Spatial Price Adjustment with and without TradeEMMA C. STEPHENS†, EDWARD MABAYA‡, STEPHAN VON CRAMON-TAUBADEL§ and CHRISTOPHER B. BARRETT*

†Pitzer College, Claremont, CA 91711 USA(e-mail: estephen@pitzer.edu)‡Emerging Markets Program, Cornell University, Ithaca, NY 14850 USA(e-mail: em37@cornell.edu)§Department of Agricultural Economics and Rural DevelopmentUniversity of Gottingen, Gottingen, Germany(e-mail: scramon@gwdg.de)*Department of Applied Economics and ManagementCornell University, Ithaca, NY 14850 USA(e-mail: cbb2@cornell.edu)

November 2010

Word Count=5824

AbstractIn this paper we investigate the possibility that price transmission between spatiallydistinct markets might vary during periods with and without physical trade flows.We are able to test for differences in price transmission between trade and non-traderegimes by using Generalized Reduced Rank Regression (GRRR) techniques sug-gested by P.R. Hansen (2003). We apply these techniques to semi-weekly price andtrade flow data for tomato markets in Zimbabwe and find that intermarket priceadjustment occurs in both trade and non-trade periods. Indeed, the adjustments aregenerally larger and more rapid in periods without physical trade flows. This findingunderscores the importance of information flow for market performance.

JEL Codes: Q13, R12, C32, P42

Keywords: Spatial price transmission, cointegration, Zimbabwe, reduced rank re-gression, tomatoes.

I. Introduction

A large literature explores the behavior over time of distinct markets that are linked

together in a network. This network can be spatial, as in markets for a commod-

ity within a given region or country, or it may represent other kinds of integration,

perhaps through vertical marketing channels as product is transformed or through

intertemporal arbitrage via storage (Williams & Wright, 1991; Deaton & Laroque,

1996; Brummer, von Cramon-Taubadel, & Zorya, 2009). The primary purpose of

such research is often to determine how quickly markets respond to shocks and how

these shocks transmit through the network via price adjustment. The dominant an-

alytical approach has exploited spatial market equilibrium conditions, described in

detail by Takayama and Judge (1971). Deviations from these equilibrium conditions

yield key information on overall market efficiency. Understanding these dynamics

with respect to food markets may be of particular importance for policy makers in

developing countries (Fackler & Goodwin, 2002), where large subpopulations are em-

ployed in the agricultural sector and where the considerable budget shares devoted to

food expenditures leave many poor households vulnerable to price spikes commonly

associated with market disequilibrium.

The underlying theory of spatial market equilibrium suggests particular patterns

of price behavior under competitive arbitrage, based on the transactions costs as-

sociated with movement of goods between markets and observed trade flows. More

specifically, if physical trade flows occur between markets, these markets are said

to be in competitive spatial equilibrium if and only if the price differential exactly

equals the costs of moving goods between them, such that excess returns to trade

1

are completely exhausted. Further, with constant per unit costs of commerce, any

price change in one market due to a local demand or supply shock should generate

an equal price change in the other market. This strong spatial price transmission is

the familiar Law of One Price.

The absence of trade may also imply that markets are in spatial equilibrium. This

can occur when price differentials exactly equal transactions costs, leaving traders

indifferent between trading and not trading, or when the intermarket price differen-

tials are insufficient to cover the costs of arbitraging between the markets. Where

competitive spatial equilibrium with trade implies strong spatial price transmission,

however, this latter, segmented spatial equilibria is consistent with uncorrelated price

series as well as with the Law of One Price. Thus spatial price transmission dynamics

may be markedly different in periods with and without trade even when markets are

always in competitive spatial equilibrium.

Markets may also be out of equilibrium, with either apparent missed arbitrage

opportunities (i.e., no trade in spite of intermarket price differentials in excess of the

costs of arbitrage) or positive trade in the face of negative returns to arbitrage. The

different possible combinations of trade flows and returns to trade are examined in

detail in the switching regime branch of the spatial price analysis literature, which

finds empirically that markets are frequently out of spatial equilibrium (Baulch, 1997;

Barrett & Li, 2002). However, this literature is limited in its ability to comment on

the actual process of transition between equilibrium and non-equilibrium regimes, as

the approach is inherently static and does not make explicit use of the time series

2

nature of the data at hand.1

There is, however, a large body of work that performs spatial price analysis dy-

namically and includes the possibility of disequilibrium periods, primarily through

the use of threshold autoregressive and vector error correction models to character-

ize price dynamics (e.g. Dercon, 1995; Goodwin & Piggott, 2001; B. E. Hansen &

Seo, 2002). But one of the main, implicit assumptions of these models is the pri-

macy of trade flows in bringing about spatial equilibrium. This assumption has been

largely unexamined thus far in the literature. For the most part, lack of available

complementary price, trade flow and transaction cost data has hampered the ana-

lysts’ ability to test empirically whether or not trade flows are the main mechanisms

behind spatial equilibrium patterns.2 Further, until recently, the appropriate meth-

ods in cointegration analysis necesary to fully compare spatial price dynamics in the

presence of multiple trading regimes did not exist.

