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University of Innsbruck Working Papers in Economics and Statistics Milking The Prices: The Role of Asymmetries in the Price Transmission Mechanism for Milk Products in Austria Octavio Fernández-Amador, Josef Baumgartner and Jesús Crespo-Cuaresma 2010-21
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Page 1: Working Papers in Economics and Statistics - uibk.ac.at · tems Analysis (IIASA) and Austrian Institute of Economic Research (WIFO). E-mail address: je- ... When modeling the asymmetry

University of Innsbruck

Working Papers in

Economics and Statistics

Milking The Prices:

The Role of Asymmetries in the Price Transmission Mechanism for Milk Products in Austria

Octavio Fernández-Amador, Josef Baumgartner and

Jesús Crespo-Cuaresma

2010-21

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Milking The Prices: The Role of Asymmetries

in the Price Transmission Mechanism for Milk

Products in Austria∗

Octavio Fernandez-Amador† Josef Baumgartner‡

Jesus Crespo-Cuaresma§

July, 2010

Abstract

We assess empirically the vertical price transmission mechanism between producerand consumer prices of milk products in Austria using monthly data for the period fromJanuary 1996 to February 2010. We consider explicitly the existence of asymmetriesin the adjustment to the long-run equilibrium using two different types of thresholdvector error correction (VEC) models, where an inaction band in the adjustment to thelong-run relationship is defined and alternatively where price dynamics differ betweenperiods of increasing and decreasing trends in causal prices. Our results indicate thatasymmetries play an important role in the pass-through of prices for milk productsin Austria. We provide statistical evidence concerning the fact that the adjustmentonly tends to take place when deviations from the equilibrium are large enough. Milk,dairy and cheese products and butter tend to remain in positive margins (measured asdeviations from the long-run equilibrium) for the retailers’ side. The explicit modelingof nonlinearities does not improve out-of-sample forecasting performance.

Keywords: Asymmetric price transmission, threshold models, cointegration, milk prices.

JEL classification: C32, L11, Q13.

∗The authors would like to thank for the financial support of the project ”Marktspannen und Marktmachtdes osterreichischen Lebensmitteleinzelhandels am Beispiel Milchprodukte”, commissioned by the AustrianMinistry of Agriculture, Forestry, Environment and Water Management.†Corresponding author: University of Innsbruck, Department of Economics, SOWI Gebaude, Univer-

sitatsstrasse 15, 6020 Innsbruck (Austria). E-mail address: [email protected].‡Austrian Institute of Economic Research (WIFO), Arsenal Object 20, A-1030 Vienna (Austria). E-mail

address: [email protected].§Vienna University of Economics and Business, Department of Economics, Institute for Mone-

tary and Public Policy, Augasse 2-6 1090 Vienna (Austria), International Institute of Applied Sys-tems Analysis (IIASA) and Austrian Institute of Economic Research (WIFO). E-mail address: [email protected].

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1 Introduction

Contradicting standard economic theory, empirical research has usually pointed out the ex-istence of asymmetric price transmission (hereafter, APT) from input to output prices (seefor example, Geweke, 2004, Meyer and von Cramon-Taubadel, 2004, or Frey and Manera,2007, for surveys considering gasoline and agricultural markets). In particular, empirical re-sults tend to support larger consumer prices reactions to increases in cost prices than in thecase of decreases, both in terms of speed and magnitude of the adjustment (Peltzman, 2000).

Several theoretical underpinnings have been proposed to explain why the pass-through be-tween input and output prices tends to be neither instantaneous nor symmetric. The liter-ature has analyzed some characteristics of the markets related to menu costs at the retaillevel (Azzam, 1999), perishability of products (Ward, 1982) and storing systems at retailand production levels (Reagan and Weitzman, 1982), search costs in local markets (Bensonand Faminow, 1985), public intervention (Kinnucan and Forker, 1987), and market powerat retail level (Peltzman, 2000). McCorriston et al. (2001) show how in an equilibriumdisplacement model in the spirit of Gardner (1975), allowing for market power in the foodindustry under the assumption of non-constant returns to scale, market power is not nec-essarily a cause for price asymmetries in markets at presence of increasing returns to scale.Using a similar argumentation, but in the framework of horizontal price transmission, Az-zam (1999) concludes that asymmetries cannot be systematically attributed to a lack ofcompetition, existing even in a competitive framework. Weldegebriel (2004) and Lloyd etal. (2009) point to the impact of the combination of oligopoly and oligopsony (buyer) powerin a multi-stage vertical price transmission model. Furthermore, Xia (2009) highlights theimportance of the functional forms of farm supply and retail demand on the outcome of(possibly imperfect) price transmission.

The modern empirical literature on price transmission usually adopts a non-structural ap-proach for modeling APT. Within this approach, the relationship among non-stationaryseries of prices is modeled within the skeleton of a vector error correction (VEC) model,where it is possible to cast APT and other types of non-linearities in either the long run re-lationship or the shorter run adjustment dynamics. A useful class of models parametrizes theasymmetry by assuming a threshold adjustment to the cointegration relationship. Thresh-old VEC specifications allow us to model asymmetries which may imply, given the properstructure to the model, the existence of an inaction band of price combinations in whichthere is no response to deviations from the long run relationship (due to, for instance, fixedcosts), or a different adjustment depending on the sign of the change in the defined causalprice, allowing to assess statistically the hypothesis of an asymmetric impact of causal pricechanges in the caused prices. This asymmetry needs not take place immediately, but aftera period in which the relevant information is assimilated by market agents.

