No. ID-15

 OFFICE OF INDUSTRIES WORKING PAPER

 U.S. INTERNATIONAL TRADE COMMISSION

Ronald A. Babula,

Robert A. Rogowsky

Robert F.J. Romain

March, 2006

 

R. Babula was an Industry Economist with the Office of Industries, and on detail with the Office of

Operations, and R. Rogowsky is the Director, Office of Operations, of the U.S. International Trade

Commission. R. Romain is a Full Professor with the Center for Research in the Economics of

Agrifood (CREA), and with the Department of Agricultural Economics and Consumer Science,

Laval University, Quebec, Canada. This paper’s views do not necessarily represent those of the U.S.

International Trade Commission (or any of its individual Commissioners), Laval University,

CREA, or the Department of Agricultural Economics and Consumer Science. Working Papers are

circulated to promote the active exchange of ideas between USITC staff and recognized experts

outside the USITC, and to promote professional development of Office staff by encouraging

outside professional critique of staff research. The authors are grateful for the thorough review,

advice, and guidance of Dr. David Bessler, Professor, Department of Agricultural Economics, Texas

A&M University. Ms. Ophelia McCardell is thanked for expertly formatting this report,

particularly in processing the graph work and tables.

ADDRESS CORRESPONDENCE TO:

OFFICE OF OPERATIONS OR OFFICE OF INDUSTRIES

U.S. INTERNATIONAL TRADE COMMISSION

WASHINGTON DC 20436

 EXPLOITING LONG RUN COINTEGRATION PROPERTIES OF A 

 QUARTERLY U.S. SYSTEM OF WHEAT-RELATED PRODUCTS
1

Exploiting Long Run Cointegration Properties of a Quarterly U.S. System 

 of Wheat-Related Products

Abstract: The methods of the cointegrated vector autoregression/vector error correction (VAR/VEC)

model are applied to quarterly U.S. markets for wheat and for wheat-using products of wheat flour, mixes

and doughs, bread, wheat-based breakfast cereals, and cookies and crackers. This study extends the

recent and earlier reduced-form VAR econometric work done on these same markets, by dichotomizing

the system into a long run error-correction space of economic relationships and a short run/deterministic

component. Results include an array of empirical estimates of the parameters (some structural) and

relationships that drive the wheat-related markets and govern their inter-action. An array of empirical

estimates of market impacts on policy, institutional, and trade events is also provided.

Key words: Cointegration, wheat-based U.S. markets, vector autoregression and error correction models.
2

Our purpose is to extend some recent quarterly econometric research on U.S. wheat-based

markets with newer and advanced methods and updated samples. Rich, Babula, and Romain (RBR 2002)

applied methods of vector autoregression or VAR modeling, to a quarterly system of U.S. markets for

wheat, wheat flour, mixes and doughs (mixes/doughs), bread, wheat-based breakfast cereals (cereals), and

cookies and crackers (cookies/crackers). They then provided detailed analyses of impulse response

simulations and of other econometric estimates to illuminate the dynamic quarterly patterns with which

this reduced form system interacts and some empirical estimates of principal market parameters which

propel these markets. Babula, Bessler, and Payne (hereafter, BBP 2004) updated RBR’s (2002) sample

and methods. BBP (2002) extended RBR’s findings by having combined Bernanke (1986) structural

VAR methods with directed acyclic graph (DAG) analysis, to the same set of quarterly markets. Perhaps

for the first time, we apply methods of Johansen and Juselius’ (1990, 1992) cointegrated VAR model to

the same market system, and exploit the cointegration properties that error-correct the system of

individually nonstationary variables into a stationary system. Our results further dichotomize those of

RBR (2002) and BBP (2004) into a set of long run structural error correction or cointegration

relationships and into a set of short run/deterministic results (not focused on here) . These cointegration

results provide a set of structural, along with reduced form, insights that enhance the precision of the

findings of the previous RBR (2002) and BBP (2004) work. Our results include estimates of price

elasticities of supply, cross-price transmission or response parameters, and a rich set of empirical effects

of policy, trade, economic, and political events (hereafter, important market/institutional events).

This paper has seven ensuing sections. The first presents cointegrated VAR methods as a way to

empirically model the quarterly U.S. system of wheat-related markets. The second section analyzes data

behavior patterns to generate specification implications to avoid well-known potential econometric

problems with compromised inference and biased estimates. The third section summarizes efforts to

achieve an adequately specified levels VAR (and its unrestricted VEC equivalent) model to exploit what

are later revealed to be the system’s substantial cointegration properties. We provide a rigorous analysis

of the model’s statistical adequacy based on results from a battery of diagnostic mis-specification tests

suggested by Juselius (2004, pp. 72-82) and Juselius and Toro (2005). In a fourth section, evidence from

Johansen and Juselius’ (1990, 1992) well-known trace tests from other sources is used to determine the

number of cointegrating vectors or relationships (hereafter, CVs). The cointegration space is then

restricted for reduced rank. The fifth section employs Johansen and Juselius’ (1990, 1992) hypothesis

test procedures on the rank-restricted cointegration space to illuminate the long run economic

relationships that drive and tie-together the upstream and downstream wheat-based markets. A sixth

section provides economic interpretations of the CVs that are fully restricted for rank and for statistically

supported restrictions from the hypothesis tests. A summary and conclusions follow.

Time Series Econometrics, Modeled Markets, and Data Resources

It is well-known that economic time series often fail to meet the conditions of weak stationarity

(i.e., stationarity and ergodicity) required of valid inference, and in some cases, unbiased estimates, from

regressions using time-ordered data (Engle and Granger 1987; Granger and Newbold 1986, pp. 1-5). And

while data series are often individually nonstationary, they can form vectors with stationary linear

combinations, such that the vector of inter-related series are “cointegrated” and move in tandem as an

error-correcting system (Johansen and Juselius 1990, 1992).
1

 The U.S. wheat market year or MY extends from June 1 through May 31 of the ensuing calendar year. Hence,

1985/86:01 represents the first MY quarter extending from June through August, 1985; 1985/96:02 represents the second MY

quarter extending from September through November of 1985; 1985/86:03 reflects the third MY quarter extending from

December 1985 through February of 1986; and 1985/86:04 reflects the fourth MY quarter extending from March through May of

1986. 

3

After repeating BBP’s (2004) search for U.S. wheat-related market data, we chose an updated

quarterly sample of the following endogenous variables (denoted throughout interchangeably by the

parenthetical labels) defined and sourced as follows:

1. U.S. price of wheat (PWHEAT): reflected by the U.S. all-wheat price published by the

U.S. Department of Agriculture, Economic Research Service (USDA, ERS 2004, 2005).

2. U.S. market-clearing quantity of wheat (QWHEAT): defined as the sum of beginning

stocks, production, and imports, published by the USDA, ERS (2004, 2005).

3. U.S. wholesale price of wheat flour (PFLOUR): represented by the U.S. producer

price index (hereafter, PPI) for wheat flour, series no. PCU3112113112111, published by

the U.S. Department of Labor, Bureau of Labor Statistics (Labor, BLS 2005).

4. U.S. wholesale price of mixes and doughs (PMIXES): reflected by the U.S. PPI for

flour mixes and refrigerated and frozen doughs and batters, series no.

PCU3118223118226, published by Labor, BLS (2005).

5. U.S. wholesale bread price (PBREAD): defined as the U.S. PPI for bread, series

PCU3118123118121, published by Labor, BLS (2005).

6. U.S. wholesale price of wheat-based breakfast cereals (PCEREAL): represented by the

U.S. PPI for wheat flakes and other wheat breakfast foods, series no.

PCU311230311230112, published by Labor, BLS (2005).

7. U.S. wholesale price of cookies and crackers (PCOOKIES): represented as the U.S.

PPI for cookie and cracker manufactured products, series PCU311821311821, published

by Labor, BLS (2005).

Data are quarterly, seasonally unadjusted, and placed into natural logarithms. Data were available for the

1985/86:01–2004/05:04 sample period.1

 Since data were not available for all variables prior to 1985/86,

our analysis may have potential problems from small samples.

Analysis of Wheat-Based Time Series Data

Figures 1-7 provide the plotted endogenous variables: logged levels in the upper panels and

differences in the lower panels. A weakly stationary series has a constant and finite mean and variance,

has time-independent observations, and generates regression coefficient estimates that are time-invariant

(Juselius 2004, chapters 3 and 4). Weakly stationary data frequently cycle and mean-revert. The

following are highlights of nonstationary behavior with potential considerations for model specification:
2

This section draws heavily on the work of Johansen and Juselius (1990, 1992) and Juselius (2004).

4

• PWHEAT, figure 1 and PFLOUR, figure 3: Prices follow time-enduring cycles; seldom meanrevert; display periods of variant market behavior (slope changes) possibly from policy and

market events discussed later; trend through substantial subsamples; and display apparently nonconstant variation levels (heteroscedasticity or ARCH effects). Differences suggest possible

extraordinary effects of observation-specific events (hereafter “outlier” effects and observations). 

Model specification considerations include: various permanent shift dummy (i.e. binary)

variables, outlier variables, and a linear trend.

• QWHEAT, figure 2: Wheat quantity is clearly saddled with seasonal effects and subperiods of

trending. Specification considerations include centered seasonal variables and a linear trend.

• PMIXES, figure 4: PMIXES follows a clear upward trend; displays no cycling or meanreverting behavior; and displays marked changes in slope and behavior, particularly during 

1989/90-91/92 and after 2000/01, from market/institutional events discussed below. Differences

suggest ARCH effects with more volatile behavior in early subsamples, and periodic instances of

outlier effects during 1986/87– 1990/91, and towards the sample’s end. Specification

considerations include permanent shift and outlier binary variables, and a linear trend.

• PBREAD, figure 5 and PCOOKIES, figure 7: PBREAD and PCOOKIES display similar

nonstationary behavior: clear trending; virtually no cycling and mean-reversion; and a number of

slope changes (e.g. 1996/97 for PBREAD, late 2002/03 for PCOOKIES). Differences of both

variables exhibit potentially extraordinary outlier and ARCH effects throughout, particularly

during the early subsamples. Specification considerations include a number of permanent shift

and outlier binary variables, along with a linear trend for both prices.

• PCEREAL, figure 6. PCEREALS tends to follow trends in substantial subsamples; displays

little or no cycling or mean-reversion; and appears to experience changes in behavior and slope

from market and policy events during 1995/96–1996/97, just as the 1996 U.S. farm bill and

Uruguay Round were implemented. Differences reflect possible non-constant levels of variation,

especially in early 1993/94 and early 1996/97. Specification considerations include a number of

permanent shift and outlier binaries, and a linear trend.