Using developments in the literature on structural breaks in cointegration models

(Boswijk & Doornik, 2004; P. R. Hansen, 2003; Johansen & Juselius, 1992; Pesaran

& Shin, 2002), we examine the nature of spatial price adjustment dynamics both with

and without physical trade flows. We apply a flexible structural break model to de-

tailed semi-weekly price, transactions costs and trade flow data from tomato markets

in Zimbabwe and test for the presence of non-linearities in long run equilibrium rela-

tionships and potentially different price transmission patterns under different trading

1Negassa and Myers (2007) offer a dynamic extension to the parity bounds model, but likethe rest of the switching regime literature, their approach relies heavily on strong, atheoreticaldistributional assumptions.

2See Barrett (1996) for a break down of the types of market analysis methods by data classifi-cation.

3

regimes. This method allows for useful characterization of market performance with

respect to price adjustment while relaxing some strong, and typically indefensible,

distributional assumptions on which existing switching regime techniques depend.

It also provides different, more complete information about spatial price adjustment

dynamics. In particular, we are able to test empirically for differences in these dy-

namics in periods with and without observed trade flows. The results implicitly

demonstrate the importance of mechanisms other than physical trade flows – such

as information flows – in linking spatially distinct markets and thereby influencing

spatial price adjustment. This reinforces recent findings, such as Jensen (2007), that

more directly demonstrate the impact of information flows on spatial price and trade

patterns. Our application to Zimbabwean tomato markets demonstrates that failure

to allow for such structural differences in intermarket price transmission can lead to

serious errors of inference with respect to market efficiency.

II. Models of Cointegration and Regime-Specific

Error Correction

Cointegration models have been used to great effect in many spatial analysis stud-

ies.3 These studies make use of the fact that it is possible to use competitive spatial

equilibrium conditions to find an error correction representation of the relationships

between prices and transactions costs in two different markets, as we explain below.

Based on this model, one can then estimate parameters that characterize how mar-

3See Fackler and Goodwin (2002) for a detailed summary.

4

ket prices adjust to random shocks that move connected markets out of long run

equilibrium.

Error correction models have the attractive property that they allow for analysis

of both long run and short run dynamics in the presence of a cointegrating rela-

tionship. Short run and long run price adjustment dynamics may be quite different,

especially for markets with significant transactions costs, like those for perishable

commodities in developing countries. Underlying error correction models of spatial

market networks is the idea that price time series may display long run equilib-

rium relationships, and short run deviations from equilibrium should be ‘corrected’

in subsequent time periods through the particular mechanisms that control price

adjustment.

We use a generalization of the error correction model to examine the nature of this

adjustment in periods with and without trade flows. We are particularly interested

in isolating price adjustment in periods without trade flows, in order to establish

whether price adjustment is attributable primarily to physical arbitrage associated

with trade, or whether it is perhaps equally attributable to non-material flows, pre-

sumably of information.4 This possibility of a distinction between the mechanism

behind price adjustment and trade flows is the general reason for the importance

of separating spatial market equilibrium from market integration concepts (Barrett,

2001). Thus, if dynamic spatial price analysis is to be used to identify and under-

stand the consequences of poorly functioning market systems, parsing out relative

4Information flows may, for example, be due to the effect of elaborate networks of tradersoperating in several markets simultaneously or the overall complexity of spatial market networks(Fackler & Tastan, 2008).

5

differences in adjustment due to direct linkages via physical trade flows versus more

indirect connections that exist without them seems a useful and novel exercise.

We study spatial equilibrium and integration by making use of data on prices,

transactions costs and trade flows by treating disruptions and resumptions of trade

as structural breaks in the cointegration relationship and then using the General-

ized Reduced Rank Regression techiques (GRRR) described in P. R. Hansen (2003).

GRRR provides estimates of error correction model parameters for structurally dis-

tinct periods, in our case, with and without observed trade. This method generates

estimates of both the long run equilibrium and speed of price adjustment to tempo-

rary disequilibria when linkages between markets are in part due to the behavior of

traders who operate in both markets and take advantage of arbitrage opportunities,

as well as estimates of these relationships when commodities do not move between

markets, which may be attributable to other mechanisms more indirect than physical

trade. The main innovation of GRRR is that it provides a straightforward method for

comparing all of the model parameters in these two regimes using nested hypothesis

tests, which was not previously possible using more conventional tests for structural

breaks due to the fact the parameters in the long run cointegration relationship have a

non-standard distribution (P. R. Hansen, 2003; Johansen, 1988). It also differs from

threshold cointegration models models (Balke & Fomby, 1997; B. E. Hansen & Seo,

2002) in that it takes structural breaks as known and exogenously determined and

incorporates this extra information directly, rather than indirectly using the magni-

tude of the estimated long run error term to identify distinct regimes. While many

other studies have examined different aspects of non-linear cointegration, GRRR is

6

a comprehensive framework for testing multiple hypotheses about both the long run

and short run parameters that was not previously available to researchers.

The model’s theoretical foundation is the standard competitive equilibrium rela-

tionship between prices in spatially distinct markets. The equilibrium conditions are

a function of both the returns to trade and the observed trade flows. With positive

trade flows, two markets (source market i and destination market j) are said to be

in competitive equilibrium if the price margin (mijt = Pjt − Pit) is exactly equal to

the cost to transfer goods between the markets, τijt.5 At this point, traders are indif-

ferent between moving and not moving goods between the two markets. Note that

these costs need not be symmetric. Including non-trading periods into the definition,

the generalized conditions for efficient spatial arbitrage (Barrett, 2001; Takayama &

Judge, 1971) are:

Pjt

≤ Pit + τijt if qij = 0 (a)

= Pit + τijt if q ∈ (0, qij) (b)

(1)

where qij represents trade flows from market i to market j and qij represents a

potential trade flow ceiling, due to either a quota or some other imposed restriction.