The empirical literature remarks the existence of APT in food markets and usually thechain of causality goes from downstream to upstream, independently of the subsector andcountry analyzed. In order to characterize price transmission among retail, wholesale, andshipping-point prices for a subset of fresh vegetables in US, Ward (1982) makes use of Wolf-fram’s (1971) asymmetry modeling procedure and shows that wholesale price changes are

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not totally reflected at the retail level, whereas the later adjusts to decreases in wholesaleprice. In contrast, the adjustment of shipping point prices is more fully when wholesaleprice decreases than when it increases. Ward (1982) suggests oligopolistic structure at theretail level, perishability of products and the possibility of reducing sales as the potentialmajor explanation underlying the asymmetric pass-through found. Analyzing the US beefsector for the period 1981 to 1998, Goodwin and Holt (1999) find support for the generalassumption that the line of causality on price transmission is from farm to wholesale and toretail level, though also from wholesale to farm level. Nevertheless, their findings point atthe fact that asymmetries are modest and could even be of no economic relevance. Usingfrequency domain regressions, Miller and Hayenga (2001) analyze the pork meat sector ininterior Iowa-Southern Minnesota for the period 1981 to 1995 and find support for retailprice asymmetric transmission for low-frequency dynamics of wholesale prices, while in therelationship between farm and wholesale prices no APT is found at any frequency. Abdulai(2002) also offers evidence of asymmetries in pricing behavior of retailers in the pork sec-tor in Switzerland during the period 1988 to 1997. The causality line appears to be fromproducer to retail levels and, in particular, increases in the producer price that induce areduction in the margin of the retailers are passed on to retail level faster than reductionsin the producer price that imply an increase in the marketing margin. Ben-Kaabia and Gil(2007) find evidence for full price transmission in the long-run in the Spanish lamb sector forthe period 1996 to 2002. However, their results show asymmetric adjustments and benefitsfor the retailers independently of the size, sign or origin of the price shocks. Also, Vavraand Goodwin (2005) find significant asymmetries in the farm, wholesale and retail chain forUS beef, chicken and eggs sectors.

Concerning dairy products, the empirical literature has shown similar results. Kinnucan andForker’s (1987) results highlight that asymmetries in both magnitude and time of responseare found in retail prices of dairy products (fluid milk, cheese, butter, and ice cream) in theUS, with larger and speedier reactions when farm prices are increasing. Serra and Goodwin(2003) find evidence for APT in dairy products in Spain. However, these asymmetries do notseem to be present in highly perishable dairy products. In accordance to McCorriston et al.(2001), their results do not suggest a relationship between APT and market concentration.Based on a dynamic reduced-form model of APT, Chavas and Mehta (2004) analyze the but-ter market in the US for the period 1980 to 2001. They find strong support for asymmetryin the adjustment of retail prices, with a stronger reaction when confronting wholesale priceincreases than when wholesale price decreases. However, the evidence of APT for wholesaleadjustments is weak and based on the asymmetry of retail price adjustments. These authorssuggest search costs, menu costs and imperfect competition as causes of the asymmetry atthe retail level.

A broader perspective is taken by Peltzman (2000) and Gwin (2009). Peltzman (2000) an-alyzes 15 2-digit Standard Industrial Classification (SIC) subsectors in US where a singleinput is the major cost component and finds evidence on APT as a stylized fact. APTappears as a characteristic of competitive and oligopolistic market structures and thus, noevidence on a market concentration foundation for asymmetries is obtained. Also, inven-tory holdings and menu costs are rejected as plausible explanations for APT. Even thoughadjustment costs would be a reasonable explanation to his results, Peltzman finds that less

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input volatility and fragmentation of the supply chain are behind the existence of asymme-tries. Gwin (2009) analyzes 269 industries over the 24 2-digit sectors of the North AmericanIndustrial Classification System (NAICS) during the period 1966-2006. The results suggestthat there is little support for the existence of a economy-wide APT mechanism, findingevidence on APT in nondurable goods (food) and natural resource manufacturing, but notin mining, durable goods manufacturing and service sectors. Due to the differences in pricetransmission among sectors, Gwin highlights inventory management as the potential expla-nation for asymmetries.

In this paper we assess the existence of relevant asymmetries in milk products marketsin Austria in terms of both speed and magnitude of the changes in consumer and pro-ducer prices. We evaluate the vertical price transmission mechanism between consumer andfarm-gate producer prices for monthly data of milk, dairy products, cheese and butter forthe period 1996 to 2010. We explicitly model potential asymmetries in the transmissionmechanism using (a) threshold VEC (TVEC) models, which define an inaction band in theadjustment to the long-run relationship and (b) models where price dynamics differ betweenperiods of increasing and decreasing trends in causal prices (we dub this type of specifica-tion SIGN model). We also evaluate the out-of-sample forecasting ability of the estimatedasymmetric models and compare them to their linear counterparts.

Our findings give evidence of asymmetries in retail and producer price relationships whichmaterialize in the existence of a band of inaction around the cointegration relationshipswhich link the prices of milk and dairy products in the long run. These asymmetries showpersistence in the regime above the inaction band and quick reversion when below the bandfor all consumer products considered. When modeling the asymmetry in terms of the trendof causal prices, the trigger appears to take place over relatively long periods (about 1 year)for dairy and cheese products whereas for milk and butter it takes just one month. Impulseresponse functions reflect the trend of the markets to establish the actual relationship of re-tail and producers prices beyond the band of inaction around the long-run relationship. Ourout-of-sample forecasting exercise shows that the estimated models possess good predictingabilities for consumer prices, but do not out-perform linear models.

This paper is structured as follows. Section 2 and 3 describe the main characteristics ofthe Austrian milk sector and the data, respectively. Section 4 presents the results of linearVEC models. We present the non-linear approach in Section 5, assessing the pass-throughin prices by using two types of asymmetric models and analyzing the impulse response func-tions of such models. Section 6 evaluates the out-of-sample forecasting properties of theproposed models and Section 7 concludes.

2 The main characteristics of the Austrian milk anddairy sector

The raw milk production system in the European Union (EU) is still highly regulated. In1984 a strict milk quota system, and a reference price for raw milk and intervention prices

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for butter and skim milk powder were introduced. Hence, the quantity and prices wereregulated to reduce overproduction. From 1988 onwards several reforms in this regulatoryframework were introduced to allow market forces to play an increasing role.1 However, thequantity of supply of raw milk is still limited by the quota system, though prices are much lessso.2 Consequently, price changes have become more and more a signal of changes in demand.

As a consequence of the accession to the EU in January 1995, Austria had to implement theEU common market legal framework, which introduced a new set of regulations and strongerinternational competition in particular to the former highly sheltered agricultural and foodprocessing sector. As a result, the Austrian milk-producing and dairy sector experiencedsignificant changes in the last 15 years resulting in a decrease in the number of farms and inthe cowherd, and increasing concentration in the milk-processing industry and among foodretailers.