The Statistical Model: The Unrestricted Levels VAR and VEC Equivalent2

Throughout, a number of terms are used: (1) the unrestricted levels VAR denotes a VAR model in

logged levels; (2) the unrestricted VEC denotes the algebraic equivalent of the unrestricted levels VAR,

before the cointegration space is restricted for rank or for statistically supported restrictions; (3) the

cointegrated VEC is the unrestricted VEC with its cointegration space restricted for reduced rank; and (4)

the fully restricted cointegrated VEC is the unrestricted VEC after the cointegration space’s restriction for

reduced rank and for the statistically supported restrictions from the hypothesis tests. The “p” denotes the

number (seven) of endogenous variables; “p1" denotes the number of variables 
5

PWHEAT

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.4

-0.3

-0.2

-0.1

-0.0

0.1

0.2

0.3 Differences

Figure 1

Plots of logged levels and differences: Wheat price.

QWHEAT

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

6.6

6.8

7.0

7.2

7.4

7.6

7.8

8.0

8.2

8.4 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25 Differences

Figure 2

Plots of logged levels and differences: Wheat quantity.
6

PFLOUR

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

4.4

4.5

4.6

4.7

4.8

4.9

5.0 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15 Differences

Figure 3

Plots of logged levels and differences: Wheat flour price.

PMIXES

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

4.60

4.65

4.70

4.75

4.80

4.85

4.90 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03 Differences

Figure 4

Plots of logged levels and differences: Price of mixes and doughs
7

PBREAD

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

4.8

4.9

5.0

5.1

5.2

5.3

5.4

5.5

5.6 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040 Differences

Figure 5

Plots of logged levels and differences: Bread price.

PCEREAL

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

4.72

4.80

4.88

4.96

5.04

5.12

5.20

5.28 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.09

-0.06

-0.03

0.00

0.03

0.06 Differences

Figure 6

Plots of logged levels and differences: Price of wheat-based breakfast cereals.
8

in the cointegration space (seven endogenous, and other deterministic variables introduced later); and “r”

represents the cointegration space’s reduced rank and the number of cointegrating vectors or CVs. Our

chosen methods involve specification and estimation of an adequately specified levels VAR (and

unrestricted VEC), such that residual behavior approximates well-known assumptions of multivariate

normality (Juselius 2004, chapter 5). 

The Levels VAR and unrestricted VEC of the wheat-based model system.

Following Bessler (1984) we posit the above wheat-related variables as the following VAR

model, where each endogenous variable is a function of k lags of itself and of each of the remaining

endogenous variables in the system:

(1) X(t) = a(1,2)*PWHEAT(t-1) + . . .. . . . + a(1,k)*PWHEAT(t-k)+ 

 a(2,1)*QWHEAT(t-1)+ . . . . . . . . + a(2,k)*QWHEAT(t-k)+

 a(3,1)*PFLOUR(t-1) + . . . . . . . . .+a(3,k)*PFLOUR(t-k)+ 

a(4,1)*PMIXES(t-1)+ . . . . . . . . . .+a(4,k)*PMIXES(t-k)+

 a(5,1)*PBREAD(t-1)+ . . . . . . . . . +a(5,k)*PBREAD(t-k) + 

a(6,1)*PCEREAL(t-1)+ . . . . ... . . +a(6,k)*PCEREAL(t-k)+

a(7,1)*PCOOKIES(t-1)+ . . . . . . . +a(7,k)*PCOOKIES(t-k)+

 a(c)*CONSTANT + a(S)* SEASONALS + ,(t) 

PCOOKIES

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

4.74

4.80

4.86

4.92

4.98

5.04

5.10

5.16

5.22 Levels

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

-0.005

0.000

0.005

0.010

0.015

0.020

0.025 Differences

Figure 7

Plots of logged levels and differences: Price of cookies and crackers.
9

The asterisk and ) denote multiplication and difference operators throughout. The ,(t) are white noise

residuals. X(t) = PWHEAT(t), QWHEAT(t), PFLOUR(t), PMIXES(t), PBREAD(t), PCEREAL(t), and

PCOOKIES(t). The a-coefficients are ordinary least squares (OLS) estimates with the first parenthetical

digit denoting the seven endogenous variables as ordered above, and with the second referring to the lags

1, 2, .... , k. The a(c) denotes an intercept. The parenthetical terms on the endogenous variables refer to

the lag: t to the current period-t, and t-k to the kth lag. Equation 1 also includes three quarterly centered

seasonal variables and other potential permanent shift and outlier binaries not shown notationally. We

applied Tiao and Box’s (1978) lag selection procedure that uses a likelihood ratio test corrected for small

samples, and results suggested a two-order lag structure (k=2). 

Johansen and Juselius (1990) and Juselius (2004, p. 66) demonstrated that the VAR model in

equation 1 is rewritten more compactly as an unrestricted VEC:

(2) x(t) = '(1) * )x(t-1) + A*x(t-1) + M*D(t) + ,(t)

The ,(t) are residuals distributed as white noise. The x(t) and x(t-1) are p by 1 vectors of the above seven

wheat-based variables in current and lagged levels, '(1) is a p by p matrix of short run regression

coefficients on the lagged differences, and A is a p by p error correction term to account for endogenous

variable levels. The M*D(t) is a set of deterministic variables: three seasonals and a host of other trend

and dummy variables which will be added to address the data issues identified above as the analysis

unfolds. The rank-unrestricted A or error correction term is decomposed as follows

(3) A = "*$’ where " is a p by r matrix of adjustment speed coefficients and $ is a p by r vector

of error-correction coefficients.

The A = "*$’ term is interchangeably denoted as the levels-based long run component, error

correction term, or cointegration space of the model. The [)x*(t-1), M*D(t)] is collectively considered

the short run/deterministic model component.

Data analysis and previous research by BBP (2004), RBR (2002), and Babula and Rich (2001)

suggested possible inclusion of a linear trend and nine permanent shift binaries discussed below in

equation 2's long run levels-based cointegration space. These same variables in differenced form and a

set of three centered seasonals were considered for equation 2's short run/deterministic component. 

Analysis also led to consideration of various outlier binaries in the short run/deterministic component. 

The permanent shifters include (hereafter denoted by the upper-cased labels):

•URUGUAY: valued at 1.0 for 1994/95:02–2004/05:04 MY period and 0.0 otherwise, to capture

the effects of the Uruguay Round’s January 1995 implementation.

•NAFTA: valued at 1.0 for the 1993/94:02–2004/05:04 MY period, and 0.0 otherwise, to capture

the effects of the North American Free Trade Agreement’s implementation in January 1994.

•CUSTA: valued at 1.0 for the 1988/89:02–2004/05:04 MY period, and 0.0 otherwise, to capture

the effects of the January 1989 implementation of the Canadian/U.S. Free Trade Agreement.
3 PCOOKIES and PMIXES are influenced by movements in confectionary and cocoa input costs. Analysis and

information leading to the justification and formulation of this binary variable was received in private communications with

market analysts of the U.S. International Trade Commission, Office of Industries, and with analysts from Labor, BLS during 

August, 2004. 4

 The ten included variables were URUGUAY, CUSTA, NAFTA, QUOTA, FBILLS, TITLE7, DROU88, HIDD9396,

CONFECT, and TREND.

10

•QUOTA: valued at 1.0 for the 1994/95:02–1995/96:02 MY period, and 0.0 otherwise, to capture

the effects of the two temporary U.S. tariff rate quotas (hereafter, TRQs) placed on certain

imports of Canadian durum and non-durum wheat for the year ending September 11, 1995.

•FBILLS: valued at 1.0 for the 1996/97:01-2004/05:04 MY period , and 0.0 otherwise, to capture

the effects of the last and current U.S. farm bills.

•TITLE7: valued at 1.0 for the 2002/03:02–2004/05:04 MY period, and zero otherwise, to

account for effects of the U.S. implementation of preliminary and final antidumping and

countervailing duties on certain imports of Canadian durum and/or hard red spring wheat, as a

result of U.S. International Trade Commission Investigation Nos. 701-TA-430A and 430B, and

731-TA-1019A and 1019B (Final). See USITC (2003).

•DROU88: valued at 1.0 for the 1987/88:02–1989/90:04 MY period, and 0.0 otherwise, to

account for the effects of the U.S. Midwest drought.

•HIDD9396: valued at 1.0 for the 1993/94:01–1996/97:01 MY period, and 0.0 otherwise, to

account for the effects of the period of high levels of world grain/oilseed demands and prices.

•CONFECT: valued at 1.0 for 2001/02:01–2004/05:04 to account for sustained increases in

confectionary and bakery production costs from (1) a steep, sustained rise in world cocoa prices

that began in early 2001 from effects of the Ivory Coast Civil War, and (2) sustained non-cocoa

confectionary increases in non-cocoa input costs that began in late-2002.3

The starting point for the unrestricted VEC was equation 2 with no deterministic trend or binary

variables. A well-specified unrestricted VEC was ultimately achieved in a series of sequential

estimations. These estimations added the seasonal variable and then a linear trend, various permanent

shift binaries, and a number of quarter-specific outlier binaries – generally one variable for each

estimation. An added variable was retained if the diagnostic test values moved in favorable patterns

indicative of improved specification. Juselius (2004, chapters 4, 7, and 9) recommends the following

battery of diagnostics: (a) trace correlation as an overall goodness-of-fit indicator, (b) likelihood ratio test

of autocorrelation, (c) Doornik-Hansen (D-H) tests for equation residual normality, (d) and indicators of

skewness and kurtosis. The estimations were stopped when the array of diagnostic values failed to further

improve with inclusion of additional variables. After achievement of an adequately specified levels VAR

and unrestricted VEC, tests for parameter constancy and for the presence of I(2) trends were performed.

There were two sets of sequential estimations aimed at achieving a statistically adequate VAR

model. The first focused on including each of the above-mentioned permanent shift binary variables (and

a trend), and all 10 were retained.4

 
5

 We followed a procedure for examination and analysis of potential outlier events developed by Juselius (2004,

chapter 6). An observation-specific event was judged as potentially “extraordinary” one if its standardized residual was 3.0 or

more in absolute value. Such a rule for outliers was designed based on the 76-observation sample size using the Bonferoni

criterion: INVNORMAL(1-1.025)T

 , where T=76, INVNORMAL is a function for the inverse of the normal distribution function

that returns the variable for the c-density function of a standard normal distribution. In our case, the Bonferoni variate was a 3.4

absolute value. Given that a number of seemingly influential quarter-specific events generated absolute standardized residual

values within the 3.0–3.3 range, we opted to choose a conservative and flexible Bonferoni criterion of absolute standardized

residual values of 3.0 or more, rather than 3.4 or more. Observations with absolute standardized residuals of 3.0 or more were

considered potential outliers, and we devised an appropriately defined binary variable for the relevant observation (see Juselius

2004, chapter 6). The binary was then placed in the appropriate form in the differences-based short run/deterministic component

of equation 2, the model was re-estimated, and the binary variable was retained if the battery of diagnostic values suggested

improved specification. 6

 To conserve space, we do not include extensive variable-by-variable analyses and estimation results. All included

outlier binary variables were of the transitory “blip” form following formulation procedures in Juselius (2004, chapter 6). The

form is appropriate for the short run/deterministic component of the model. The variables are as follows denoted/named

numerically for the quarter during which the outlier event’s influences were likely manifest: DTR8701, DTR8801, DTR9003, 

DTR9201, and DTR0201. So for example, DTR8701 is defined as unity for 1987/88:01, and 0.0 otherwise. DTR8701 and

DTR8801 likely captured quarter-specific expectationary influences of CUSTA’s implementation and of the 1987-1990 drought

on the U.S. wheat market not captured by the relevant permanent shift binary variables. DTR9003 likely captured influences on

the cookies/crackers and mixes/doughs markets from wheat-related input cost effects from implementation of CUSTA and the

1990 U.S. farm bill that the relevant permanent shift binaries did not manage to capture. The effects captured by DTR9201 on

PCEREALS likely arose from escalating prices of wheat, a major input cost for production of wheat-based breakfast cereals. 