Note that in equation (1), the relationship that prevails between prices in different

markets depends upon the observed trade flows, qij. However, as we show below, it

is possible for other mechanisms to affect this relationship.

When the equilibrium relationship between Pjt and Pit binds with equality (as in

1(b)), this equality can be used to develop an error correction representation (Engle

5Subscripts indicate the direction of trade flows. For example, mijt = Pjt − Pit, indicates theintermarket price differential for goods flowing from market i to market j in period t. Similarly,transactions costs to move commodities from market i to market j are listed as τijt.

7

& Granger, 1987) of the dynamic relationship between market prices and transactions

costs over time, with 1(b) characterizing the long run equilibrium (i.e., the cointe-

grating relationship) between markets. However, in the short run, shocks to prices

and/or transactions costs may cause temporary deviations from this equilibrium. In

a dynamic context, the long run difference between destination and source market

prices, et ≡ Pjt−Pit, should be a stationary process, in that any temporary deviation

from long run spatial market equilibrium is expected to disappear over time.6 For

market prices, this process can be expressed quite generally as the residual from the

linear estimated relationship in (1b) (Engle & Granger, 1987):

Pjt − B1Pit ≡ et(B) (2)

with et thus representing an I(0), stationary random variable.7 Analysis of this resid-

ual allows one to establish exactly how long it takes for intermarket price adjustment

to return markets to their long run equilibrium state.

If et truly represents a long run, stationary process, then market prices are said

to be cointegrated time series. In the spatial market analysis literature, cointegrated

prices are often (if controversially) taken as indicators of the degree of market effi-

ciency in a given network.8

6Typically, the long run relationship is thought to exist between market prices, therefore wethus ignore any possible endogenous relationship between prices and transactions costs in thisstudy. Coleman (2009) provides a model of spatial arbitrage that incorporates the effects of tradeflows on the cost of transport, however this model is not appropriate to the data we use.

7As has been pointed out by Dercon (1995) and others (Goodwin & Piggott, 2001), the long-runequilibrium relationship between prices may involve price movements that are proportional to oneanother, rather than one-for-one. Hence the inclusion of the B parameter in equation (2).

8Barrett (1996), Fackler and Goodwin (2002) and others have noted that cointegration is neithernecessary nor sufficient for market efficiency, and that violations of some common assumptions

8

Regime-specific cointegration

For linear cointegration, an error correction representation of the relationship be-

tween prices in a source and destination market can be written as:

(∆Pjt

∆Pit

)= AB′Xt−1 +

∑d

Γd

(∆Pjt−d

∆Pit−d

)+ CZt + ut, ut ∼ N(0,

∑2x2

) (3)

In equation (3), Xt−1 = (Pj,t−1, Pi,t−1)′ are the (lagged) variables in the long run

equilibrium relationship included in the error correction model, and the B (a 2x1

matrix) parameters form the cointegration vector:9

Pjt −B1Pit ≡ et(B) ≡ B′Xt (4)

The parameters in A (a 2x1 matrix) govern the speed of adjustment of each market’s

price from short-term shocks back to the long run equilibrium. The Γd matrices (2x2)

capture the autocorrelation in the system between the price series, with d indicating

the lag length(s) included in the estimation. Zt includes any additional, exogenous

explanatory variables, like seasonal dummies or other factors.10

The model in equation (3) is appropriate only under the assumption that discon-

tinuities in trade flows do not matter to price adjustment dynamics, as it specifies

underlying cointegration models, such as stationary transactions costs and continuous trade flows,may be more to blame for the frequent rejection of efficiency found in the literature than an absenceof efficiency itself. We attempt to address some of these issues in this work.

9The cointegration vector in (4) is typically normalized on Pj in order to identify B.10Due to the particular way that bus fares and fuel prices are determined in Zimbabwe, we

combine them to account for intermarket transfer costs and can include it as an exogenous variablein Zt in our estimation. We also include an unrestricted constant in Zt to preserve degrees offreedom in our small sample.

9

that only one set of parameters govern behavior for the entire length of the price

series, instead of distinguishing between periods with and without trade flows.

Recognizing that the model in equation (3) may be too restrictive to represent

market relationships with multiple regimes, threshold cointegration models, initially

proposed by Balke and Fomby (1997), have been used to test spatial market equi-

librium in the presence of unobserved constant transactions costs (Dercon & van

Campenhout, 1999; Goodwin & Piggott, 2001; B. E. Hansen & Seo, 2002). These

transactions costs divide spatial market data into distinct regimes, within which the

spatial price adjustment dynamics may vary. Further, it is often assumed that no

error correction occurs for prices within a price band defined by the transactions

costs(described by equation (5) below):

|Pjt − Pit| ≤ τijt (5)

since arbitrage is not profitable and thus trade flows should not occur to bring prices

into long run equilibrium.11

Markets linked by trade flows are potentially different from those not linked by

trade flows, as the conditions in relation (1) based on spatial equilibrium theory

suggest. Not only might the speed of adjustment and short run parameters differ

between trade and no trade periods, but there may also be different mechanisms at

play effectively linking market prices in periods with and without trade in long run

equilibrium relationships.

11Equation (5) is just a reformulation of the efficient spatial arbitrage condition shown in (1a)that prevails when trade flows do not occur due to excessively high transactions costs.