Milk farmers in Austria are of a small scale compared to EU-15 (10 cows per farm in Austriaas opposed to 35 in the EU-15) and typically located in alpine regions (around 65% of rawmilk production in Austria compared to 12% in the EU-15), where production conditions aretough and alternative production possibilities are rather limited. Consequently, the averageannual yield per dairy cow is 10% lower than in the EU-15 (and 28% lower than in the mostproductive European countries, Denmark and Sweden).3

From 1995 to 2008 the number of milk producers in Austria decreased from around 77,000 to42,000 and the herd of dairy cows shrank from 638,000 to 527,000, whereas the total volumeof production increased from 2.9 to 3.2 million tons. An atomized raw milk production sectoris confronted with a quite concentrated dairy sector. In 2008 the Austrian top three dairycompanies had a market share of almost 55%. However, the next stage in the productionchain is even more concentrated. With a market share of 78.5% of the top three food retailersin Austria in 2008, this sector is among the most concentrated in Europe.4

3 Data description and time series properties

We analyze publicly available monthly time series for agricultural producer prices of rawmilk and consumer price data for milk, dairy products, cheese and butter based on the Aus-trian consumer price index (CPI) items obtained by Statistics Austria. Taking into accountthe regime change introduced by the accession to the EU in January 1995 and a majorchange in the construction of CPI basket operative from January 1996 onwards, the sam-ple period for the empirical analysis spans from January 1996 to February 2010. StatisticsAustria provides agricultural producer prices for milk in value terms for two types of raw

1The main initiatives were the McSherry reform in 1992, the Agenda 2000, the Common AgriculturalPolicy reform in 2003, and the Health Check reform in 2008. To prevent milk farmers from income losses asresult from cuts in intervention prices they were compensated by direct payments. See Oskam et al. (2010)for further details.

2During the period 1990 to 2008 the total annual raw milk production in the EU-15 was in the rangefrom 118.8 to 122.9 million tons.

3Figures are for 2005 and from Eurostat and Kirner et al. (2007).4Figures are from the annual report of the Austrian agricultural sector (Austrian Minstry of Agriculture,

2009) and from Nielsen (2009).

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milk, depending on the content of fat. We use the arithmetic mean of these two series as thefarm-gate producer price for raw milk. In the goods and services basket for the AustrianCPI 12 single items are included for milk, dairy products, cheese and butter, representing aweight of 1.5% of an average households expenditure in 1995. For dairy products (7 items,milkshake, sour cream, whipped cream, curd cheese, condensed milk, fruit flavored yogurtand curd cream with fruits) and for cheese (3 items, Emmental cheese, Gouda cheese andCamembert cheese) a composite price index is generated as a weighted average from thesingle items, respectively. In order to make the producer price series comparable with retailprices, index numbers (1996M1=100) were constructed. For the analysis we take naturallogarithms of all series and seasonally adjust them applying the TRAMO/SEATS method(Gomez and Maravall, 1996). Due to the fact that the results for dairy and cheese categoriesare very similar to those of the respective composite indices, we concentrate on the resultsof the corresponding indices (denoted micp, dacp, chcp and bucp for milk, dairy products,cheese and butter, respectively).5

Augmented Dickey and Fuller (1979, ADF) and Kwiatkowski et al. (1992, KPSS) tests werecarried out in order to assess the order of integration of the series in the models. Bothtests give evidence of the existence of a unit root in the series under consideration, with theonly exception of milk producer prices. For this price index, the results are contradictorydepending on the test statistic and setting used. We consider the series to be integrated oforder one and use the framework of error correction models in the presence of cointegratingrelationships for the bivariate modeling exercise.

Table 1: Unit root test resultsSetting with intercept Setting with intercept and linear trend

ADF test stat. KPSS test stat. ADF test stat. KPSS test stat.ln(micp) 0.944 1.446∗∗∗ -1.952 0.187∗∗

ln(dacp) -0.390 1.354∗∗∗ -2.845 0.190∗∗

ln(chcp) -0.457 1.323∗∗∗ -2.286 0.265∗∗∗

ln(bucp) -2.094 1.037∗∗∗ -2.846 0.086ln(mipp) -3.117∗∗ 0.433∗ -4.055∗∗∗ 0.057

Note: ∗, ∗∗ and ∗∗∗ stands for significance at the 10, 5 and 1% level, respectively.

4 Price transmission of milk prices in a linear frame-work

In a first step we analyze the price transmission of milk product prices using a linear VECrepresentation of the bivariate dynamics of producer and consumer prices. We thus assumethat the price dynamics can be represented as

∆pt = γ0 + αβ′pt−1 +l∑

j=1

Γj∆pt−j + εt, εt ∼ N(0,Σ) (1)

5Additional information on all 12 individual products are available from the authors upon request.

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where pt = (pct , ppt )′ is a vector composed by the consumer price of a given product and the

corresponding producer price (both in logs), γ0 is a vector of parameters, β′pt−1 defines thelong-run equilibrium relationship between the two price levels, given by the cointegratingvector β′ = (1 −β1) and α = (α1 α2)′ is a vector of adjustment parameters. Price dynamicsalso depend on previous changes in both variables up to the l -th lag through the parametermatrices Γj for j = 1, . . . , l.

We estimate the VEC model for two possible specifications of the long-run relationship. Onthe one hand, we obtain estimates of the long-run elasticity by estimating the system givenby (1), including the long run relationship, using maximum likelihood methods. On theother hand, we restrict the long-run elasticity to be equal to unity (β1 = 1), as economictheory would suggest in a constant mark-up framework. The optimal lag length in (1)is obtained by minimizing the Schwarz (1978) information criterion (Bayesian InformationCriterion, BIC) over lag lengths ranging from one to eighteen.

Johansen’s (1991) cointegration test is performed for all the pairs considered in the bivariatespecification for unrestricted and restricted (β1 = 1) long-run specifications. Model selec-tion using BIC resulted in specifications with two lags in the first differences of the pricevector for all cases. The results of the estimation of the linear models are presented in Table2 and give strong evidence of the existence of cointegration between the pairs of variablesconsidered, for unrestricted specifications for milk, dairy and cheese indices, and restrictedspecifications, in the case of butter. In order to assess the stylized facts of the lag structureof the relationship, we also performed Granger’s (1969) causality tests on the vector autore-gressive model in first differences defined by specification (1) without the error correctionterm. As shown in Table 2, the direction of the relationship is from producer prices to theconsumer prices at 5% of significance in all the price pairs considered.