DTR0201 likely captured effects on PWHEAT as the commodity boom of 2002-2004 unfolded. 7

 Each equation for the levels VAR and its unrestricted VEC equivalent was estimated over the 1986/87:03–2004/05:04

period. Four quarterly observations for the 1985/86 MY were set-aside for the Tiao and Box lag search. Given the two lags, the

full sample was 76 observations and there were 74 observations in the estimation period. 

11

The second set further improved specification of the unrestricted VEC that included the ten justmentioned variables. When a potential outlier was identified as extraordinarily influential based on a

“large” standardized residual, an appropriately specified variable was included in equation 2's short 

run/deterministic component, and retained if the battery of diagnostic values indicated improved

specification.5

 Five quarter-specific transitory outlier binaries were included.6 

An adequately specified model should generate statistically normal residuals. Table 1 provides a

battery of diagnostic test values for two estimations: the initially estimated unrestricted VEC before

sequential estimations aimed at improved specification and with no deterministic variables, and for the

unrestricted VEC judged as adequately specified after inclusion of centered seasonals, nine permanent

shift and five outlier binaries, and a linear trend. 7 Table 1's results reveal clear benefits from efforts

to improve specification: the model’s ability to explain data variation increased 70 percent, as

the trace correlation, a goodness of fit indicator for the 7-equation model, rose from 0.50 to 0.85.
8

 The )PMIXES equation residuals generated a 9.3 D-H value that nearly equals 9.2 critical value, and the test value’s

margin of excess over the critical value was too marginal to use as a sole criterion for conclusions of non-normal residual

behavior. We opted to consider the equation’s residuals as approximately normally behaving ones, given the generally favorable

battery of other diagnostics generated by this )PMIXES equation.

12

Table 1.

Mis-specification Tests for the Unrestricted VEC: Before and After Specification Efforts.

Test and/or equation

Null hypothesis and/or test

explanation

Prior to efforts at specification

adequacy

After efforts at specification

adequacy

Trace correlation

System-wide goodness of fit:

large proportion desirable 0.5 0.85

ARCH tests for

heteroscedasticity

Ho: no heteroscedasticity by 1st

and 4th lags. Reject for p—0.05

;ag 1: 101.2 (p=0.000)

lag 4: 101.1 (p=0.000)

lag 1: 61.1 (p=0.12)

lag 4: 55.8 (p=0.23)

Doornik-Hansen tests for

normal residuals

Ho: residuals are normal. Reject

for values above 9.2 critical

value

)PWHEAT 8.3 4.9

)QWHEAT 13.4 9.3

)PFLOUR 15.9 7.9

)PMIXES 9.4 13.4

) PBREAD 1.3 1.2

)PCEREAL 36.3 2.5

)PCOOKIES 1.8 2.2

A Doornik-Hansen (D-H) value tests the null hypothesis that the relevant equation’s residuals are

normal, which is rejected at the 1-percent level when the D-H value exceeds 9.2. In all cases but the

)QWHEAT equation, residuals follow normal behaviour for the unrestricted VEC after efforts at

improved specification.8

 D-H values improved noticeably for the )PFLOUR and )PCEREAL equations.

Table 1 provides indications on skewness and kurtosis of each equation’s residuals. Results

suggest both sets of values generated by the model that benefited from specification efforts fell within

ranges considered acceptably indicative of approximately normal residual behaviour.

Specification efforts did improve )QWHEAT specification, but not adequately to have suggested

approximately normal residuals. However, table 1 shows clear, substantial progress from specification

efforts, and that the entire system generates approximately normal residuals as a system. We followed

Juselius (2004, chapter 4) and concluded that overall evidence suggested that the VAR system achieved

reasonable adequacy of specification despite )QWHEAT’s weak evidence of normality.
13

Table 1.

Mis-specification Tests for the Unrestricted VEC: Before and After Specification Efforts (continued).

Test and/or equation

Null hypothesis and/or test

explanation

Prior to efforts at

specification adequacy

After efforts at specification

adequacy

Skewness (kurtosis) values skewness: ideal is 0.0; small

absolute values #1.0

acceptable

kurtosis: ieal is 3.0; values

3-5 acceptable.

)PWHEAT 0.83 (4.46) 0.05 (3.9)

)QWHEAT -0.80 (3.04) -0.34 (4.5)

)PFLOUR 1.3 (6.0) 0.10 ( 4.2) 

)PMIXES 0.38 (4.56) 0.15 (4.8)

) PBREAD 0.28 (3.1) 0.28 (3.0)

)PCEREAL -1.36 (10.5) 0.39 (3.4)

)PCOOKIES 0.14 (3.35) -0.12 (3.4)

Cointegration: Choosing and Imposing Reduced Rank on the Error Correction Space

The endogenous variables are shown below to be I(1), and so their differences are I(0).

Cointegrated variables are driven by common trends, stationary linear combinations, or cointegration

(Juselius 2004, p. 86). For the adequately specified unrestricted levels VAR, the A-matrix in equations 2

or 3 is a p1 by p1 matrix equal to the product of a p1 by r matrix $ of long run error correction

coefficients that under cointegration, combine into r#p stationary linear combinations of the seven wheatrelated variables (Johansen and Juselius 1990, 1992). As a result of a reduced rank for A, $’*x(t) is I(0),

even though x(t)’s seven endogenous variables are nonstationary.

Determination of cointegration rank is a three-tiered process. First, one conducts trace tests of

Johansen and Juselius (1990, 1992). Second, one examines patterns of characteristic roots of companion

matrices generated under relevant assumptions of reduced rank. And third, one examines plotted

cointegrating relationships for elements of stationary behaviour.

Nested Trace Tests and Other Evidence for Choosing the Reduced Rank of A.

Table 2 provides trace test evidence for rank determination. Trace test values are adjusted

(increased) for the restriction of nine permanent shift binaries restricted to the cointegration space (see

table 2's notes). Tests are nested and evidence at the five percent significance level is sufficient to

soundly reject the first five nested hypotheses, suggesting that r#4; is marginally sufficient to reject the

sixth that r#5 as the test value approaches the 42 critical fractile; and is insufficient to reject that r#6.

Trace results alone suggest that r=6 and that there are six CVs, although evidence marginally rejects that

r#5, suggesting that r may be less than 6. We follow Juselius’ (2004, chapter 8) strong suggestion against

sole reliance on trace test evidence.
9

 This analysis follows methods of Juselius (2004, chapter 8). We thoroughly examined patterns of characteristic roots

for companion matrices generated under all possible reduced-rank levels: 1, 2, 3, 4, 5, 6. Because of space considerations, we do

not report these six matrices and full analyses. Companion matrices and characteristic roots under these alternative r-levels are

available from the authors on request. Generally and summarily, patterns of characteristic roots under r=1 through 6 suggests

that reduced rank is less than 6, and most likely within the range of 1-3, with evidence pointing particularly to a reduced rank of

3. If r=3 is appropriate, then one expects p-r or 4 characteristic roots of unity, with the fifth and subsequent roots less than unity. 

When r=3 was imposed, the first five of the characteristic roots were as follows, suggesting that r=3: 1.0, 1.0, 1.0, 1.0, 0.87, with

the fifth, 0.87, below unity. 10 We follow Juselius’ (2004, chapter 8) procedures and realize that no economic relation is likely to follow perfectly

stationary behavioral paths. Each CV generally behaves with stationarity, with a couple of short term deviations

notwithstanding: some short-lived cycling in 1995 for CV1 and CV2, and some volatile behavior in 1993-1994 for CV3.

14

Table 2

Trace test statistics and related information for nested tests for rank determination.

Null hypothesis Trace value 95% fractile (critical value) Result

rank or r # 0 370.6 166.5 Reject null that rank is zero

rank or r # 1 279.8 133.7 Reject null that rank # 1

rank or r # 2 184.8 104.8 Reject null that rank # 1

rank or r # 3 120.6 79.9 Reject null that rank # 1

rank or r # 4 89.6 59 Reject null that rank # 1

rank or r # 5 45.7 41.9

(Marginally) Reject null that

rank # 1

rank or r # 6 15.7 28.7 Fail to reject that rank # 6

Notes. - As recommended by Juselius (2004, p. 171), CATS2-generated fractiles are increased by 9*1.8 or 16.2 to account for the 9 permanent

shift binary variables restricted to lie in the cointegration space. Trace values are corrected with Bartlett’s adjustment for small samples.

If r is an appropriate choice, then one expects p-r characteristic roots that are unity or near-unity

in the companion matrix. When r is imposed, and there are p-r+1 roots that are unity or near unity, then

rank should be reduced to r-1. Patterns of characteristic roots under alternative r-assumptions suggest that

r is likely between 1 and 3 with evidence pointing especially to r=3.9

The plots of the three CVs are in figures 8, 9, and 10. The BETA*x(t) plots are for the model

with short run effects, and the BETA*R1(t) plots are for the model corrected for short run effects, with

Juselius (2004, chapter 8) favouring the latter as more reliable. Figures 8-10 suggest that all three CVs

are for the most part stationary, and hence that r=3 rather than one or two: plots cycle and mean-revert

frequently, and variation levels appear constant (Juselius 2004, chapter 8).10 All three evidence sources

above suggest that the reduced rank of equation 2's A-matrix is likely three, with three stationary linear

combinations of the seven I(1) wheat based variables error-correcting the system.
15

Be ta1'*X(t)

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

52.50

52.75

53.00

53.25

53.50

53.75

54.00

54.25

Be ta1'*R1(t)

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

Figure 8

Plotted cointegrating relation 1 with and without correction for short run effects

Beta2'*X(t)

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

-9.24

-9.18

-9.12

-9.06

-9.00

-8.94

-8.88

-8.82

-8.76

Beta2'*R1(t)

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Figure 9

Plotted cointegrating relation 2 with and without correction for short run effects.
16

Further Diagnostic Tests for Parameter Constancy and I(2) Trends.