10

This is precisely the effect we wish to explore in order to better understand the

role physical trade flows play in bringing about spatial competitive equilibrium via

price adjustment. Evidence of cointegration between markets in non-trade periods

suggests that the role of physical trade may be overstated in the literature and that

information flows that may impact market function and efficiency independent of

trading activity may be underappreciated. Allowing for complete variation in param-

eters across trading regimes is therefore critical to our analysis, however asymptotic

theory and tools for tesing for structural breaks in the cointegration vector itself have

not been available until relatively recently (Gonzalo & Pitarakis, 2006; P. R. Hansen,

2003).

P. R. Hansen (2003) presents a method to test for these prospective non-linearities

that enables us to specify and estimate the following model:

(∆Pjt

∆Pit

)=

(Atrade ∗B′tradeXt−1 +

∑d

Γtraded

(∆Pjt−d

∆Pit−d

)+ CtradeZt

)Itradet +(

Ano trade ∗B′no tradeXt−1 +∑

d

Γno traded

(∆Pjt−d

∆Pit−d

)+ Cno tradeZt

)Ino tradet + ut

(6)

where the Itradet and Ino trade

t are indicator functions for the specific trade regime into

which each time period, t, falls.12

The specification in (6) allows for potential differences in both long run price re-

lationships between markets under different trading regimes (the B parameters), as

12Siklos and Granger (1997) initially proposed the concept of regime-sensitive cointegration inthe context of interest-rate parity and structural breaks in monetary policy rules.

11

well as in how quickly the markets respond to shocks in each regime (the A parame-

ters) and the effects of autocorrelation and other factors (the Γ and C parameters).

With this model and necessary data on trade flows, as well as standard price and

transaction cost time series, we are able to examine empirically a key assumption in

the literature: that the Ano trade parameters equal zero when there are no trade flows

because physical arbitrage is commonly assumed to be the mechanism that returns

markets to equilibrium (Balke & Fomby, 1997, pg. 629).13

Therefore, our main hypothesis is that Ano trade = 0 and all the action in spatial

price adjustment occurs only during trading periods. Also we would like to test

whether the cointegrating vector is the same in both regimes (i.e., Btrade = Bno trade).

However, in order to examine these hypotheses, we need a method that accounts

for the possibility of regime-specific cointegrating relationships. This is because, if

adjustment is taking place in non-trade periods, then a cointegrating relationship

must be present. However, as it is clearly not due to the effect of trade flows,

it could be distinct from the relationship that prevails during trading periods and

should therefore be estimated separately.14

Note that we are assuming that a cointegration vector is defined in non-trade

periods. Although many of the studies in the spatial price adjustment literature

specifically model prices within the price band as a random walk (and often assume

that no trade takes place, although actual trade flow data are typically not avail-

13Our null hypothesis is an extension of the null found in other studies that spatial price adjust-ment with linear cointegration models, where inability to reject the null of a zero-valued adjustmentparameter is taken to mean that prices in a market are weakly exogenous to other prices in thespatial network (Fackler & Goodwin, 2002).

14Also, assuming linearity in the case of nonlinear long-run equilibrium relationships results ininconsistent estimation of the (misspecified) cointegration vector (Gonzalo & Pitarakis, 2006).

12

able), we are unable to include this possibility in our analysis, given the estimation

technique we plan to use. However, it has been observed that periods without trade

may still be consistent with a long run equilibrium relationship, for example, if all ar-

bitrage opportunities are exhausted such that traders are indifferent between trading

and not (Barrett & Li, 2002; Dercon & van Campenhout, 1999). Other recent work

on spatial price transmission in Ghana also finds error correction in non-trade periods

(Ihle, Amikuzuno, & von Cramon-Taubadel, 2010). The Generalized Reduced Rank

Regression method we use begins with the assumption of cointegration and then

allows for relatively straight-forward tests of whether the equilibrium relationship in

non-trade periods is distinct from that in the periods with trade.

III. Data

We estimate the regime-specific cointegration model specified in (6) with semi-weekly

data between January and December 2001 on prices, transactions costs and trade

flows for tomatoes in three important spot markets in Zimbabwe (T = 104). The

geographical distribution of these markets is shown in Figure 1. The data collected

include unit prices for tomatoes (in Zimbabwean dollars ($Z) per crate), intermarket

transfer costs as a proxy for transactions costs ($Z/crate), estimated from fuel prices

and bus fares, and a measure of trade flows between markets. The data were collected

through direct semi-weekly interviews with tomato traders and transporters over 52

weeks in 2001, as well as through monthly surveys of bus operators. The tomato

prices used represent the average price for the best grade of tomato currently available

13

in the market. The trade flow variable used to identify the structural breaks is a

binary indicator of the presence of tomatoes in a destination market from the set

of main source markets as observed by survey enumerators. During this period

in Zimbabwe, tomatoes were primarily transported as excess cargo on busses, the

pricing of which was administratively imposed by government, resolving what might

otherwise be a potential problem of endogenous intermarket transfer costs.15 These

data also have the attractive feature that they are available even when there are no

tomato trade flows, allowing estimation of the error correction term in the non-trade

periods in our model. More details on data collection can be found in Mabaya (2003)

and Mabaya (2004).