Table 2 also presents the estimates of the long-run elasticity and the adjustment parametersfor the linear VEC models given by (1) for unrestricted and unit-elasticity specifications.The adjustment to the long-run attractor takes place through changes in the producer pricein all models. For milk and cheese there is also weak evidence that some adjustment (butwith an unexpected sign in the case of cheese) is carried out through changes from consumerprices as well. The long-run elasticities of milk, cheese and dairy products reflect a morethan proportional pass-through between prices.

5 Modeling asymmetric price transmission

We consider two types of asymmetric adjustment models for the system formed by producerand consumer prices. We firstly consider a model where the adjustment to the cointegrationrelationship takes place exclusively for relatively large deviation of the equilibrium relation-ship, while a band of inaction appears for smaller deviations from the long-run relationship.We also consider models where the asymmetry is triggered by the short-run trend in causalprices, so that the parameters of the error correction model (but not the long-run elastic-ities) differ between periods which follow increasing causal prices and those preceded bydecreasing causal prices.

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Table 2: Linear VEC modelsln(micp)− ln(mipp) Unrestricted RestrictedLong-run elast.: 2.7242∗∗∗ (0.7132) 1EC Adjustment: ln(micp) 0.0066∗ (0.0039) 0.0072 (0.0096)EC Adjustment: ln(mipp) 0.0183∗∗∗ (0.0066) 0.0309∗ (0.0163)Lag length: 2 2P-val coint. test (H0 : 1 CEs) 0.6095Unit long-run elasticity test (p-value) 0.021104Causality test F-Stat. P-valueH0 : No ln(mipp)→ ln(micp) 4.06781 0.0189H0 : No ln(micp)→ ln(mipp) 2.24412 0.1093ln(dacp)− ln(mipp) Unrestricted RestrictedLong-run elast.: 3.4061∗∗∗ (0.8484) 1EC Adjustment: ln(dacp) -0.0021 (0.0019) -0.0076 (0.0075)EC Adjustment: ln(mipp) 0.0148∗∗∗ (0.0049) 0.0458∗∗ (0.0196)Lag length: 2 2P-val coint. test (H0 : 1 CEs) 0.8101Unit long-run elasticity test (p-value) 0.036532Causality test F-Stat. P-valueH0 : No ln(mipp)→ ln(dacp) 8.13299 0.0004H0 : No ln(dacp)→ ln(mipp) 2.15983 0.1187ln(chcp)− ln(mipp) Unrestricted RestrictedLong-run elast.: 5.7261∗∗∗ (1.3024) 1EC Adjustment: ln(chcp) -0.0033∗ (0.0018) -0.0112 (0.0088)EC Adjustment: ln(mipp) 0.0091∗∗∗ (0.0030) 0.0138 (0.0147)Lag length: 2 2P-val coint. test (H0 : 1 CEs) 0.5221Unit long-run elasticity test (p-value) 0.000514Causality test F-Stat. P-valueH0 : No ln(mipp)→ ln(chcp) 4.33201 0.0147H0 : No ln(chcp)→ ln(mipp) 1.31275 0.2719ln(bucp)− ln(mipp) Unrestricted RestrictedLong-run elast.: 0.9855∗∗∗ (0.1713) 1EC Adjustment: ln(bucp) -0.0142 (0.0234) -0.0129 (0.0230)EC Adjustment: ln(mipp) 0.0765∗∗∗ (0.0260) 0.0757∗∗∗ (0.0256)Lag length: 2 2P-val coint. test (H0 : 1 CEs) 0.0188Unit long-run elasticity test (p-value) 0.964649Causality test F-Stat. P-valueH0 : No ln(mipp)→ ln(bucp) 6.72453 0.0016H0 : No ln(bucp)→ ln(mipp) 0.55824 0.5733

Note: ∗, ∗∗ and ∗∗∗ stands for significance at the 10, 5 and 1% level, respectively.

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Our TVEC model postulates potentially different adjustment parameters above and belowthe band of inaction, and no adjustment to the long-run equilibrium within the band. It isthus parametrized as follows,

∆pt =

γ0L + αLβ

′pt−1 +∑lj=1 ΓLj∆pt−j + ξLt, if β′pt−1 ≤ θL,

γ0M +∑lj=1 ΓMj∆pt−j + ξMt, if θL < β′pt−1 < θH ,

γ0H + αHβ′pt−1 +

∑lj=1 ΓHj∆pt−j + ξHt, if β′pt−1 ≥ θH ,

(2)

where the band of inaction is thus given by the interval (θL, θH), defined in the range ofdeviations from the cointegration relationship. Based on the results of the linear modeland in order to simplify the interpretation of the results we fix the cointegrating vectorβ = (1 − β1) to both cases considered in the linear specification, where β1 is the estimatedparameter from the linear VEC estimation in the unrestricted case and one in the restrictedunitary elasticity case. With the same aim, we restrict the lag length of the TVEC modelto that of the linear one. The model in (2) in the restricted case, for instance, hypothesizesthat price adjustment to the long-run equilibrium only takes place if the price differencebetween consumer and producer prices exceeds θH or falls below θL and the speed of such anadjustment is potentially different in both regimes. Furthermore, intercepts and parametersdefining the short-run dynamics in the regimes defined by these thresholds are also allowedto differ across regimes. In practice, we do not set the thresholds exogenously, but estimatethem as

(θL θH) = arg minθLθH

SSR(θL θH), (3)

where SSR(θL θH) is the sum of squared residuals of the model with thresholds given by θLand θH . The sum of squared residuals is minimized using a grid search over (θL θH). Wedesign the grid search so that at least 10% of the observations fall in the medium regimeand 15% in the extreme regimes, in order to avoid model estimates based on regimes withtoo few observations. The estimated thresholds (θL, θH) are not restricted to be symmetricaround the band of inaction.