Two final diagnostic tests were applied to the cointegrated VEC and results suggested that the

model achieved statistical adequacy: tests are for constancy of error correction parameter estimates and

for the presence of trends that are integrated of order-2 or I(2). The “known” beta test detailed in Juselius

(2004, pp. 186-190) tests if there is constancy or time-invariance of cointegration parameter estimates. 

This method tests if the full sample “baseline” model’s cointegration relations could have been accepted

as those of each recursively estimated model over the 2002/03:02-2004/05:04 period. Known-beta values

in figure 11 are for the model versions including and corrected for short run effects (BETA_X and

BETAR1) with Juselius (2004, chapter 8) favoring the corrected model as more reliable. Values are

indexed by the 95 percent fractile, and should ideally be unity or less to indicate parameter estimate

constancy. All values in figure 8 are below unity and suggest time-invariant estimates.

Be ta3'*X(t)

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

12.60

12.65

12.70

12.75

12.80

12.85

12.90

Be ta3'*R1(t)

1985 19 87 1989 1991 1993 1995 1997 1999 2001 2003

-0.050

-0.025

0.000

0.025

0.050

0.075

Figure 10

Plotted cointegrating relation 3 with and without correction for short run effects.

The test statistic is scaled by the 5% critical value

2001 2002 2003 2004

0.00

0.25

0.50

0.75

1.00 B eta_X

B eta_R1

T est o f B eta(t) = "K n o wn B eta"

Figure 11

Recursively calcuated “known beta” tests of parameter constancy. 
11 Nielson’s (2002) test for I(2) trends compares the I(2) model of H(r,s): p variables, r I(0) directions, s I(1) directions,

and p-r-s I(2) directions, against the unrestricted model of H(p). In our case, p=7 and r = 3. The null hypotheses are H(r,s)*H(p)

and one rejects the null when models are too restricted. Rejecting all models where (p-r-s)TM0 implies evidence that is

sufficient to reject I(2) trends. To conserve space, we do not report results and analysis of the 28 tests where (p-r-s)TM0. In all

cases, however, evidence at both the one- and five-percent significance levels was sufficient to reject the null hypothesis of I(2)

trends. Also see Juselius (2004, chapter 16). 12 This methods section closely follows the thosed developed and/or refined in Johansen and Juselius (1990, 1992) and

Juselius (2004, chapter 11).

17

Nielson (2002) and Juselius (2004, chapter 16) note that imposing reduced rank restrictions on an

unrestricted VEC’s error correction space when there are I(2) trends encounters well-known and

potentially serious econometric problems of compromised inference and in some cases biased parameter

estimates because the data still have unit roots. Evidence form Nielson’s series of tests for I(2) trends was

sufficient to reject the null hypotheses of I(2) trends in all cases.11 

Equations 4-6 are the three CVs that emerged after imposing rank and re-estimation with

Johansen and Juselius’ (1990, 1992) reduced-rank estimator. Statistically supported restrictions that

emerged from the next section’s hypothesis tests have not yet been imposed on these CVs.

(4) QWHEAT = -1.77*PWHEAT + 2.30*PFLOUR - 4.94*PMIXES + 4.51*PBREAD - 0.28*PCEREAL -10.80*PCOOKIES

 -0.49*URUGUAY + 0.59*CUSTA -0.11*NAFTA + 0.52*QUOTA +1.25*FBILLS + 0.65*TITLE7

 +0.07*DROU88 + 0.40*HIDD9396 - 0.26*CONFECT + 0.01*TREND

(5) PWHEAT = 0.10*QWHEAT + 2.24*PFLOUR -3.18*PMIXES + 1.78*PBREAD -2.51*PCEREAL + 3.60*PCOOKIES

 -0.12*URUGUAY - 0.02*CUSTA -0.04*NAFTA + 0.05*QUOTA -0.26*FBILLS + 0.17*TITLE7 

 -0.09*DROU88 + 0.19*HIDD9396 -0.04*CONFECT -0.01*TREND

(6) PFLOUR = 0.53*PWHEAT - 0.12*QWHEAT + 0.09*PMIXES - 1.11*PBREAD + 0.14*PCEREAL -0.76*PCOOKIES

 + 0.06*URUGUAY + 0.03*CUSTA - 0.08*NAFTA -0.03*QUOTA +0.08*FBILLS - 0.08*TITLE7

 -0.03*DROU88 - 0.02*HIDD9396 - 0.05*CONFECT + 0.02*TREND

Hypothesis Tests and Inference on the Economic Content of the Three Cointegrating Relations12

We begin with equations 4-6, the three unrestricted CVs, conduct a series of hypothesis tests on 

A = "’*$, and then re-estimate the system with the statistically-supported restrictions imposed.

Hypothesis tests on the beta coefficients take the form:

(7) $ = H*n

Above, $ is a p1 by p1 vector of coefficients on variables included in the cointegration space; H is a p1 by

s design matrix, with “s” being the number of unrestricted or free beta coefficients; and n is an s by r

matrix of the unrestricted beta coefficients. The hypothesis test value or statistic is:

(8) -2ln(Q) = T*j[(1-8i 

*

)/(1- 8i )] for i = 1, 2, and 3 (=r).

The asterisked (non-asterisked) eigenvalues (8i

 , i = 1-3) are generated by the model estimated with

(without) the tested restriction(s) imposed.
13 This test can be conducted in CATS2 (beta version) in two settings: with and without inclusion of the nine

deterministic variables and trend restricted to the cointegration space. We chose to include these deterministic variables in the

tests, due to the institutional importance of events for which the variables were defined, and as discussed in earlier research

(BBP, 2004; RBR 2002). Note that results from both sets were similar. In equation 10, $c

 is the p1 by r (17 by 3) beta matrix

with one of the variable’s levels restricted to a unit vector; b is a p1 (or 17) by 1 vector with a unity value corresponding to the

relevant variable whose stationarity is being tested; and n is a p1 by (r-1) or 17 by 2 matrix of the remaining two unrestricted

cointegrating vectors. 14 Equation 8's test value was distributed under the null hypotheses as a chi-squared variable with three degrees of

freedom, and were calculated as follows (with parenthetical p-values): 32.5 (0.000) for PWHEAT; 31.88 (0.000) for QWHEAT;

25.54 (0.000) for PFLOUR; 17.6 (0.000) for PMIXES; 23.35 (0.000) for PBREAD; 20.4 (0.000) for PCEREAL; and 11.07

(0.03) for PCOOKIES. The null hypothesis was rejected for p-values below 0.05, corresponding to the five-percent significance

level.

18

Likewise, the hypothesis tests concerning the " or adjustment speed coefficients permit a 

characterization of relative speeds of error-correcting adjustment with which the system responds to a

given shock. The null hypothesis or H(0) is:

(9) H(0): " = A*R

Above, A is a p by s design matrix; s is the number of unrestricted coefficients in each of the r=3 columns

of the " matrix; and R is the s by r matrix of the non-restricted or “free” adjustment speed coefficients. 

Equation 8's test statistic also applies here, and is distributed asymptotically as a chi-squared distribution

with degrees of freedom equal to the number of imposed coefficient restrictions. Hypothesis tests on the

betas, followed by tests on the alphas, are provided below.

Hypothesis Tests on the Betas.

There are three sets of hypothesis tests on the beta coefficients. The first set of six examines if

each endogenous variable is stationary under the imposed rank of three. Second, there are 17 “exclusion”

hypothesis tests of whether each of the variables included in the CVs have zero-valued $-estimates. A

third set is performed on individual $-estimates in equations 11-13, with any statistically supported

stationarity and/or exclusion restrictions imposed.

Tests of Stationarity. Juselius (2004, pp. 220-222) recommends a likelihood ratio test of each

endogenous variable’s stationarity within a system setting and given the imposed rank (here r=3). She

recommends such a test over univariate stationarity tests (e.g. Dickey-Fuller tests) which are independent

of the cointegrated system’s chosen rank. The recommended likelihood ratio tests examine if each

endogenous variable itself constitutes a separate stationary cointegrating relation, with a unity value for

the tested variable’s betas. Equation 7 is rewritten as follows:13

(10) $c = [b,n]

With a rank of r=3, equation 8's test value is distributed under the null hypothesis of stationarity as a chisquared variable with three degrees of freedom. Evidence was sufficient to reject that all seven

endogenous variables were stationary, leading to our conclusion that they are nonstationary.14

Tests of Beta Exclusions. There are p1=17 variables in equation 2's cointegration space, and so in

turn, as many exclusion tests are performed. Failure to reject the null that a variable’s betas are zero-
15 The hypothesis test value in equation 7 would include a 17 by 3 $-vector; a 17 by 16 design matrix, H, with 16 being

the number of unrestricted beta coefficients in each relation; and a 16 by 3 matrix n of 16 unrestricted coefficients in each of the

three cointegrating relationships (Juselius 2004, chapter 10) Basically, the n matrix is the $-matrix without the beta coefficients

for the variable being tested for exclusion. 16The exclusion test values (and parenthetical p-values) for the following fifteen variables reflected evidence at the five

percent significance level that was sufficient to reject the null hypotheses of zero-valued beta coefficients: 28.03 (0.000) for

PWHEAT; 29.1 (0.0000) for PFLOUR; 23.1 (0.0000) for PMIXES; 17.1 (0.001) for PBREAD; 22.65 (0.0000) for PCEREAL;

27.28 (0.0000) for PCOOKIES; 9.75 (0.03) for URUGUAY; 9.12 (0.03) for NAFTA; 8.3 (0.04) for QUOTA; 30.12 (0.000) for

FBILLS; 17.76 (0.000) for TITLE7; 8.9 (0.03) for DROU88; 20.15 (0.000) for HIDD9396; 9.95 (0.04) for CONFECT, and 20.5

(0.000) for TREND. Evidence at the five percent significance level was not sufficient to reject the null hypothesis of zerovalued beta coefficients for QWHEAT, with a test value of 5.7 and p-value of 0.12 and for CUSTA with a test value of 7.0 and a

p-value of 0.07. We decided to include CUSTA, given the marginal test value that suggested evidence that was suficient to

reject the null of zero beta’s at the seven percent significance level. We also chose to retain QWHEAT in the error-correction

space. QWHEAT was retained, despite the test value’s p-value of 0.12 because of substantial evidence by Babula, Bessler, and

Payne (BBP 2004, pp. 12-18). Their analyses of impulse response simulations and/or forecast error variance decompositions

generated by a Bernanke structural VAR of these same markets suggested that QWHEAT has rich and bidirectional causal

interplay at long run and short run horizons in the system. In particular, QWHEAT’s causal importance to the system appeared

to escalate at the longer run horizons of the BBP analysis of FEV decompositions, suggesting that we should perhaps retain

QWHEAT in the long-run error-correction space, at least initially. To exclude QWHEAT from our long run space based solely

on exclusion test evidence would seem overly simplistic and would ignore the strong findings of BBP’s similar and recent

award-winning study. As well, this test value for QWHEAT approaching rejection at the 10 percent level may indicate that the

variable should be included in some and excluded from other CVs. Results from the third set of hypothesis tests presented below

indeed verified that QWHEAT should remain in CV1 and be excluded from CV2 and CV3. 17This reduced-rank estimator is summarized in Johansen (1988), Johansen and Juselius (1990, 1992), and Juselius

(2004, chapters 8-10). We do not summarize this well-known reduced rank estimator here.