The primary players in these spot markets are traders who have purchased pro-

duce from local smallholder farmers and then sell the tomatoes in the market mostly

to low- or middle-income urban consumers. This constitutes a relatively informal

marketing structure, with more formal contract farming transactions occurring di-

rectly between private wholesalers or other large buyers (such as supermarkets or

public institutions like schools) and larger commercial farmers in other venues.

Tomato prices are more volatile in these spot markets than in the formal sector,

due to the absence of formal contracts and produce perishability.

We study price transmission between the following three directional market

pairs:16 Harare to Gweru, Harare to Bulawayo and Gweru to Bulawayo.17 Fig-

15Thus we treat these costs as an additional, exogenous control variable as explained above.16Only market dyads are considered in our analysis and we do not take into explicit account the

possible higher order effects of trade in a network with multiple linkages. See Fackler and Tastan(2008) on this issue.

17Harare is the capital of Zimbabwe and is close to major tomato production areas, which mayexplain the fact that there are no trade flow reversals observed during the sample year.

14

ures 2-4 plot out the price and trade flow data for the three market pairs. These

market pairs display the key characteristics necessary to test our hypotheses, in that

the relevant prices are non-stationary and integrated of order one, and that a suffi-

cient balance of observations of trade and non-trade periods were observed for each

pair.18 The market dyads in this study also display regime-specific cointegration

and seem most suitable for the analysis we wish to conduct. Table 1 presents the

Johansen trace tests for cointegration between market prices for each dyad as well as

the results of cointegration tests on the trade and non-trade period subsamples. As

can be seen, prices in both market pairs appear to be cointegrated overall as well as

within each trade regime, for the most part (tests for the Harare-Bulawayo pair offer

weaker support). However, in order to test our hypotheses of interest, GRRR must

be employed to be able to statistically compare the two regimes, as the distribution

of the B parameters is non-standard in reduced rank regressions.

Although data is available on tomato prices in several other major urban spot

markets in Zimbabwe in the same sample that we have used, there is no inter-market

trade flow of tomatoes between them. These spot markets are instead typically sup-

plied by nearby agricultural production regions. Thus we are not able to incorporate

these markets explicitly into our analysis that compares trade and non-trade peri-

ods. However our results potentially have more general implications for spatial price

adjustment dynamics for these markets in Zimbabwe, as do we find evidence for

cointegration in four out of the eight market pairs that had no trade flows between

them at any point during the year of the study. Moreover, these pairs all contain

18Augmented Dickey-Fuller test statistics were used to determine the integration order of thedifferent time series. Details are available from the authors by request.

15

the Chitungwiza market. Chitungwiza prices are strongly cointegrated with Harare

prices, which are also cointegrated with these other spot markets. While evidence

of a cointegration relationship without trade flows (usually in the absence of data

on transactions costs and trade flows) has previously been taken as evidence of the

limitations of cointegration analysis to understand the efficiency of a spatial mar-

ket network (Barrett, 1996), our current findings (in combination with our specific

knowledge of trade regimes and transaction costs) suggest that some of these re-

lationships might in fact represent real long run adjustment dynamics even in the

absence of trade.

IV. Estimation Strategy

Estimating and testing for trade regime-specific cointegration presents an econo-

metric challenge. Under the null hypothesis, the speed of adjustment parameters

in the non-trading periods (Ano trade) should equal zero and prices in non-trade pe-

riods should not show any tendency towards long-run adjustment. During trade

periods, there is a unique long-run relationship under the null, et, which is a sta-

tionary process. The alternative hypothesis is that the trade and no trade regimes

have statistically significant speeds of adjustment in both trading regimes and/or

different long-run relationships. Given our desire to compare the relative strength of

the impact on price adjustment of physical flow of goods between markets with the

impact of other forces that operate in non-trading periods, we need to test the linear

cointegration model (shown in (3)) against one in which the alternative is non-linear

16

cointegration in the sense that the long run relationship may differ across regimes

(6).

Our estimation strategy is as follows. First, we follow P. R. Hansen (2003) and

estimate equation (6) using GRRR and analyze the Atrade, no trade and Btrade, no trade

parameters for each regime.19 We then estimate a restricted model, which imposes

that A and B are identical across trade regimes. As GRRR is used to examine non-

linear adjustment processes with structural breaks, conventional maximum likelihood

techniques are not appropriate for parameter estimation. To overcome this difficulty,

GRRR makes use of the fact that the parameters can be estimated iteratively, and

with specific sets of parameters held constant, estimation reduces to a set of sim-

pler GLS problems for which there are analytical solutions. Oberhofer and Kmenta

(1974) first outlined an iterative algorithim for these kinds of estimation problems.

P. R. Hansen (2003) follows Oberhofer and Kmenta and then demonstrates that

the likelihood ratio statistic obtained after estimating the system with parameter

restrictions can determine whether the restricted model is appropriate for the data

and describes the distribution of this test statistic for these reduced rank regressions.

V. Results

The parameter estimates from equation (6) are presented in Tables 2-4 for the three

market pairs. We used the Akaike Information Criterion and the Hannan-Quinn’s

Criterion on the linear model to both determine that one lag of the dependent variable

19We also allow the C parameters on transaction costs to vary across trade regimes, although weconstrain the Γ parameters and the constant, due to our small sample size.

17

was appropriate for each market pair in the associated vector autoregression and also

provide additional model selection information for jointly determining the lag length

and the cointegration rank of both the linear and the non-linear cointegration models,

following Baltagi and Wang (2007).