In addition, we use an alternative modeling strategy by considering that the pass-throughbetween prices is different depending on the past trend of the causal price for a periodwhich the market takes as the relevant information period. Thus, the APT model based onincreases versus decreases of the causal price is given by the following specification (SIGNmodel),

∆pt =

{φ0L + δLβ

′pt−1 +∑lj=1 ΦLj∆pt−j + υLt, if pt−1 − pt−w ≤ 0,

φ0H + δHβ′pt−1 +

∑lj=1 ΦHj∆pt−j + υHt, if pt−1 − pt−w > 0,

(4)

where the adjustment parameter and short-run dynamics parametrized through the Φ ma-trices differ depending on whether the growth rate of producer prices over the last ω − 1periods was positive or negative. The parameter ω is estimated using a grid search over areasonable set of lags. In our case, we search in the set of lag lengths ω = 2, . . . , 13, whichrange from considering the change in producer prices in the last month to considering thetrend in the last year. Therefore, we estimate the period of information of the market as

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ω = arg minω

SSR(ω), (5)

where SSR(·) is the sum of squared residuals, minimized now using a grid search over (ω).We design the grid search to ensure that at least 15% of the observations fall in one regime,in order to avoid model estimates based on regimes with too few observations.

The main results of the estimation of nonlinear models are presented in Table 3 and the de-viations from the cointegration relationships together with the estimated thresholds for theTVEC specifications are presented in Figure 1. Table 3 presents also the results of a nonlin-earity test in the spirit of Hansen (1996). It is well known that the test of a model such as (1)against the nonlinear alternative (2) suffers from the problem that the threshold parametersare nuisance parameters which are not identified under the null hypothesis of linearity. Thisimplies that the usual likelihood ratio (LR) test for model (2) against model (1) cannot beevaluated using standard probability distributions (see Andrews and Ploberger, 1994). Weobtain a simulated distribution of the test statistic under the null of linearity as follows. Fora given pair of prices, we use the estimates of the parameters in model (1) together withsimulated shocks in order to obtain price paths under the maintained linearity assumption.We estimate nonlinear models such as (2) for each of the simulated datasets and calculatethe corresponding LR test statistic. By repeating this procedure 1,000 times, we reconstructthe distribution of the test statistic under the null hypothesis. The corresponding p-valueis given by the proportion of simulated test statistics which exceed the value obtained us-ing the actual data. LR tests were carried out for the null of linearity against the SIGNmodel of (4) and for the null of (5) against the alternative of the TVEC model specified in (2).

In every bivariate model considered the TVEC model appears as the preferred one whencomparing it to the linear VEC and the SIGN model. Therefore, consumer and producerprices, if they adjust to equilibrium, they only do it as a response to relatively large devi-ations from long-run equilibrium. However, as shown in Figure 1 the widths of the bandsof inaction given by the estimated thresholds differ considerably, from a very narrow onefor butter to the widest band for cheese. The ranges of the deviations from the long-runequilibria differ considerably, too. Cheese shows higher volatility, whereas milk and dairyproducts display similar figures, and butter shows the lowest range. However, their dynam-ics look like very similar. Furthermore, the adjustment to equilibrium seems to follow anasymmetric pattern. For all products considered in our analysis, there is a tendency of a(very) slow adjustment if deviations from long-run equilibria are positive, whereas negativedeviations are corrected much faster. This stylized fact is interpreted as a (small) positivemargin which benefits retailers. For milk none of the adjustment coefficients is significant.For dairy products and butter the adjustment comes from the consumer price from belowand from the producer price from above. The adjustment coefficients are the largest forbutter, yielding the smallest margin. Cheese products show a similar adjustment pattern asdairy products. The adjustment takes also place from above for consumer prices, but withan unexpected negative sign.

When modeling the cointegration relationship depending on the trend of the causal variabledetermined, the producer price, the estimate of the lag in the price change that triggers the

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Table 3: Threshold VEC modelsln(micp)− ln(mipp) TVEC Unrestricted SIGN UnrestrictedLong-run elast.: 2.7242 2.7242EC Adjustment (above/increasing trend): ln(micp) -0.0029 (0.0100) 0.0020 (0.0061)EC Adjustment (below/decreasing trend): ln(micp) 0.0086 (0.0130) 0.0139∗∗ (0.0060)EC Adjustment (above/increasing trend): ln(mipp) 0.0278 (0.0170) 0.0046 (0.0091)EC Adjustment (below/decreasing trend): ln(mipp) -0.0183 (0.0220) 0.0394∗∗∗ (0.0089)Low threshold: -0.131485Upper threshold: -0.003001Threshold lag length (ω − 1): 1LR test (H0 : Linear model) : 106.0097 (0.0000) 57.7301 (0.0000)LR test (H0 : SIGN model) : 48.2797 (0.0000)ln(dacp)− ln(mipp) TVEC Unrestricted SIGN UnrestrictedLong-run elast.: 3.4061 3.4061EC Adjustment (above/increasing trend): ln(dacp) -0.0048 (0.0064) -0.0023 (0.0022)EC Adjustment (below/decreasing trend): ln(dacp) 0.0115∗∗ (0.0049) 0.0078 (0.0052)EC Adjustment (above/increasing trend): ln(mipp) 0.0374∗∗ (0.0170) 0.0117∗∗ (0.0055)EC Adjustment (below/decreasing trend): ln(mipp) 0.0187 (0.0130) 0.0742∗∗∗ (0.0130)Low threshold: -0.17363Upper threshold: 0.015916Threshold lag length (ω − 1): 12LR test (H0 : Linear model) : 119.3508 (0.0000) 64.7407 (0.0000)LR test (H0 : SIGN model) : 62.3543 (0.0000)ln(chcp)− ln(mipp) TVEC Unrestricted SIGN UnrestrictedLong-run elast.: 5.7261 5.7261EC Adjustment (above/increasing trend): ln(chcp) -0.0196∗∗∗ (0.0068) -0.0019 (0.0021)EC Adjustment (below/decreasing trend): ln(chcp) 0.0133∗∗∗ (0.0047) -0.0064 (0.0052)EC Adjustment (above/increasing trend): ln(mipp) 0.0190∗ (0.0111 0.0064∗∗ (0.0033)EC Adjustment (below/decreasing trend): ln(mipp) 0.0092 (0.0077) 0.0478∗∗∗ (0.0079)Low threshold: -0.301596Upper threshold: 0.062167Threshold lag length (ω − 1): 12LR test (H0 : Linear model) : 102.6462 (0.0000) 63.3686 (0.0000)LR test (H0 : SIGN model) : 29.4331 (0.0000)ln(bucp)− ln(mipp) TVEC Restricted SIGN RestrictedLong-run elast.: 1 1EC Adjustment (above/increasing trend): ln(bucp) -0.0154 (0.0439) 0.0254 (0.0320)EC Adjustment (below/decreasing trend): ln(bucp) 0.1653∗ (0.0915) -0.0284 (0.0337)EC Adjustment (above/increasing trend): ln(mipp) 0.0854∗ (0.0515) 0.0271 (0.0337)EC Adjustment (below/decreasing trend): ln(mipp) 0.0727 (0.1073) 0.1304∗∗∗ (0.0355)Low threshold -0.038843Upper threshold -0.013852Threshold lag length (ω − 1) 1LR test (H0 : Linear model) : 53.2870 (0.0490) 41.5226 (0.0000)LR test (H0 : SIGN model) : 11.7645 (0.0000)