19

valued suggests that the variable should be excluded from the cointegration space.15 On balance,

evidence suggested that all variables should be, at least initially, retained in the cointegration space.16

Set of Sequential Hypothesis Tests on Individual Beta Coefficients. Since no variables were

excluded or stationary, one must now meet the rank condition of identification by imposing at least r-1

identifying restrictions directly on each of equations 4-6. (Juselius 2004, pp. 245-246). These added

hypotheses arose from theory, market knowledge, prior research, and/or suggestions implied by

coefficient estimates in equations 11-13 and are tested using equations 7-8 (Juselius 2004, pp. 245-246). 

A restriction to be tested is imposed, the model re-estimated with the well-known Johansen-Juselius

reduced rank estimator,17 and the test value for the hypothesized restriction calculated. If statistically

supported at the 5-percent level of statistical significance (hereinafter, the 5-percent level), the restriction

is retained. We repeated this process on the three CVs. Space limitations preclude reporting results for

all sequential estimations, although table 3 summarizes this multi-iterative process. We intensely

scrutinized the finally restricted error correction space for economic content in equations 11-13 below.

Test set 1 (TS-1) provides the first set of zero restrictions on selected $-estimates: three on

PCOOKIES, PMIXES, and PCEREAL in CV1 normalized on QWHEAT; two on QWHEAT and

TREND in CV2 normalized on PWHEAT; and three on QWHEAT, PCOOKIES, and PMIXES in CV3,

normalized on PFLOUR. These restrictions imply low levels of influence on the normalized variables,

and were chosen based on previous research’s analyses of forecast error variance (FEV) decompositions

and/or impulse response simulations generated by VAR models of the same markets (BBP 2004, pp. 14-

18; RBR 2002, pp. 109-111). TS-1 restrictions meet the rank condition of identification, although as is

often the case, the test value fails to initially accept the restrictions, suggesting the need for added

economic content through other restrictions to generate a statistically accepted set at the chosen 5-percent

significance level (when p-values TM 0.05).
18 The sequential estimation under test set 8's restrictions yielded the following CV1 results: coefficient value of -0.881

on $(TITLE7) with a t-value of -4.5, and of -0.883 on $(NAFTA) with a t-value of -5.5. Clearly, these significant beta

coefficients in CV1 should be tested for equality. 19 The sequential estimation under test set 9's generated for CV2 the following: $(PCOOKIES) = 15.8 (t = 7.1) and

$(PCEREAL) = -16.8 (t=-12.8). This places the following as a testable hypothesis: $(PCOOKIES) = -$(PCEREAL),

which suggests that CV2's dependent variable, PWHEAT, is a function of the difference of these two prices. The economic

and/or market importance of this restriction is discussed below when the finally-restricted CVs are examined. 20 Test set 10's estimates generated the following in CV3: $(TITLE7) of -0.20 (t = -3.9) and $(QUOTA) = -0.19 (t =-

3.3). This suggests a testable hypothesis of $-equality thta, when added to TS-10, rendered test set 11.

20

Test sets 2 through 8 postulate, impose, re-estimate, and then test a series of zero restrictions on

beta coefficients in CV1, CV2, and CV3 that arise from theory, counsel from recognized market experts, 

and patterns of the estimated beta t-values (statistically insignificant ones, generally). Table 4's results

reflect that the increasing sets of imposed restrictions gain statistical strength, with TS-8's test value in

table 3 accepting the restrictions at the one-percent significance level. More economic content is yet

required for acceptance at the chosen 5-percent level. 

Test set 8's beta estimates suggested the following testable hypothesis in CV1 that was added to

render test set 9: $(TITLE7) = $(NAFTA). This restriction suggests that the events concurrent with the

AD/CVD investigation and NAFTA’s 1994 implementation had, on average, equal quarterly effects on

QWHEAT, CV1's dependent variable.18 Adding this restriction to TS-8 rendered TS9, and reestimation

with TS-9 supported this last equality restriction: t-values of -5.9 for both restricted CV1 coefficients. 

All TS-9 restrictions were statitically supported at the 2-percent level. 

Test set 9's coefficient estimates in CV2 normalized on PWHEAT suggest that the following is

clearly a testable hypothesis: $(PCEREAL) = -$(PCOOKIES), which implies that PWHEAT is

influenced by the difference in PCOOKIES and PCEREAL.19 Adding this latter condition to TS-9

renders test set 10. The test value improves, as evidence accepts the restrictions at the 3-percent level.

Test set 10's coefficient estimates suggested that $(QUOTA) = $(TITLE7) in CV3, suggesting

that the set of two temporary U.S. TRQs on certain imports of Canadian wheat, and the array of AD/CVD

duties during 2002-2004 had (collectively with other concurrent events) approximately equal market

impacts.20 The addition of this equality restriction in CV3 to TS-10 rendered test set 11, which generated

restricted coefficients which were statistically significant (t-values of -6.2), and a test value which

accepted restrictions at an increased 4 percent significance level (p-value = 0.042).
21

Table 3. 

Sequential Hypothesis Tests on Beta Estimates in the Error-Correction Space of the U.S. System of Wheat-Based

Products.

Tested restrictions restriction numbers

(Marginally added restriction(s) in bold Explanation, reasoning

Test values, test results, and interpretation of

coefficient estimates.

Test set 1(TS-1): Various restrictions suggested by previous research and needed to meet rank condition of identification.

3 in CV1: $(PCEREAL)=$(PMIXES)=

$(PCOOKIES) = 0

2 in CV2: $(QWHEAT)=$(TREND)=0

3 in CV3: $(QWHEAT)=$(PCOOKIES)=

$(PMIXES) = 0

Suggested by BBP(2004) FEV analysis. 

Suggested by data analysis and BBP(2004),

RBR(2001).

BBP(2004), RBR(2001)

Test value of 19.2 (df=2) with p=0.000

suggests more restrictions need to be found

for a statistically supported set at the five

percent significance level.

Estimate interpretation:t[ $(CUSTA)]=0.1 in 

CV1; add zero restriction for PMIXES.

Test set 2: previous TS-1 restrictions plus $(CUSTA)=0 in CV1.

4 in CV1: 3 TS-1 restrictions retained, plus

$(CUSTA)=0 

2 in CV2: 2 TS-1 restrictions retained.

2 in CV3: 2 TS-1 restrictions retained.

Weak t-value on $(CUSTA), prior estim’n. Test value of 19.1 (df=3) with a p=0.003

suggests some progress towards statistical

acceptance. More restrictions needed for a

statistically acceptable set.

Estimate interpretation: t[$(HIDD9396)]=

1.8, in CV1; add zero restriction on

HIDD9396. 

Test set 3: TS-2 restrictions plus $(HIDD9396)=0 in CV1.

5 in CV1: 4 prior TS-2 restrictions retained.

$(HIDD9396)=0 

2 in CV2: 2 TS-2 restrictions retained.

3 in CV2: 3 TS-2 restrictions retained.

Weak t[$(HIDD9396)] , prior estimation

Test value of 19.9 (df=4) with p-value of

0.001 suggests some progress; more

restrictions needed for statistically supported

set.

Estimate interpretation: t[$(CUSTA)]=-0.6. 

In CV2; add zero restriction on CUSTA.

Test set 4: TS-3 restrictions plus $(CUSTA) in CV2.

5 in CV1: 4 TS-3 restrictions retained, plus

$(CUSTA) = 0

3 in CV2: TS-3 restrictions retained

3 in CV3: TS-3 restrictions retained

Weak t[$(CUSTA)], prior estimation Test value of 19.9 (df=5) with p-value of

0.0013 suggests some progress in statistical

support; more restrictions needed for

statistically supported set.

Estimate interpretation: t[$(QUOTA)] = -2.2

in CV2.; add as zero restriction.

Test set 5: TS-4 restrictions plus $(QUOTA) = 0 in CV2.

5 in CV1: 5 TS-4 restrictions retained.

4 in CV2: 3 TS-4 restrictions retained, plus

$(QUOTA) = 0

3 in CV3: 3 TS-4 restrictions retained.

Weak t[ $(QUOTA)], prior estimation.

Test value of 21.1 (df=6) with p-value of

0.02 suggests progress: statsistical

acceptance at 2% level. More restrictions

needed for acceptable set at 5% level.

Estimate interpretation: t[$(URUGUAY)] =

1.0; add as zero restriction.

Test set 6: TS-5 restrictions plus $(URUGUAY) = 0 in CV2

5 in CV1: 5 TS-5 restrictions retained.

5 in CV2: 4 TS-5 restrictions retained, plus

$(URUGUAY) = 0

3 in CV3: 3 TS-5 restrictions retained.

Weak t[$(URUGUAY)], prior estimation

Test value of 21.3 (df=7), p-value = 0.0033. 

More restrictions needed for statistically

supported set.

Estimate interpretation: t[$(DROU88)] = -

0.02 in CV3; add as zero restriction.
22

Table 3. 

Sequential Hypothesis Tests on Beta Estimates in the Error-Correction Space of the U.S. System of Wheat-Based

Products (cont’d).

Tested restrictions restriction numbers

(Marginally added restriction(s) in bold Explanation, reasoning

Test values, test results, and interpretation of

coefficient estimates.

Test set 7: TS-6 restrictions plus $(DROU88) = 0 in CV3.

5 in CV1: 5 TS-6 restrictions retained.

5 in CV2: 5 TS-6 restrictions retained

4 in CV3: 3 TS-6 restrictions retained, plus

$(DROU88) = 0 Weak t[$(DROU88)], prior estimation

Test value of 21.3 (df=8), p-value = 0.007. 

More restrictions needed for statistically

supported set.

Estimate interpretation: t[$(FBILLS)] = 

1.3 in CV3; add as zero restriction.

Test set 8: TS-7 restrictions plus $(FBILLS) = 0 in CV3

5 in CV1: 5 TS-7 restrictions retained.

5 in CV2: 5 TS-7 restrictions retained

5 in CV3: 4 TS-7 restrictions retained, plus

$(FBILLS) = 0 Weak t[$(FBILLS)], prior estimation

Test value of 21.4(df=8), p-value = 0.01. 

More restrictions needed for statistically

supported set at 1% level.

Estimate interpretation: $(TITLE7) =

$(NAFTA) in CV1; add as equality restr’n 

Test set 9: TS-8 restrictions plus $(TITLE7) = $(NAFTA) in CV1.