We present the unrestricted and restricted parameters and the likelihood ratio

test results for equality between the trade and no trade parameters for each market

pair. P. R. Hansen (2003) demonstrates that the speed of adjustment A, along

with the Γ and C parameters have a Gaussian distribution, so standard errors can

be easily calculated. The B parameters have a mixed Gaussian distribution, so

standard errors are not presented, however the likelihood ratio test does not depend

on the standard errors and can still be performed. The likelihood ratio test has a chi-

squared distribution, with the degrees of freedom equal to the number of parameter

restrictions (which for each market pair equals 6). Table 5 presents the predicted

half-lives for each market pair and trade regime.20

For the Harare to Gweru market dyad, in trading periods, the speed of adjustment

is significantly different from zero in both the source and destination markets, which

is what is typically assumed in most spatial price transmission models. However,

in non-trade periods, statistically significant price adjustments also occur in both

markets. This signals qualitatively different spatial price adjustment mechanisms

20For ease of interpretation, the speed of adjustment parameters can be expressed as a half-life,Thalf , which indicates how long it takes for half of the deviation from long run equilibrium to becorrected. Thalf = ln(0.5)/ln(1 − |ak|), k = {Pj , Pi},where ak is the parameter estimate from thematrix A for the destination price (k = Pj) and the source price (k = Pi) equation, respectively(Dercon and Van Campenhout (1999)). In all of our estimates, since our time observations aresemi-weekly, Thalf has been multiplied by 3.5 (days/semi-week) to convert the half-life into unitsof days, rather than ‘semi-weeks.’

18

under trade and no trade regimes, an impression confirmed by the likelihood ratio

test statistic, which strongly rejects the null of similar mechanisms across trade

regimes (p=0.011). Thus the data do not support linear cointegration; the data

favor modeling price transmission for this market pair as two separate processes

during trade and non-trade periods. The estimated half-life for price adjustment

in the source market is likewise shorter during the non-trade regime, underscoring

that price adjustment does not seem to be driven exclusively by physical arbitrage

activity. The long run relationship between the prices also changes between trade

regimes, with prices more closely proportional to one another (0.977) during non-

trade periods.

The results are broadly similar for the Harare to Bulawayo and Gweru to Bu-

lawayo market pairs (Tables 3 and 4, respectively). The likelihood ratio test also

strongly rejects the restricted model or equivalent adjustment processes across trade

regimes for these two market pairs (p=0.017 and p=0.013, respectively). The error

correction process appear distinct for trade and non-trade periods in all three market

pairs. Between Harare and Bulawayo, the Bulawayo prices do most of the adjusting,

primarily during non-trade periods (the adjustment parameter for the trade periods

is significant at the 20% level). Intermarket transfer costs only seem to influence

destination market prices (i.e. Bulawayo) and in a manner we would expect by

raising destination market prices (CPj> 0). Intermarket transfer costs also affect

destination market prices during periods both with and without trade.

Between Gweru and Bulawayo, Bulawayo prices adjust in all periods, while Gweru

prices only seem to adjust to shocks when there are physical trade flows. In this

19

market dyad, intermarket transfer costs only affect the source market (Gweru), again

in an expected manner by lowering source market prices (CPi< 0).

If one were to assume linear cointegration between these markets (as reflected in

the rightmost columns of Table 5), the estimated adjustment speed would generally

appear slower than that estimated for the trade regimes separately. The implication

is that failure to allow for potential differences in the spatial price adjustment mech-

anism between trade and no trade periods can understate the speed at which price

convergence occurs.

There are several ways to interpret the finding that prices are cointegrated with-

out trade flows. It is possible that tomato prices in the source and destination markets

for all three pairs were influenced by a common, exogenous factor, such as overall

inflation or seasonality. However, Mabaya (2003) still found general evidence for

this ‘segmented integration’ between the different price series even after controlling

for both of these processes. Another possibility is that participants in the different

spot markets engage in formula pricing (Tomek & Robinson, 1990) during non-trade

periods, using information about tomato prices in larger markets as a baseline to

adjust local spot prices. Informal conversations with traders during the data collec-

tion period revealed that information about Harare prices was readily available to

traders in smaller markets through bus drivers and passengers coming from the cap-

ital. As well, in some, but not all, of the spot markets, survey respondents indicated

that they used this information to set prices when there were relatively few market

participants (Mabaya, 2003).

Furthermore, trade flows under domestic market conditions (unlike international

20

trade) are difficult to capture clearly. Local spot markets draw produce from ‘catch-

ment areas ’ (McNew, 1996; Mabaya, 2003) made up of farms within a defined radius

of the urban market. In some instances, farmers may reside in the intersection of two

(or more) catchment areas and may supply to multiple urban spot markets, depend-

ing on potential profits. The activities of such farmers will serve to link prices in all

of the markets in which they participate, regardless of whether a trader subsequently

physically ships produce between the urban spot markets. Finally, prices between

two markets where there are no physical trade flows may also be cointegrated if both

markets trade with a common third market (Fackler & Tastan, 2008). The appar-

ent cointegration between the tomato prices in Chitungwiza and several other spot

markets, despite the fact that no produce was observed to move between them, may

be informal evidence for this last possible mechanism. This indirect evidence seems

to suggest one plausible mechanism by which price transmission may occur in the

absence of trade flows and supports our contention that developing a method for

comparing trade and non-trade periods is important in understanding the behavior

of these markets more completely. However without additional data we are not able

to further explore all of these particular information channels in more detail.