Note: ∗, ∗∗ and ∗∗∗ stands for significance at the 10, 5 and 1% level, respectively.

11

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-.8

-.6

-.4

-.2

.0

.2

.4

.6

1996 1998 2000 2002 2004 2006 2008

Milk Consumer Price Index

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

1996 1998 2000 2002 2004 2006 2008

Dairy Products Consumer Composite Index

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1996 1998 2000 2002 2004 2006 2008

Cheese Consumer Composite Index

-.16

-.12

-.08

-.04

.00

.04

.08

.12

.16

1996 1998 2000 2002 2004 2006 2008

Butter Consumer Price Index

Figure 1: Deviations from cointegration relationships and TVEC thresholds

nonlinearity is one year for dairy and cheese products and one month for milk and butter.Considering the significance of the adjustment, when the causal relationship is from theproducer to the consumer price, for all the four product categories the adjustment takesplace from the producer side when the trend of change is decreasing, and in the case ofdairy and cheese products also when this trend of change is increasing. All of the estimatedadjustment parameters have the expected sign. In the case of milk the adjustment takesplace also from the side of retailers for a decreasing trend.

The different price dynamics implied by the nonlinear models can be examined by using sim-ulation methods. We performed multiple simulations by starting with a vector of producerand consumer prices in the long-run equilibrium given by the cointegration relationship andapplying a shock to the dynamic system that deviates the causal price index of the cointe-gration relationship by f percentage points. Obtaining a general function which summarizesthe dynamics after such a shock is not straight forward in the framework of nonlinear mod-els. On the one hand, the response of a variable to a shock in another one in models such

12

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as the TVEC put forward above depends on the history of the variables, in particular onthe regime which is active at the moment of the shock. While in the case of linear modelsdifferences in the size of the shock do not lead to qualitatively different dynamics in thevariables of interest, this is not the case in the nonlinear models considered. Therefore, inspirit of Potter (1995 and 2000) and Koop et al. (1996) the generalized impulse response(GIR) functions are estimated as

GIRY (n, κt, µt−1, ..., µt−j) = E [Yt+n|κt, µt−1, ..., µt−j ]− E [Yt+n|µt−1, ..., µt−j ] , (6)

where n are the periods for which the GIR is estimated, ranging from 1 to an horizon hperiods (24 months in our case), κt is the shock (1% at period n = 0), and µt−1, ..., µt−j isthe history of the vector of variables determined on the long-run equilibrium of period n = 0up to lag j, the lag length of the model. For the set of nonlinear models under consideration,the conditional expectations are obtained by simulating the response using a Monte Carloprocedure based on 10,000 replications of the model after the assumed shock takes place.

Figure 2 shows the response of consumer prices over 24 months after a deviation of 1% of theproducer price for raw milk from the (sustained) long-run equilibrium computed using thepreferred (TVEC) model described above. A detailed analysis of the responses to shocksof different size allows us to draw some general conclusions about the out-of-equilibriumdynamics of the prices under study. First of all, TVEC models reveal that shocks havepersistent effects on consumer prices, reflecting the trend for different products to remain inone regime beyond the band of inaction.6 Secondly, independently of the sign of the shock,the responses of the consumer prices go in the same direction, suggesting that the band ofinaction gives a boost to the vector of prices so as for the consumer price to move to theregime above or below the inaction band. Thirdly, these reactions are positive in the caseof milk, dairy products and cheese, and negative in the case of butter.

6 Out of sample prediction: Do asymmetries help fore-casting?

In a further step, we evaluate whether nonlinear modeling of the price transmission mecha-nism in prices helps us to improve forecasts of consumer prices. Since some of the regimesin the TVEC and SIGN model are not stable, we concentrate on the accuracy of qualitativeforecasts about the direction of change in consumer prices (increases versus decreases). Thedesign of the out-of-sample forecasting exercise is as follows. We estimate the linear and thetwo asymmetric models using data ranging from January 1996 to January 2004. We use theestimated models to obtain predictions for the direction of changes in consumer prices in theperiod February 2004 - January 2005. We add the observation corresponding to February2004 to the sample, reestimate our models and repeat the exercise for the out-of-sampleperiod March 2004 - February 2005. This is repeated until the end of the available sample is

6We also simulated shocks of very small size, confirming that this trend to stay in one regime beyond theinaction band origins from the dynamics within the band.

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Milk Consumer Price Index

Cheese Consumer Composite Index

Dairy Products Consumer Composite Index

Butter Consumer Price Index

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 2 4 6 8 10 12 14 16 18 20 22 24

Linear Vec unrestricted (negative shock) Linear VEC unrestricted (positive shock)

TVEC unrestricted (negative shock) TVEC unrestricted (positive shock)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16 18 20 22 24

Linear VEC unrestricted (negative shock) Linear VEC unrestricted (positive shock)

TVEC unrestricted (negative shock) TVEC unrestricted (positive shock)

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 2 4 6 8 10 12 14 16 18 20 22 24

LIMP_P1_NEGUNRCOST LIMP_P1_POSUNRCOST

IMPTVEC_P1_NEGUNRCOST IMPTVEC_P1_POSUNRCOST

-0.5

-0.5

-0.4

-0.4

-0.3

-0.3

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0 2 4 6 8 10 12 14 16 18 20 22 24

Linear VEC restricted (negative shock) Linear VEC restricted (positive shock)

TVEC restricted (negative shock) TVEC restricted (positive shock)

Figure 2: Generalized impulse response functions

reached and the average proportions of correctly forecast directions of change are computed.