6 in CV1: 5 TS-8 restrictions retained, plus

$(TITLE7) = $(NAFTA) 

5 in CV2: 5 TS-8 restrictions retained

5 in CV3: 5 TS-8 restrictions retained

Examination of last estimates: average 

market impacts of TITLE7 and NAFTA

events about equal on QWHEAT.

Test value of 21.6 (df=10) with p-value of

0.02 suggests progress in statistical

acceptance at 2%; more restrictions needed

for acceptance at 5% level.

Estimate interpretation: $(PCEREAL) = 

-$(PCOOKIES) in CV2; add as equality

restriction.

Test set 10: TS-9 restrictions plus $(PCEREAL) = -$(PCOOKIES) in CV2.

6 in CV1: 5 TS-9 restrictions retained. 

6 in CV2: 5 TS-9 restrictions retained, plus

$(PCEREAL) = -$(PCOOKIES) 

5 in CV3: 5 TS-9 restrictions retained.

Examination of last estimates. Equality

restriction suggests that PWHEAT is

dependent on the difference in prices of

wheat cereal and cookies/crackers.

Test value of 21.6 (df=11) with p-value of

0.03 suggests progress in statistical

acceptance at 3% level; more needed for

acceptance at 5% level.

Estimate interpretation: $(QUOTA)

=$(TITLE7) in CV3; add as equality restr’n 

Test set ll: TS-11 restrictions plus $(QUOTA) =$(TITLE7) in CV3.

6 in CV1: 5 TS-10 restrictions retained.

6 in CV2: 6 TS-10 restrictions retained

6 in CV3: 5 TS-10 restrictions retained, plus

$(QUOTA) =$(TITLE7) 

Examination of last estimates: average

market impacts were about the same from

QUOTA and TITLE7 events.

Test value of 21.6 (df=12) with p-value of

0.042 suggests progress: statistical

acceptance at 4% level. More restrictions

needed for acceptance at 5%.

Estimate interpretation: : $(QUOTA)

=$(TITLE7) = -$(NAFTA) in CV3.

Test set 12: TS-11 restrictions plus $(QUOTA) =$(TITLE7) = -$(NAFTA) in CV3.

6 in CV1: 6 TS-11 restrictions retained.

6 in CV2: 6 TS-11 restrictions retained

7 in CV3: 6 TS-11 restrictions retained, plus

$(QUOTA) =$(TITLE7) = -$(NAFTA) 

Examination of last estimates: average

market impacts of QUOTA events or of

TITLE7 events were about negated by

NAFTA events.

Test value of 21.6 (df=13) with p-value of

0.063 suggests statistical acceptance at more

than the desired 5% level: at 6% level.

Estimate interpretation: $(PBREAD) = -

$(PCEREAL) in CV3

Test set 13: TS-12 restrictions plus $(PBREAD) = -$(PCEREAL) in CV3

6 in CV1: 6 TS-11 restrictions retained.

6 in CV2: 6 TS-11 restrictions retained

8 in CV3: 7 TS-11 restrictions retained, plus

$(PBREAD) =-$(PCEREAL) 

Examination of last estimates: average

market impacts depend on difference

between bread and wheat cereal product

prices.

Test value of 22.5 (df=14) and p-value of

0.07 reflects that we have achieved evidence

of a statistically supported set of restrictions

at 7% level (above desired 5% level).
21 Test set 11's restrictions and sequential estimation generated the following CV3 results: #(QUOTA) = $(TITLE7) =

-0.195 (t= -6.2), and $(NAFTA) = 0.196 (t=3.3). 22 Test set 12's coefficient estimates generated the following in CV3: $(PCEREAL) = 2.92 (t=11.1) and $(PBREAD) =

-3.4 (t=-7.3). 23 The weak exogeneity test values and (parenthetical) p-values were as follows: 32.9 (0.000) for PWHEAT, 16.2

(0.001) for QWHEAT, 26.5 (0.000) for PFLOUR, 7.4 (0.06) for PMIXES, 10.1 (0.02) for PBREAD, 15.1 (0.002) for PCEREAL,

and 36.6 (0.000) for PCOOKIES. Evidence was sufficient at the 5-percent level or less to reject the null of zero-valued "-

coefficients for all endogenous variables except PMIXES. Evidence was sufficient at the 6-percent level to reject PMIXES weak

exogeneity – a very marginal result. BBP (2004, pp. 16-19), however, provided an analysis of FEV decomposition patterns

generated by a Bernanke structural VAR (with directed acyclic graph analysis) of the same markets, and revealed evidence of

endogenous participation of PMIXES in the system, particularly among other wheat-using value-added product prices. Given

the marginal test value and this added BBP evidence of PMIXES’ endogenous participation, we chose to treat PMIXES as

endogenous and not weakly exogenous. As a result, evidence, on balance, supports the hypothesis that all seven wheat-based

variables are not weakly exogenous. 24 In the vector definitions that follow, t-values are included parenthetically. DCV1 is a vector of the following CV1

permanent shift binary variable coefficient estimates: 1.0*URUGUAY (t= 6.1); -1.6*FBILLS (t = -8.95); -0.34*DROU88 (t=-

2.8). DCV2 is a vector of the following CV2 permanent shift binary variable coefficient estimates: -2.45*FBILLS (t= -9.1); -

0.53*DROU88 (t= -3.98); 1.63*HIDD9396 (t= 8.1). DCV3 is a vector of the following CV3 permanent shift binary variable

coefficient estimates: -0.21*CUSTA (-3.0); -0.57*HIDD9396 (t= -8.4); 0.31*URUGUAY (t=4.0).

23

Test set 11's coefficient estimates suggested further that $(QUOTA) = $(TITLE7) = -$(NAFTA)

in CV3. 21 The interpretation of this multi-parameter restiction is left to the next subsection on economic

content. Adding this restriction in CV3 to TS-11 rendered test set 12 in table 3. The re-estimation

restricted for this equality condition generated statistically significant coefficients, and strong support for,

this restriction: t = -7.3 for betas on QUOTA and TITLE 7; t = -7.3 on NAFTA. The test value’s p-value

(0.063) reflected evidence that accepted all restrictions at the 6-percent level.

Test set 12's coefficient estimates suggested that in CV3, perhaps $(PCEREAL) = -$(PBREAD),

which implies that market effects through PFLOUR hinge on the difference between PBREAD and

PCEREAL.22 An economic interpretation of this restriction follows below. Adding this restriction to TS12 rendered test set 13. Evidence suggested that the last CV3 restriction was statistically significant (tvalues of ±10.3), and that TS-13's restrictions were accepted at the 7-percent significance level (p-value

of 0.07), which exceeds our decision rule of 5-percent.

Hypothesis Tests on the Adjustment Speed or " Coefficients.

A principal hypothesis on the estimated adjustment speed coefficients is if each of the variables is

weakly exogenous. A variable is weakly exogenous if it influences the error-correction process without

itself adjusting or responding to the process, thereby implying a one-way causal relation to the

equilibrating relation. Equivalently, one tests if, given the statistical significance of at least some of a

variable’s $-estimates, the variable’s r=3 "-coefficients are all zero (Juselius 2004, pp. 231-232). 

Evidence in all cases was sufficient to reject the null of weak exogeneity.23

Economic Analysis of the Three Cointegrating Relationships for the U.S. Soy-Based Markets

The fully restricted CVs are equations 11-13. To conserve space, we present CV1, CV2, and

CV3 in abbreviated form, with DCV1, DCV2, and DCV3 reflecting vectors of econometric estimates for

permanent shift binaries that we deemed to be of lesser relevance and/or interest, but whose inclusion was

required to achieve a statistically adequate model.24 The CVs are followed by the "-estimates. 

Parenthetical t-values reflect that most estimates have achieved clear statistical strength. 
25 For example, NAFTA was defined for the quarterly period encompassing the trade agreement’s January 1994

implementation. Yet other events undoubtedly occurred that influenced the modeled wheat-based markets since January 1995:

September 11 tragedy, currency market effects, oil price movements, the 1997 Asian financial crisis, etc. The coefficient on

NAFTA in a CV cannot be solely attributed to the NAFTA alone, but must be interpreted more imprecisely as the effects of

NAFTA and other collective concurrent events having occured during the subsample for which the binary variable was defined.

See USITC (1995). 26 For example, the -0.91 NAFTA coefficient in CV1 is stated as having captured the negative effects of the trade

agreement, when in fact, we imply the net negative effects from NAFTA and all other relevant events concurrent with NAFTA

binary’s period of definition.

24

Limitations of imprecision in interpreting the coefficient estimates on binary (dummy) variables

are well known (USITC 1995). Typically, partial effects cannot be solely attributed to an event for which

a binary is defined, but must be collectively attributed to that event and all other relevant events that

concurrently occurred during the period (USITC 1995; Babula 1997).25 For ease of exposition, we

provide uni-event attribution with multi-event attribution implied.26

There are three CV’s: the first appears to be the beginnings of a U.S. wheat supply, and the other

two, long run price transmission relationships. We focus on the relationships as demand and price

transmissions first, followed by a separate discussion on the information collectively inherent in an array

of the coefficient estimates on the permanent shift binary variables from all CVs.

(11) QWHEAT = 5.76*PWHEAT - 10.95*PFLOUR -13.04*PBREAD - 0.91*NAFTA -0.91*TITLE7

 (10.0) (-10.24) (-9.2) (-5.98) (-5.98)

 - 0.72*QUOTA - 0.30*CONFECT + 0.18*TREND + DCV1

(-4.47) (-2.70) (9.89)

(12) PWHEAT = 3.19*PFLOUR - 10.9*PMIXES + 6.84*PBREAD + 18.03*(PCEREAL - PCOOKIES) - 1.15*NAFTA

(5.2) (-5.8) (7.86) (±13.4) (-5.78)

 + 0.56*TITLE7 - 0.55*CONFECT + DCV2

(8.1) (-2.96)

(13) PFLOUR = 0.49*PWHEAT + 5.0*(PBREAD - PCEREAL) - 0.33*QUOTA -0.33*TITLE7 + 0.33* NAFTA -

(4.6) (±10.3) (-7.1) (-7.1) (7.1)

 + 0.19*CONFECT + 0.02*TREND + DCV3

(2.2) (8.9)

ALPHAs

 Alpha1 Alpha2 Alpha3

)PWHEAT 0.0997 -0.1407 -0.1031

 (3.8849) (-6.5953) (-2.1826)

)QWHEAT -0.0356 0.0471 0.3062

 (-0.7805) (1.2400) (3.6431)

)PFLOUR -0.0123 -0.0501 -0.0293

 (-0.9774) (-4.8001) (-1.2669)

)PMIXES -0.0040 0.0028 0.0102

 (-1.0472) (0.8823) (1.4613)

)PBREAD -0.0119 0.0060 0.0078

 (-4.0674) (2.4786) (1.4557)
27 For example, the modeled variables’ have standard errors of 19.6 percent for PWHEAT and 40 percent for

QWHEAT, which may partially account for the very elastic price-elasticity of supply in the very long run.

