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Transcript of Price Adjust
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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
Country Empirical Value
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*
Country Empirical Value
of the Test
Statistic
Country Empirical Value
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*
Country Empirical Value
of the TestStatistic
Country Empirical Value
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*
Country Empirical Value
of the Test
Statistic
Country Empirical Value
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.