0 to

20; also, the behavior of the non parametric fit is quite erratic for price differentials 40 and

lower suggesting even perverse (positive) responses for a range of values around 50.

3.2 Price Transmission in the Poultry Markets

As in the case of pork, the price differentials for poultry has been subjected to ADF for

unit roots. Table 4 presents the ADF test results. For six countries (Austria, Finland, Ireland,

the Netherlands, Sweden, and the UK) the null of unit root cannot be rejected at the 5 percent

level. Given the presence unit roots in almost half of the series there were two options

available: either not to pursue estimation of parametric and non parametric regressions for the

above mentioned countries or to search among them for other benchmarks hoping to obtain

additional stationary price differentials. Given that the objective has been to consider as many

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models of price differentials as possible we took the second option (which is admittedly ad

hoc). The ADF tests suggested that the price differentials between Sweden and the UK,

Sweden and Finland, and the Netherlands and Austria do not contain units. 4 Therefore, the

HH-test has been performed for 10 price differentials in total (for Belgium, Denmark, Spain,

Greece, France, Italy, and Portugal, with Germany as benchmark; for Finland and the UK

with Sweden as benchmark; and for Austria with Netherlands as benchmark).

Figures B.1 to B.10 in the Appendix present the parametric and the non parametric

regression fits, while Table 5 presents the HH test results. The null hypothesis (linearity and

symmetry of price adjustments) is rejected at the 5 percent level only for the Spain (with

Germany as benchmark) and for Finland (with Sweden as benchmark). Again, for countries

where the null cannot be rejected, the parametric approach yields more efficient estimates

than the non parametric one. Table 6 presents the parametric estimates of along with the

respective t-statistics. The estimates have the theoretically expected sign but they are

generally quite low. Indeed, the highest speed-of-adjustment coefficient is 0.14 (Portugal)

and the lowest 0.005 (Greece). It is remarkable that for Denmark, Belgium, and France,

which have common borders with Germany, the speed-of-adjustment coefficients are well

below 0.10. For Spain, price differentials below 30 appear to be corrected faster than those

above 15; for price differentials, however, between 30 and 15 (where the bulk of

observations lie) the parametric and the non parametric fit almost coincide. For Finland,

differences between the two fits exist both at the upper as well as at the lower part of the

distribution of price differentials in 1t .

4. Conclusions

4

The ADF test statistics (with constant and linear trend) for the price differentials between Sweden and Finlandare 4.177 and 4.238, respectively, while for the price differential between the Netherlands and Austria is

3.628.

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The objective of this paper has been to assess price transmissions in spatially separated

pork and poultry markets in the EU, with emphasis on non linearities and/or asymmetries.

This has been pursued using non parametric regression techniques along with a specification

test for the parametric AR(1) model of price adjustments. The parametric AR(1) model has

been rejected in favor of a non-linear and/or asymmetric smooth model of transmissions in

only 3 (1 for pork and 2 for poultry) out of the 23 cases considered. The test results have been

generally in line with the visual comparison of the respective parametric and non parametric

fits; the non-linear portions of the latter have been almost invariably located at the very

extremes of the price differential distributions, while quite often the two competing fits have

been indistinguishable from each other over the parts of the distributions where the majority

of observations lie.

The idea of the presence of an inactivity (transaction costs) band within which price

differentials behave like a random walk process is intuitively appealing. But when a price

differential lies in that band, the markets are in competitive spatial equilibrium. As noted by

Barrett and Li (2002) the notion of competitive spatial equilibrium is a different (although

related) notion to that of market integration, where the latter is defined as tradability and

transmission of price shocks between markets. In the light of the arguments by Barrett and Li

(2002), the failure of the HH test to reject the null should not be necessarily interpreted as

evidence against the existence of inactivity bands. The reason is that it may simply indicate

that, over the period considered, the EU pork and poultry markets only rarely attained

competitive spatial equilibrium. In such case, possible inactivity bands will not be easily

captured by statistical designs because of the lack of an adequate number of observations

within those bands. As far as the market integration is concerned, price transmission appears

to take place but in most cases the speed-of-adjustment is quite low. The latter certainly raises

questions about how well integrated are the pork and the poultry markets in the EU.

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The present work may be extended in a number of directions. First, future works may

consider price transmissions in other food commodities; second, they may apply alternative

non parametric tests and compare their results; third, they may consider different

specifications of the parametric null (e.g. AR(p) models instead of AR(1)).

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References

Ardeni., P. (1989). Does the Law of One Price Really Hold for Commodity Prices? American

Journal of Agricultural Economics, 71:661-669.

Asche, F., Bremnes, H., and C. Wessels (1999). Product Aggregation, Market Integration and

Relationships Between Prices. American Journal of Agricultural Economics, 81:568-81.

Balcome, K., Bailey, A., and J. Brooks (2007). Threshold Effects in Price Transmission.

American Journal of Agricultural Economics, 89:308-323.

Barrett, C., and J.R. Li (2002). Distinguishing Between Equilibrium and Integration in Spatial

Price Analysis.American Journal of Agricultural Economics, 84:292-307.Delgado, M., and D. Miles (1997). Household Characteristics and Consumption Behavior: A

Non Parametric Approach.Empirical Economics, 22:409-429.

Ghosh, M. (2003). Spatial Integration of Wheat Markets in India: Evidence from

Cointegration Tests. Oxford Development Studies, 31:159-71.

Goodwin, B., and T. Schroeder (1991). Cointegration Tests and Spatial market linkages in

Regional Cattle Markets.American Journal of Agricultural Economics, 73:452-464.Goodwin, B., and T. Grennes (1998). Tsarist Russia and the World Wheat Market.