25

)PCEREAL -0.0230 0.0199 0.0647

 (-4.6858) (4.8955) (7.1729)

)PCOOKIES -0.0072 0.0125 0.0280

 (-3.6892) (7.6537) (7.7581)

We note initially that the first CV has a more precise structural interpretation as a wheat supply

curve, probably because the available information set included both prices and quantities for the wheat

market. Earlier research noted that such quantity data generally do not exist for commodity-based value

added products: they are typically considered business proprietary and excluded from the public domain

(BBP, 2004; RBR, 2002; Babula and Rich 2001). As a result, we followed established research

procedure and modeled the downstream markets with reduced form price relationships, which in turn,

likely rendered cointegrating relationships (CV2, CV3) that had less precise, non-structural

interpretations. Pinning-down such structural relationships as price elasticities of supply from reduced

form relationships is difficult, and characterized equations 12-13.

Our less precise interpretations for equations 12 and 13 is common in cointegration analysis, as

noted by Juselius (2004, p. 175):

“It is important to note that the cointegration rank is not in general equivalent to the number of

theoretical equilibrium relations derived from an economic model . . . . Thus, cointegration

between variables is a statistical property of the data and only exceptionally can be given a direct

interpretation as an economic equilibrium relation. The reason for this is that a theoretically

meaningful relation can be (an often is) a linear combination of several ‘irreducible’ cointegration

relations.”

And as such, a single relation may reflect elements from both the demand and supply sides of a market.

Our economic analysis below makes first-cut progress in illuminating long run structural relationships

among U.S. wheat-based markets (particularly with CV1). We leave more complete economic structural

interpretations for the more reduced form CVs (equations 12, 13) to future research when more

comprehensive information sets and certainly larger time series samples will be available.

CV1: The First Cointegrating Relation, A U.S. Wheat Supply

Equation 11 or CV1 achieved notable statistical strength, and despite some perhaps ambigously

interpreted elements from the both sides of the market, appears to be a U.S. wheat supply. There is a

positive and very statistically significant own price elasticity of 5.8. This parameter may initially appear

overly elastic – a concern which may be abated after considering that these CVs are very long run and

extend beyond a single annual cycle of planting decisions. The elasticity may also appear less

implausible when one consults the relative QWHEAT/PWHEAT variation levels, with PWHEAT

movements constrained by the U.S. loan rate price support program.27 What is evident is that in the very

long run, and after intense efforts on separating-out market impacts of numerous, specific, and important

market/institutional events, QWHEAT appears highly responsive to PWHEAT changes..
28This weakly exogenous PBREAD behavior is confined soley to CV3, and is not general to all three CVs, such that

tests for weak exogeneity did not support such behavior for PBREAD generally throughout the error correction space.

26

 The quantity of wheat in CV1 appears negatively but sensitively related to movements in major

wheat-based products, PFLOUR and PBREAD. When price levels of wheat flour and bread products fall,

demand for flour and bread may rise to augment volume of wheat ultimately used as an input. These

statistically strong influences of flour and bread price behavior on QWHEAT is consistent with BBP’s

(2004, pp. 16-18) analysis of FEV decompositions that suggested high levels of influence by PFLOUR

and PBREAD variation on QWHEAT behavior.

CV2: A Reduced-Form Price Transmission Relationship Normalized on PWHEAT.

Equation 12 or CV2 appears to be a reduced form relationship among wheat-related prices

reflecting elements of both demand and supply. U.S. wheat price appears positively related to PFLOUR

and PBREAD. This positive price transmission coincides with recent analyses of FEV decompositions

that suggested that flour and bread price movements are prime determinants of wheat price behavior, and

from analysis of impulse response simulations that suggest a positive PWHEAT/PFLOUR relationship

(RBR’s 2002 and BBP’s 2004, pp. 14-16) . 

PWHEAT appears negatively related in this reduced form relation to the value-added

manufacturing product prices further downstream for mixes/doughs. A structural interpetation of this

negative relationship is not straightforward. As production costs raise PMIXES, perhaps mixes/doughs

supply shifts negatively, leading to less wheat ultimately delivered as an input and a fall in PWHEAT. 

PWHEAT appears positively related in this reduced form relation to the difference between

PCEREAL and PCOOKIES, and again, a structural interpretation is not straightforward. The price of

wheat-based cereals embodies prices of products with generally a lower degree of value-added processing

and a higher wheat-related proportion of production costs than the more processed product array

represented by PCOOKIES. As demand conditions tighten in the wheat-intensive cereal market relative

cookies/crackers market, more wheat is demanded as an input and a higher wheat price may result. 

Findings from BBP’s (2004, pp. 16-19) analysis of FEV decompositions suggested that PCEREAL and

PCOOKIES behavior had important collective influences on PWHEAT, with PCEREAL’s influences

having dominated that of PCOOKIES. 

CV3: A Reduced-Form Price Transmission Relationship Normalized on PFLOUR.

CV3 posits flour price as positively related to PWHEAT, with each percentage change in

PWHEAT eliciting, on average historically, a 0.49 percent, similarly-directed change in PFLOUR. This

reduced form response elasticity coincides closely with prior comparable estimates generated by reduced

form VAR impulse response simulations of 0.40 by BBP (2004, p. 14) and RBR (2002, p. 110).

As well, flour price appears positively related to the difference between PBREAD and prices of

wheat-using value added products reflected by PCEREAL. BBP (2004, pp. 16-19) uncovered evidence

for these markets that PBREAD takes on a weakly exogenous role by influencing other variables, with

little or no feedback from the latter to PBREAD.28 Their results and further analysis suggested that bread

price may be a widely-watched “bell weather” indicator of general bakery market conditions. Our more

precise, and BBP’s (2004) more general results are consistent with these prior findings. In CV3,

PBREAD generates a very significant t-value, suggesting an influence on CV3's error correction process
29More specifically, consider the $(CONFECT)-estimate of -0.30 in equation 11. Halvorsen and Palmquist’s (1980)

method takes “e,” the base of the natural logarithm, and raises it to the power of the value of the coefficient (here the power of -

0.30), subtracts 1.0, and multiplies the result by 100. What results is an average percentage change effect, here –25.9 percent, on

the dependent variable (QWHEAT in equation 11). This suggests that the sustained run-up in confectionary input costs that

began in 2001 resulted in an ultimate drop in the supply of wheat, presumably as demand for wheat-based confectionary products

fell off, rendering less wheat supplied as an input. As noted earlier, other relevant and concurrent factors/events over this

2001:01-2004:04 subsample for which CONFECT was defined also contribute to this effect. 30 The array of preliminary and final AD/CVD tariffs imposed on certain U.S. imports of durum and/or hard red spring

wheat was rather complicated and is not recounted here. Interested readers should see USITC (2003). The final tariffs imposed

were on imports of Canadian hard red spring wheat and amounted to just over 14 percent.

27

and on PFLOUR. As well, PBREAD’s low-valued and insignificant adjustment speed coefficient in

CV3 (t=1.46) suggests that PBREAD is weakly exogenous in CV3 and influences but does not respond to

CV3 error correction mechanisms. As widely-watched demand bread market conditions rise and reflect

improved market conditions for bakery-related agents generally (ceteris paribus), PBREAD rises, the

PBREAD/PCEREAL wedge widens, and PFLOUR rises as perhaps more flour is demanded for multiple

wheat-based markets. The importance of PWHEAT, PBREAD, and PCEREAL movements in

determining PFLOUR behavior coincides with BBP (2004, pp, 16-17) analyses of FEV decompositions

for PFLOUR.

Analysis of Error-Correction Estimates on Deterministic Components.

Most binary $-estimates in equations 11-13 achieved strong statistical significance. Given that

non-binary variables were modeled in logarithms, we used Halvorsen and Palmquist’s (1980) well-known

method to convert the binary $-estimates into average percent change effects on the dependent variable

from concurrent events associated with the sub-sample for which the binary was defined. 29 (Hereafter,

HP calculated effects.) Based on prior VAR econometric research on these same markets and market

analysis by USDA, ERS (2004, 2005), we restricted numerous permanent shift binaries to the

cointegration space. For space considerations, we focus on the implied effects associated with the

AD/CVD case (TITLE7 binary), the NAFTA agreement (NAFTA binary), the sustained increases in

confectionary production costs that began in early-2001 (CONFECT binary), and the two temporary U.S.

tariff rate quotas imposed on certain imports of Canadian wheat (QUOTA binary). 

Effects of the antidumping/countervailing duty case. The filing of the AD/CVD case against 

certain U.S. imports of Canadian wheat ultimately led to a series of preliminary or final AD/CVD duties

on certain imports of Canadian durum and/or hard red spring wheat from 2002/03:02 through the end of

the sample (see USITC 2003 for a case summary). The HP calculated effects from $-estimates in CV1-

CV3 were rather pronounced: on average, the AD/CVD and related concurrent events resulted in

quarterly QWHEAT levels that were 59.7 percent lower; quarterly PWHEAT levels that were 75 percent

higher; while quarterly U.S. flour prices were 28.2 percent lower. The preliminary and final tariffs30

were relatively more modest than the HP calculated effects, and likely insufficient to have generated such

large AD/CVD effects. As clear from USITC (2003) and USDA (2004, 2005a) analyses, other concurrent

events such as the tight world grain supplies and high world levels of wheat prices and wheat demand

during 2002/03 - 2004/05 likely added influences that magnified these HP calculated effects for TITLE7

on QWHEAT (CV1) and PWHEAT (CV2). 

An interesting result is the negative TITLE7 $-estimate and -28.2 percent HP calculated effect on

CV3's PFLOUR. After U.S. AD/CVD tariffs were imposed on certain U.S. imports of Canadian wheat on

2002/03:02, official trade data from the USITC (2005) clearly reflected a shift in imports Canadian wheat
31 These calculations were based on USITC (2005) data for 1996-2004.

32 The source of this analysis and information was compiled by a U.S. International Trade Commission industry analyst

responsible for monitoring markets for sugar and confectionary products, in two emails received by an author on August 18 and

19, 2004. A more in-depth analysis on the effects on U.S. sugar-based product markets of these two run-ups in confectionary

input costs is provided in Babula and Newman (2005). Given that many confectionary products, both cocoa-based and noncocoa, use wheat, we included CONFECT in our analysis, and with clear statistical support as seen from our statistical results.

28

to imports of wheat flour, which were not covered by the AD/CVD orders. More specifically, average

annual U.S. imports of wheat flour quantity for 2002-2004 coinciding with the imposed AD/CVD duties

were 50 percent above the pre-duty average annual imports. (USITC 2005).31 Such sustained increases in

U.S. wheat imports associated with the AD/CVD orders’ implementation resulted in the perhaps

unexpected negative PFLOUR effects.