VI. Conclusions

Using a newly developed test for non-linear cointegration analysis, we specify and

estimate a trade regime-sensitive cointegration model and analyze the similarities

and differences between spatial price adjustment dynamics in tomato markets in

21

Zimbabwe in periods with and without physical trade flows. It appears that er-

ror correction between price margins and transactions costs occurs both with and

without trade. This provides clear evidence that the mechanisms governing spatial

price adjustment dynamics extend well beyond the physical arbitrage activities of

traders, and thus that analysis of market integration and efficiency must allow for

the multiple price transmission mechanisms that may be at work in a given network.

In particular, in this instance, by ignoring the possibility of multiple spatial pricing

equilibria, time series analysis based on linear cointegration would have suggested

that tomato markets in Zimbabwe adjust more slowly than they do and would not

reflect the quite distinct processes that appear to govern price transmission during

non-trade periods. Our more general method, by accounting for trade and non-trade

regime dynamics separately, leads to the conclusion that these markets are actually

very efficient in transmitting market signals across space through price adjustment

dynamics. Given the very different policy implications of each of these analyses, it

seems clear that testing and accounting for non-linearities in long run equilibrium

states characterized by trade flows is important. It also opens up questions as to the

precise nature of spatial price adjustment in non-trade periods, which has been given

very little attention in the spatial price analysis literature, despite the acknowledged

importance of trade flows on spatial price adjustment (Barrett & Li, 2002).

For market studies with the full complement of prices, transactions costs and

trade flow time series, our method should provide a useful means to characterize the

time series behavior of these variables and to avoid the possible mistaken inference

likely to result from spatial price analysis with trade and non-trade regime data mixed

22

together. This should serve as an additional tool for researchers and policy makers

working to understand spatial price transmission and the competitive performance

of commodity markets.

23

Figure 1Location of sample spot markets in Zimbabwe

24

Figure 2Semi-weekly tomato prices and trade flows, Harare to Gweru

25

Figure 3Semi-weekly tomato prices and trade flows, Harare to Bulawayo

26

Figure 4Semi-weekly tomato prices and trade flows, Gweru to Bulawayo

27

Table 1Johansen trace tests for cointegration between Harare and Gweru, Harare and

Bulawayo and Gweru to Bulawayo market pairs

Market Pair Rank Trade Non-Trade Whole Sample†

Harare-Gweru 0 20.555 (0.044) 19.595 (0.060) 20.002 (0.053)1 8.838 (0.058) 4.907 (0.304) 8.384 (0.071)

T=64 T=40 T=104Harare-Bulawayo 0 12.493 (0.414) 17.592 (0.113) 17.084 (0.131)

1 3.853 (0.447) 5.362 (0.255) 7.485 (0.108)T=48 T=56 T=104

Gweru-Bulawayo 0 17.610 (0.112) 25.761 (0.007) 24.787 (0.010)1 5.471 (0.244) 5.588 (0.233) 7.294 (0.114)

T=58 T=46 T=104† p-values are reported in parentheses. The underlying model contained one lag

and a restricted constant in the cointegration vector.

28

Table

2P

aram

eter

esti

mat

esof

equ

atio

n(6

)-

Har

are

toG

wer

um

arke

tpa

ir

Tra

de

Regim

eN

oT

rade

Regim

eR

est

rict

ed

(θT

=θN

T)

Eq.

Para

mete

rC

oeffi

cien

t†Std

.C

oeffi

cien

tStd

.C

oeffi

cien

tStd

.(θ

T)

Err

.(θ

NT

)E

rr.

Err

.[e

t−1(B

)]B

1-0

.642

-0.9

77-1

.012

[Pjt

]A

Pj

-0.1

95**

*0.

081

-0.1

94*

0.11

9-0

.026

0.05

1C

Pj−

tran

s.co

sts

-0.2

000.

514

-0.8

96**

0.52

0-0

.374

0.50

5C

Pj−

con

s.93

.793

*62

.987

93.7

93*

62.9

8754

.099

64.4

34Γ

Pj,P

jt−

10.

060

0.10

60.

060

0.10

6-0

.002

0.10

9Γ

Pj,P

i t−

1-0

.058

0.08

6-0

.058

0.08

60.

001

0.08

8

[Pit]

AP

i0.

184

**0.

098

0.39

0**

*0.

144

0.18

8**

**0.

059

CP

i−

tran

s.co

sts

-0.7

120.

621

-0.3

250.

628

-0.8

54*

0.58

3C

Pi−

con

s.47

.924

76.1

3647

.924

76.1

3696

.217

74.3

42Γ

Pi,P

jt−

1-0

.087

0.12

8-0

.087

0.12

8-0

.063

0.12

6Γ

Pi,P

i t−

10.

051

0.10

40.

051

0.10

40.

033

0.10

2

AIC

17.9

0817

.974

HQ

18.0

7418

.088

Log

Lik

elih

ood

-118

6.76

0-1

195.

109

df86

80L

RS

tati

stic‡

χ2(6

)16

.698

(0.0

11)

†N

ote:∗,∗∗,∗∗∗,∗∗∗∗

indic

ate

sign

ifica

nt

at20

%,

10%

,5%

and

1%re

spec

tive

ly.

Subsc

ripti

refe

rsto

the

sourc

em

arke

tan

dsu

bsc

riptj

refe

rsto

the

des

tinat

ion

mar

ket.

‡p-v

alue

rep

orte

din

par

enth

eses

.