Explorations in Economic History, 39:154-182.Goodwin, B., and N. Piggot (2001). Spatial Market Integration in the Presence of Threshold

Effects.American Journal of Agricultural Economics, 83:302-317.Hrdle, W. (1989).Applied Non Parametric Regression. Cambridge University Press.

Hrdle, W., Muller, M., Sperlich, S., and A. Werwatz (1999). Non and Semiparametric

Modeling. Berlin: Humboldt-Universitt du Belrin.Horrowitz, J., and W. Hrdle (1994). Testing a Parametric Model Against a Semiparametric

Alternative.Econometric Theory, 10:821-848.Serra, T., Gil, J., and B. Goodwin (2006a). Local Polynomial Fitting and Spatial Price

Relationships: Price Transmission in EU Pork Markets. European Review ofAgricultural Economics, 33: 415-36.

Serra, T., Gil, J., and B. Goodwin (2006b). Non Parametric Modeling of Spatial Price

Relationships.Journal of Agricultural Economics, 57:501-22.

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Table 1. ADF Test Results on Pork Price Differentials*

Country Empirical Value

of the Test

Statistic


of the Test

Statistic

Austria -8.238 Ireland -6.225

Belgium -5.452 Italy -4.845Denmark -7.059 Netherlands -7.122

Spain -7.7 Portugal -6.447

Greece -5.676 Sweden -4.416

Finland -4.122 United Kingdom -6.205

France -8.581* The ADF regression includes constant and linear trend;

the lags have been selected optimally using the Schwartz criterion;

the 5 percent critical value is -3.145.

Table 2. HH Test Results on Pork Price Differentials*


of the Test

Statistic


of the Test

Statistic

Austria -0.26 Ireland 0.7

Belgium 0.43 Italy 0.02

Denmark 1.03 Netherlands 3.19

Spain 0.23 Portugal 0.16Greece -0.92 Sweden 0.003

Finland 0.03 United Kingdom -0.13

France 1.61* The 5 percent critical value is 1.65.

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Table 3. Speed-of-Adjustment Parameter Estimates for Pork*

Country Estimate Country Estimate

Austria -0.232

(-9.04)

Ireland -0.027

(-3.38)

Belgium -0.037(-4.05)

Italy -0.021(-3.06)

Denmark -0.026

(-3.29)

Netherlands N.A

Spain -0.128

(-7.57)

Portugal -0.058

(-5.01)

Greece -0.017

(-2.59)

Sweden -0.03

(-3.08)

Finland -0.021

(-2.55)

United Kingdom -0.034

(-3.73)

France -0.082

(-5.91)* N.A: Non Applicable;

t-statistics in parentheses. The 5 percent critical value is 1.65 (one-sided test).

Table 4. ADF Test Results on Poultry Price Differentials*


of the TestStatistic


of the TestStatistic

Austria -2.337 Ireland -1.079

Belgium -7.188 Italy -6.782

Denmark -3.492 Netherlands -3.122

Spain -8.203 Portugal -7.804

Greece -3.421 Sweden -1.585

Finland -2.084 United Kingdom -1.438

France -4.194* The ADF regression includes constant and linear trend;

the lags have been selected optimally using the Schwartz criterion;

the 5 percent critical value is -3.145;benchmark country is Germany.

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Table 5. HH Test Results on Poultry Price Differentials*


of the Test

Statistic


of the Test

Statistic

Austria**** 1.51 Finland*** 5.5Belgium** -0.12 France** 0.42

Denmark** 1.27 Italy** 0.18

Spain** 2.30 Portugal** 0.96

Greece** 0.02 United

Kingdom***

1.48

* The 5 percent critical value is 1.65;

** benchmark country is Germany;

*** benchmark country is Sweden;

**** benchmark country is the Netherlands.

Table 6. Speed-of-Adjustment Parameter Estimates for Poultry*

Country Estimate Country Estimate

Austria**** -0.011

(1.93)

Finland *** N.A.

Belgium** -0.057

(-4.82)

France** -0.022

(-3.20)

Denmark** -0.072(-5.40) Italy** -0.038(-4.02)

Spain** N.A. Portugal** -0.138

(-7.36)

Greece** -0.005

(-1.70)

United

Kingdom***

-0.026

(-2.91)* N.A: Non Apppicable;

t-statistics in parentheses. The 5 percent critical value is 1.65 (one-sided test);

** benchmark country is Germany;

*** benchmark country is Sweden;

**** benchmark country is the Netherlands.

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APPENDIX:

Graphs of Parametric and Non Parametric Fits

Figure A.1. Pork: Austria-Germany

Figure A.2. Pork: Belgium-Germany.

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Figure A.3. Pork: Denmark-Germany.

Figure A.4. Pork: Spain-Germany.

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Figure A.5. Pork: Greece-Germany.

Figure A.6. Pork: Finland-Germany.

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Figure A.7. Pork: France-Germany.

Figure A.8. Pork: Ireland-Germany.

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Figure A.9. Pork: Italy-Germany.

Figure A.10. Pork: Netherlands-Germany.

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Figure A.11. Pork: Portugal-Germany.

Figure A.12. Pork: Sweden-Germany.

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Figure A.13. Pork:United Kingdom-Germany.

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Figure B.1. Poultry:Austria-Netherlands.

Figure B.2. Poultry: Belgium-Germany.

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Figure B.3. Poultry:Denmark-Germany.

Figure B.4. Poultry markets: Spain-Germany.

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Figure B.5. Poultrymarkets: Greece-Germany.

Figure B.6. Poultry: Finland-Sweden.

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Figure B.7. Poultry:France-Germany.

Figure B.8. Poultry:Italy-Germany.

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Figure B.9. Poultry:Portugal-Germany.

Figure B.10. Poultry: United Kingdom-Sweden.

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