The results for 3, 6, 9 and 12 months ahead forecasts for the models considered underthe accepted cointegration relationship specification are presented in Figure 3 for consumerprices for milk, dairy and cheese products and butter. In Figure 3 we show the proportionof correct forecasts of direction of change for each forecasting horizon and each model. Ingeneral, the forecast performance of non-linear models is good but not superior to linearmodels. The SIGN model specifications seem to offer a better forecasting performance thanthe TVEC model. This result is not surprising in the context of results in the forecastingliterature which favor parsimonious models, showing the SIGN model as a good combinationof parsimony and complexity.

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Milk Consumer Price Index

Cheese Consumer Composite Index

Dairy Products Consumer Composite Index

Butter Consumer Price Index

50

55

60

65

70

75

80

3 6 9 12

%

Horizon

Linear VEC unrestricted

TVEC unrestricted

SIGN VEC unrestricted (causal: producer)

50

55

60

65

70

75

80

3 6 9 12

%

Horizon

Linear VEC unrestricted

TVEC unrestricted

SIGN VEC unrestricted (causal: producer)

50

55

60

65

70

75

80

3 6 9 12

%

Horizon

Linear VEC unrestricted

TVEC unrestricted

SIGN VEC unrestricted (causal: producer)

50

55

60

65

70

75

80

3 6 9 12

%

Horizon

Linear VEC restricted

TVEC restricted

SIGN VEC restricted (causal: producer)

Figure 3: Out of sample forecasting performance

7 Conclusions

In this study we assess the price transmission mechanism between producer and consumerprices of milk and dairy products in Austria using monthly data for the period January 1996to February 2010. The asymmetric price transmission mechanism between consumer andproducer prices for monthly data of milk, dairy and cheese products, and butter is explic-itly modeled using threshold VEC models defining an inaction band around the long-runrelationship (TVEC models) and models where price dynamics differ between periods ofincreasing and decreasing trend of change in causal prices (SIGN models). We also analyzethe short-run dynamics of the models proposed and their forecast performance.

Our results show robustly that asymmetries play a role in milk and dairy markets in Austria.These asymmetries can be modeled as triggered by the magnitude of the deviation fromequilibrium, as well as the trend in prices in a reference period. The preferred modelsimply that long-run attraction forces seem to be relevant only for relatively large deviations

15

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from the equilibrium of the market. For all products persistent positive deviations fromthe long-run equilibrium are revealed. This situation seems to point to positive mark-upsand benefits for retailers. Impulse response analysis gives further support to the bias of themarket when establishing prices beyond the inaction band around the long-run equilibrium.Modeling nonlinearities explicitly does not help to improve the forecast performance.

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University of Innsbruck – Working Papers in Economics and Statistics Recent papers 2010-21 Octavio Fernández-Amador, Josef Baumgartner and Jesús Crespo-

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2008-19 Michael Kirchler: Curse of Mediocrity - On the Value of Asymmetric Fundamental Information in Asset Markets.

2008-18 Jürgen Huber and Michael Kirchler: Corporate Campaign Contributions as a Predictor for Abnormal Stock Returns after Presidential Elections.

2008-17 Wolfgang Brunauer, Stefan Lang, Peter Wechselberger and Sven Bienert: Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna.

2008-16 Harald Oberhofer, Tassilo Philippovich: Distance Matters! Evidence from Professional Team Sports. Extended and revised version forthcoming in Journal of Economic Psychology.

2008-15 Maria Fernanda Rivas and Matthias Sutter: Wage dispersion and workers’ effort.

2008-14 Stefan Borsky and Paul A. Raschky: Estimating the Option Value of Exercising Risk-taking Behavior with the Hedonic Market Approach. Revised version forthcoming in Kyklos.

2008-13 Sergio Currarini and Francesco Feri: Information Sharing Networks in Oligopoly.

2008-12 Andrea M. Leiter: Age effects in monetary valuation of mortality risks - The relevance of individual risk exposure. Revised version forthcoming in The European Journal of Health Economics.

2008-11 Andrea M. Leiter and Gerald J. Pruckner: Dying in an Avalanche: Current Risks and their Valuation.

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2008-10 Harald Oberhofer and Michael Pfaffermayr: Firm Growth in Multinational Corporate Groups.

2008-09 Michael Pfaffermayr, Matthias Stöckl and Hannes Winner: Capital Structure, Corporate Taxation and Firm Age.

2008-08 Jesus Crespo Cuaresma and Andreas Breitenfellner: Crude Oil Prices and the Euro-Dollar Exchange Rate: A Forecasting Exercise.

2008-07 Matthias Sutter, Stefan Haigner and Martin Kocher: Choosing the carrot or the stick? – Endogenous institutional choice in social dilemma situations. Revised version published in Review of Economic Studies, Vol. 77 (2010): 1540-1566.

2008-06 Paul A. Raschky and Manijeh Schwindt: Aid, Catastrophes and the Samaritan's Dilemma.

2008-05 Marcela Ibanez, Simon Czermak and Matthias Sutter: Searching for a better deal – On the influence of group decision making, time pressure and gender in a search experiment. Revised version published in Journal of Economic Psychology, Vol. 30 (2009): 1-10.

2008-04 Martin G. Kocher, Ganna Pogrebna and Matthias Sutter: The Determinants of Managerial Decisions Under Risk.

2008-03 Jesus Crespo Cuaresma and Tomas Slacik: On the determinants of currency crises: The role of model uncertainty. Revised version accepted for publication in Journal of Macroeconomics.

2008-02 Francesco Feri: Information, Social Mobility and the Demand for Redistribution.

2008-01 Gerlinde Fellner and Matthias Sutter: Causes, consequences, and cures of myopic loss aversion - An experimental investigation. Revised version published in The Economic Journal, Vol. 119 (2009), 900-916.

2007-31 Andreas Exenberger and Simon Hartmann: The Dark Side of Globalization.

The Vicious Cycle of Exploitation from World Market Integration: Lesson from the Congo.