29

Table

3P

aram

eter

esti

mat

esof

equ

atio

n(6

)-

Har

are

toB

ula

way

om

arke

tpa

ir

Tra

de

Regim

eN

oT

rade

Regim

eR

est

rict

ed

(θT

=θN

T)

Eq.

Para

mete

rC

oeffi

cien

t†Std

.C

oeffi

cien

tStd

.C

oeffi

cien

tStd

.(θ

T)

Err

.(θ

NT

)E

rr.

Err

.[e

t−1(B

)]B

1-0

.829

-0.7

191.

705

[Pjt

]A

Pj

-0.1

17*

0.07

0-0

.380

****

0.09

5-0

.076

***

0.03

1C

Pj−

tran

s.co

sts

0.91

4**

*0.

408

0.77

1**

*0.

315

0.00

70.

268

CP

j−

con

s.-9

4.47

8*

60.4

88-9

4.47

8*

60.4

8897

.851

*61

.892

ΓP

j,P

jt−

1-0

.002

0.09

6-0

.002

0.09

6-0

.066

0.09

8Γ

Pj,P

i t−

10.

052

0.12

30.

052

0.12

30.

156

0.13

2

[Pit]

AP

i0.

091

*0.

057

0.07

80.

077

-0.0

55**

*0.

023

CP

i−

tran

s.co

sts

-0.4

260.

331

-0.2

820.

256

-0.0

460.

203

CP

i−

con

s.45

.670

49.1

0845

.670

49.1

0877

.970

**46

.800

ΓP

i,P

jt−

1-0

.082

0.07

8-0

.082

0.07

8-0

.030

0.07

4Γ

Pi,P

i t−

10.

003

0.10

00.

003

0.10

00.

035

0.10

0

AIC

19.1

5519

.008

HQ

19.1

2119

.122

Log

Lik

elih

ood

-124

0.16

3-1

247.

860

df86

80L

RS

tati

stic‡

χ2(6

)15

.396

(0.0

17)

†N

otes

asp

erT

able

2.

30

Table

4P

aram

eter

esti

mat

esof

equ

atio

n(6

)-

Gw

eru

toB

ula

way

om

arke

tpa

ir

Tra

de

Regim

eN

oT

rade

Regim

eR

est

rict

ed

(θT

=θN

T)

Eq.

Para

mete

rC

oeffi

cien

t†Std

.C

oeffi

cien

tStd

.C

oeffi

cien

tStd

.(θ

T)

Err

.(θ

NT

)E

rr.

Err

.[e

t−1(B

)]B

1-1

.140

-0.8

31-1

.146

[Pjt

]A

Pj

-0.2

31**

*0.

096

-0.6

08**

**0.

145

-0.1

85**

*0.

076

CP

j−

tran

s.co

sts

0.64

90.

724

0.57

40.

744

0.23

70.

747

CP

j−

con

s.-2

7.76

977

.452

-27.

769

77.4

52-1

6.36

182

.313

ΓP

j,P

jt−

10.

040

0.10

00.

040

0.10

00.

003

0.10

6Γ

Pj,P

i t−

1-0

.114

0.15

3-0

.114

0.15

30.

063

0.15

9

[Pit]

AP

i0.

142

***

0.06

40.

103

0.09

80.

129

****

0.04

7C

Pi−

tran

s.co

sts

-0.8

74**

0.48

8-0

.971

**0.

571

-0.8

13**

0.46

2C

Pi−

con

s.93

.405

**52

.138

93.4

05**

52.1

3890

.582

**50

.837

ΓP

i,P

jt−

1-0

.008

0.06

7–0

.008

0.06

7-0

.006

0.06

5Γ

Pi,P

i t−

10.

013

0.10

40.

013

0.10

40.

024

0.09

8

AIC

18.4

7818

.539

HQ

18.6

4418

.653

Log

Lik

elih

ood

-121

5.82

1-1

223.

943

df86

80L

RS

tati

stic‡

χ2(6

)16

.244

(0.0

13)

†N

otes

asp

erT

able

2.

31

Table

5Im

plie

dH

alf-

Liv

es(i

nda

ys)

for

Tra

devs

.N

on-T

rade

Reg

imes

and

for

the

Ove

rall

sam

ple

Mark

et

Par.

Tra

de

Reg

ime

No

Tra

de

Reg

ime

Overa

llPair

(Eq.)

(Thalf

=λ

T)

(Thalf

=λ

NT)

(Thalf

=λ)

Est

.C

oeff

.s.

e.E

st.

Coe

ff.

s.e.

Est

.C

oeff

.s.

e.H

re-G

wr

Thalf

(AP

j)

11.1

78**

*5.

201

11.2

50*

7.72

693

.091

187.

878

Hre

-Gw

rT

half

(AP

i)

11.9

36**

7.07

24.

907

***

2.34

811

.633

****

4.06

3H

re-B

yoT

half

(AP

j)

19.5

33*

12.5

375.

075

****

1.63

530

.799

***

13.0

52H

re-B

yoT

half

(AP

i)

25.4

60*

16.8

0030

.069

31.3

0842

.967

***

18.7

84G

wr-

Byo

Thalf

(AP

j)

9.25

5**

*4.

386

2.58

9**

*1.

022

11.8

81**

*5.

439

Gw

r-B

yoT

half

(AP

i)

15.8

90**

*7.

804

22.2

3022

.183

17.5

26**

*6.

845

32

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