Effects of the January 1994 implementation of NAFTA. This binary was defined to capture

effects of concurrent events during the period from the January, 1994 implementation of NAFTA to the

end of the sample, a truly “crowded” subsample when many concurrent events other than NAFTA likely

influenced the modeled markets. The U.S. imported steadily increasing volumes of Canadian wheat,

while the U.S. government also tapered down levels of farm price supports with implementation of the

U.S. farm bills of 1996 and 2002. As well, there was a mini-world commodity boom during 1994-1995

when world demand, export, and price levels were elevated; a subsequent and sustained commodity

boom during from 2002 through late-2004; and the well-known and precipitous drop in U.S. wheat

exports to Asia after the 1997 Asian economic and currency crisis, among others. The events associated

with NAFTA suggested negative QWHEAT effects (CV1). As U.S. purchases of Canadian wheat

escalated, perhaps the drop in supply price to farmers from concurrent declining levels of wheat program

price support and increasing imports led to a drop in U.S. production that was disproportionally larger

than the import increase, so as to have generated a negative QWHEAT effect. Previous research and

USDA, ERS (2005a, b) data clearly demonstrate that PWHEAT fell during a substantial period after

NAFTA’s 1994 implementation, and thereby registered as a negative PWHEAT effect in CV2 (see figure

1). Parts of the NAFTA variable’s period of definition included U.S. tariff rate quotas and AD/CVD

duties on certain imports. These two actions likely elicited more imports of wheat flour, not covered by

these barriers, at the expense of wheat imports, so as to have negatively influenced PFLOUR in CV3. 

Effects of the 2001-2002 sustained increases in confectionary production costs. During early

2001, a marked and sustained rise in cocoa prices began in response to disruptions from the Ivory Coast

civil war, and in late-2002, there was another run-up in various non-cocoa confectionary input costs.32

CONFECT was defined to capture the effects of these confectionary input cost increases (and other

relevant concurrent events) for wheat-based confectionary products included in PMIXES and

PCOOKIES. The HP calculated effects on CONFECT suggested that the input cost increases and

concurrent events associated with CONFECT resulted, on average, in a 26 percent lower QWHEAT

levels and 42 percent lower PWHEAT. These negative impacts suggest that run-ups in confectionary

input prices may have negatively shifted wheat-using confectionary supplies, and resulted in less

QWHEAT used as production inputs, with lower PWHEAT levels.

Effects associated with two temporary U.S. tariff rate quotas on Canadian-sourced wheat. Two

U.S. TRQs were imposed on certain U.S. imports of Canadian wheat for the year ending September 11,

1995. As expected, events associated with QUOTA suggested negative impacts on QWHEAT in CV1 as

imports were restricted, and on PFLOUR as importers shifted to importing more wheat flour not covered

by the tariff rate quotas (as noted above in the TITLE7 coefficient estimate analysis). HP calculated

effects were rather pronounced however: -51 percent for QWHEAT in CV1 and -28 percent on PFLOUR
29

in CV3. A number of other concurrent events may have magnified these effects suggested by the

QUOTA beta estimates: the 1995 start of a commodity boom with high world demand and price levels for

wheat, and possible expectationary market influences of the then-anticipated 1996 U.S. farm bill which

noticeably lessened the U.S. wheat program support levels (among other events).

CV3 incorporates the statistically supported restriction rewritten as: -0.33*(QUOTA + TITLE7 -

NAFTA). This restriction suggests that events (i) associated with QUOTA and TITLE7 had similar and

decreasing effects on PFLOUR as imports shifted from wheat to wheat flour during periods of TRQs and

AD/CVD duties, (ii) NAFTA raised PFLOUR by about as much as the events associated with of the two

trade remedies decreased it and (iii) net PFLOUR effects arise from the combined negative effects

associated with TITLE7 and QUOTA as offset by positive effects from NAFTA-related events.

Summary and Conclusions

We extend previous quarterly VAR econometric research by Babula, Bessler, and Payne (2004)

and Rich, Babula, and Romain (2002) on U.S. markets for wheat and wheat-using value-added products

of flour, mixes/doughs, bread, wheat-based breakfast cereals, and cookies/crackers. We applied,

apparently for the first time, Johansen-Juselius methods of the cointegrated VAR to updated samples of

these same markets. We exploited the modeled system’s cointegration properties, and incorporated a wide

array of binary variables to capture empirically estimated effects of important market/institutional events. 

These results illuminated a long run error correction space which provided structural and reduced form

estimates on how these markets run and interact. Results included parameter estimates from three

cointegrating relations – a U.S. wheat supply curve and two transmission relationships among U.S.

wheat-based prices, along with an array of estimated effects from the cited market/institutional events.

The first CV, the apparent beginnings of a wheat supply curve, suggested that in the very long

run, market-clearing wheat quantities (QWHEAT) are highly and positively related to changes in

PWHEAT, which in turn is heavily influenced by the U.S. wheat program. QWHEAT was negatively

influenced by movements in flour and bread prices. The long run price elasticity of U.S. wheat supply

appeared to be nearly 6.0.

CV2 suggested that wheat price is positively related to PFLOUR and the difference in PCEREAL

and PCOOKIES, and negatively related to PMIXES. In CV3, flour price appears positively related to

PWHEAT, with each percentage change in PWHEAT eliciting, on average historically, similarly directed

changes of 0.49 percent in PFLOUR – a response that closely corresponds to previous estimates by BBP

(2004, p. 14) and RBR (2002, p. 110). 

We provided a number of empirically estimated market effects associated with the AD/CVD case

(TITLE7 binary), NAFTA agreement implementation (NAFTA binary), 2001 sustained rises in

confectionary production costs (CONFECT binary), and the two TRQs imposed on U.S. certain imports

of Canadian wheat (QUOTA binary). While the AD/CVD case and concurrent events resulted, as

perhaps expected, in QWHEAT declines and in PWHEAT increases, effects on PFLOUR were negative

as importers shifted towards imports of wheat flour not covered by the AD/CVD orders. NAFTA’s

coefficients suggested negative effects on QWHEAT and PWHEAT. The 2001-2002 sustained rises in

confectionary input prices appeared to result in ultimate declines in QWHEAT used as confectionary

inputs and decreased PWHEAT levels. The temporary U.S. tariff rate quotas on U.S. imports of

Canadian wheat appeared to restrict QWHEAT through impeded imports, while PFLOUR fell as

importers switched to imports of wheat flour not covered by the quotas.
30

References

Babula, Ronald A. "Economic Effects of a Countervailing Duty Order on the U.S. Lamb Meat Industry." 

Agricultural and Resource Economics Review 26,1 (1997):82-93.

Babula, R., D. Bessler, and W. Payne. “Dynamic Relationships Among U.S. Wheat-Related Markets:

Applying Directed Acyclic Graphs to a Time Series Model.” Journal of Agricultural and Applied

Economics 36 (April 2004):1-22.

Babula, R., and D. Newman. “Cointegrated Vector Autoregression Methods: An Application to NonNormally Behaving Data on Selected U.S. Sugar-Related Markets.” U.S. International Trade

Commission, Office of Industries Working Paper ID-12 (March 2005):1-31.

Babula, R. and K. Rich. “Time Series Analysis of the U.S. Durum Wheat and Pasta Markets.” Journal of

Food Distribution Research 32,2 (2001):1-19.

Bernanke, B. “An Alternative Explanation of the Money-Income Correlation.” Carnegie-Rochester

Conference Series on Public Policy 25(1986):45-100.

Bessler, D. “An Analysis of Dynamic Economic Relationships: An Application to the U.S. Hog Market.”

Canadian Journal of Agricultural Economics 32(19854):109-124.

Doan, T. 1996. RATS Users’ Manual, Version 4. Evanston, IL: Estima.

Engle, R., and C.W.J. Granger. “Cointegration and Error Correction: Representation, Estimation, and

Testing.” Econometrica 55(1987):251-56.

Estima. Regression Analysis of Time Series (RATS), Version 6, Reference Manual. Evanston, IL: Estima,

2004.

Granger, C.W.J. and P. Newbold. Forecasting Economic Time Series. New York: Academic Press, 1986.

Halvorsen, R., and R. Palmquist. “The Interpretation of Dummy Variables in Semilogarithmic

Equations.” American Economic Review 70(1980):474-75.

Johansen, S. “Statistical Analysis of Cointegration Vectors.” Journal of Economic and Dynamic Control

12(1988):231-253.

Johansen, S. and K. Juselius. “Maximum Likelihood and Inference on Cointegration: With Applications

to the Demand for Money.” Oxford Bulletin of Economics and Statistics 52(1980):169-210.

Johansen, S. and K. Juselius. “Testing Structural Hypotheses in Multivariate Cointegration Analysis of

the PPP and UIP for UK.” Journal of Econometrics 53(1992):211-44.

Juselius, K. The Cointegrated VAR Approach: Methodology and Applications. Draft, forthcoming

textbook on the economometrics of the cointegrated vector autoregression model. Economics Institute,

University of Copenhagen, 2004.
31

Juselius, K., and J. Toro. “Monetary Transmission Mechanisms in Spain: The Effect of Monetization,

Financial Deregulation, and the EMS.” Journal of International Money and Finance 24(2005):509-31.

Kloek, T. and H. VanDijk. “Bayesian Estimates of Equation System Parameters: An Application of

Monte Carlo.” Econometrica 46(1978):1-20.

Rich, K., R. Babula, and R. Romain. “Chapter 5: The Dynamics in the Wheat and Wheat Products Sector:

U.S.-Canada Comparisons.” Agricultural Trade Under CUSTA. W. Koo and W. Wilson, eds., pp. 93-

118. Hauppauge, NY: Nova Science Publishers, Inc., 2002.

Tiao, G., and G. Box. “Modeling Multiple Time Series: With Applications.” Journal of the American

Statistical Association 76(1978):802-16.

U.S. Department of Agriculture, Economic Research Service (USDA, ERS 2005a). “Wheat Outlook.”

WHS-05f, July 14, 2005, Washington DC, pp. 12-15.

U.S. Department of Agriculture, Economic Research Service (USDA, ERS 2005b). Wheat Situation and

Outlook Yearbook, Washington DC, WHS-2005, 2005.

U.S. Department of Labor, Bureau of Labor Statistics (Labor, BLS). “Producer Price Index Data Bases.” 

Found at www.bls.gov. Accessed Aug. 16, 2005.

U.S. International Trade Commission, Database of imported products into the United States. Located at

http://dataweb.usitc.gov, and accessed for U.S. imports of wheat flour from Canada on December 8,

2005.

U.S. International Trade Commission (USITC). Durum and Hard Red Spring Wheat from Canada,

Investigations Nos. 731-TA-1019A and 1019B (Final). USITC Publication No. 3639, October, 2003. 

U.S. International Trade Commission (USITC). The Economic Effects of Antidumping and

Countervailing Duty Orders and Suspension Agreements, Investigation No. 332-344. USITC Publication

No. 2900, June, 1995.