2007-30 Andrea M. Leiter and Gerald J. Pruckner: Proportionality of willingness to pay to small changes in risk - The impact of attitudinal factors in scope tests. Revised version forthcoming in Environmental and Resource Economics.

2007-29 Paul Raschky and Hannelore Weck-Hannemann: Who is going to save us now? Bureaucrats, Politicians and Risky Tasks.

2007-28 Harald Oberhofer and Michael Pfaffermayr: FDI versus Exports. Substitutes or Complements? A Three Nation Model and Empirical Evidence.

2007-27 Peter Wechselberger, Stefan Lang and Winfried J. Steiner: Additive models with random scaling factors: applications to modeling price response functions.

2007-26 Matthias Sutter: Deception through telling the truth?! Experimental evidence from individuals and teams. Revised version published in The Economic Journal, Vol. 119 (2009), 47-60.

2007-25 Andrea M. Leiter, Harald Oberhofer and Paul A. Raschky: Productive disasters? Evidence from European firm level data. Revised version forthcoming in Environmental and Resource Economics.

2007-24 Jesus Crespo Cuaresma: Forecasting euro exchange rates: How much does model averaging help?

2007-23 Matthias Sutter, Martin Kocher and Sabine Strauß: Individuals and teams in UMTS-license auctions. Revised version with new title "Individuals and teams in auctions" published in Oxford Economic Papers, Vol. 61 (2009): 380-394).

2007-22 Jesus Crespo Cuaresma, Adusei Jumah and Sohbet Karbuz: Modelling and Forecasting Oil Prices: The Role of Asymmetric Cycles. Revised version accepted for publication in The Energy Journal.

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2007-21 Uwe Dulleck and Rudolf Kerschbamer: Experts vs. discounters: Consumer free riding and experts withholding advice in markets for credence goods. Revised version published in International Journal of Industrial Organization, Vol. 27, Issue 1 (2009): 15-23.

2007-20 Christiane Schwieren and Matthias Sutter: Trust in cooperation or ability? An experimental study on gender differences. Revised version published in Economics Letters, Vol. 99 (2008): 494-497.

2007-19 Matthias Sutter and Christina Strassmair: Communication, cooperation and collusion in team tournaments – An experimental study. Revised version published in: Games and Economic Behavior, Vol.66 (2009), 506-525.

2007-18 Michael Hanke, Jürgen Huber, Michael Kirchler and Matthias Sutter: The economic consequences of a Tobin-tax – An experimental analysis. Revised version forthcoming in Journal of Economic Behavior and Organization.

2007-17 Michael Pfaffermayr: Conditional beta- and sigma-convergence in space: A maximum likelihood approach. Revised version forthcoming in Regional Science and Urban Economics.

2007-16 Anita Gantner: Bargaining, search, and outside options. Published in: Games and Economic Behavior, Vol. 62 (2008), pp. 417-435.

2007-15 Sergio Currarini and Francesco Feri: Bilateral information sharing in oligopoly.

2007-14 Francesco Feri: Network formation with endogenous decay. 2007-13 James B. Davies, Martin Kocher and Matthias Sutter: Economics research

in Canada: A long-run assessment of journal publications. Revised version published in: Canadian Journal of Economics, Vol. 41 (2008), 22-45.

2007-12 Wolfgang Luhan, Martin Kocher and Matthias Sutter: Group polarization in the team dictator game reconsidered. Revised version published in: Experimental Economics, Vol. 12 (2009), 26-41.

2007-11 Onno Hoffmeister and Reimund Schwarze: The winding road to industrial safety. Evidence on the effects of environmental liability on accident prevention in Germany.

2007-10 Jesus Crespo Cuaresma and Tomas Slacik: An “almost-too-late” warning mechanism for currency crises. (Revised version accepted for publication in Economics of Transition)

2007-09 Jesus Crespo Cuaresma, Neil Foster and Johann Scharler: Barriers to technology adoption, international R&D spillovers and growth.

2007-08 Andreas Brezger and Stefan Lang: Simultaneous probability statements for Bayesian P-splines.

2007-07 Georg Meran and Reimund Schwarze: Can minimum prices assure the quality of professional services? (Accepted for publication in European Journal of Law and Economics)

2007-06 Michal Brzoza-Brzezina and Jesus Crespo Cuaresma: Mr. Wicksell and the global economy: What drives real interest rates?.

2007-05 Paul Raschky: Estimating the effects of risk transfer mechanisms against floods in Europe and U.S.A.: A dynamic panel approach.

2007-04 Paul Raschky and Hannelore Weck-Hannemann: Charity hazard - A real hazard to natural disaster insurance. Revised version forthcoming in: Environmental Hazards.

2007-03 Paul Raschky: The overprotective parent - Bureaucratic agencies and natural hazard management.

2007-02 Martin Kocher, Todd Cherry, Stephan Kroll, Robert J. Netzer and Matthias Sutter: Conditional cooperation on three continents. Revised version published in: Economics Letters, Vol. 101 (2008): 175-178.

2007-01 Martin Kocher, Matthias Sutter and Florian Wakolbinger: The impact of naïve advice and observational learning in beauty-contest games.

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University of Innsbruck Working Papers in Economics and Statistics 2010-21 Octavio Fernández-Amador, Josef Baumgartner and Jesús Crespo-Cuaresma Milking The Prices: The Role of Asymmetries in the Price Transmission Mechanism for Milk Products in Austria Abstract We assess empirically the vertical price transmission mechanism between producer and consumer prices of milk products in Austria using monthly data for the period from January 1996 to February 2010. We consider explicitly the existence of asymmetries in the adjustment to the long-run equilibrium using two different types of threshold vector error correction (VEC) models, where an inaction band in the adjustment to the long-run relationship is defined and alternatively where price dynamics differ between periods of increasing and decreasing trends in causal prices. Our results indicate that asymmetries play an important role in the pass-through of prices for milk products in Austria. We provide statistical evidence concerning the fact that the adjustment only tends to take place when deviations from the equilibrium are large enough. Milk, dairy and cheese products and butter tend to remain in positive margins (measured as deviations from the long-run equilibrium) for the retailers' side. The explicit modeling of nonlinearities does not improve out-of-sample forecasting performance. ISSN 1993-4378 (Print) ISSN 1993-6885 (Online)


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