Monthly Labor Review • December 2012 19

Food Price Transmisson

Jonathan C. Weinhagen

Price transmission effects through 

three stages of food production

An analysis of price transmission through three stages of food

production reveals substantial differences in price transmission

from producer food to consumer food consumed at home

versus that consumed away from home; increases in various

food-related PPIs lead to increases in the CPI for food consumed

at home but not the CPI for food consumed away from home

According to the Consumer Expenditure Survey (CE) of the Bureau of Labor Statistics, U.S. consumers 

spent $6,129, on average, on food in 2010, 

accounting for close to 13 percent of average household annual expenditures. Of total 

household food expenditures, approximately 

60 percent ($3,624) was spent on food consumed at home and 40 percent ($2,505) was 

spent on food consumed away from home. 

The CE defines food consumed at home as 

food purchased from grocery stores or other 

food stores. The CE defines food consumed

away from home as meals (including takeout) purchased from restaurants, vending 

machines, and mobile vendors. 

Given the relatively large share of 

household spending made up by food, 

changes in food prices can affect consumer 

welfare substantially. Over the past decade, 

prices for unprocessed foods have risen 

considerably. From December 2001 to 

May 2011, the Producer Price Index (PPI) 

for unprocessed foodstuffs and feedstuffs 

(also known as the PPI for crude foodstuffs 

and feedstuffs) increased approximately 

90 percent. This article uses econometric 

techniques to examine price transmission 

through three stages of food production: 

unprocessed producer foods, finished 

producer food that eventually will be sold 

to consumers, and consumer food. The 

article analyzes price transmission effects 

on consumer food, not only overall, but also 

separately for that expenditure category’s two 

components: food consumed at home and 

food consumed away from home. Analysts 

expect that price transmission from producer 

food to food consumed at home differs from 

price transmission from producer food to 

food consumed away from home, because 

the service of preparing food may represent 

a substantial component of the value of food 

consumed away from home.

The article begins by using a vector 

autoregression (VAR) model to analyze price 

transmission from producer food to total 

consumer food. Then, in the next section, 

two separate VAR models are used to examine 

whether there are differences in price 

transmission from producer food to consumer 

food purchased for home consumption as 

opposed to consumer food consumed away 

from home. Finally, conclusions drawn from 

the analysis are presented.

Producer food to total CPIfood

VAR models can be used to examine the causal 

relationships between food prices at three 

stages of food production. VAR modeling 

involves estimating a series of equations in 

Jonathan C. Weinhagen 

is an economist in the 

Division of Producer 

Price Indexes, Bureau of 

Labor Statistics. Email: 

weinhagen.jonathan@

bls.gov.
Food Price Transmission

20 Monthly Labor Review • December 2012

which each variable is expressed as a linear combination 

of itself and all other variables in the system.1 A threevariable VAR model (henceforth referred to as VAR-TOTAL

because it includes total food) using the PPI for unprocessed 

foodstuffs and feedstuffs, the PPI for finished consumer 

food, and the Consumer Price Index (CPI) for total food 

was estimated with monthly data from January 1980 

through May 2011. The PPI for unprocessed foodstuffs and 

feedstuffs measures price changes in unprocessed foods and 

feeds sold to businesses as inputs to production. The PPI for 

finished consumer food measures price changes received 

by manufacturers of both processed and unprocessed food 

that will eventually be sold to consumers. The CPI for total 

food measures the average change in the selling price that 

consumers pay for food and includes both food consumed 

at home and food consumed away from home.

All data used in this article were seasonally adjusted and 

converted to percentage-growth form by taking the first 

differences of their natural logarithms. Converting timeseries data to percentage-growth form typically induces 

stationarity in the data. A time series is stationary if 

the mean, variance, and covariance of the series are not 

dependent on time. Using nonstationary time series to 

estimate a VAR model invalidates conventional significance 

tests of the model’s coefficients and can treat insignificant 

correlations as significant, even if both variables follow 

mostly independent trends. Dickey–Fuller tests were used 

to determine whether the series, expressed in percentagegrowth terms, were stationary.2

 The tests included trends, 

intercepts, and sufficient lags to ensure white-noise 

residuals. The tests indicated that all of the time series used 

were stationary when expressed in percentage-growth 

terms. To determine the correct lag structure of the VAR, 

the Schwarz information criterion was implemented.3

The criterion suggested that a VAR whose equations have 

one lag is optimal; therefore, one lag of each variable was 

used to estimate the VAR.

The VARmodel was first used to test for Granger causality 

among the indexes. A variable is said to Granger-cause a 

second variable when adding past values of the variable to 

an autoregressive model of the second variable improves 

the predictability of the latter. Wald statistics were used 

to test the null hypothesis that there was no Granger 

causality. Wald tests are based on measuring the extent 

to which the unrestricted estimates fail to satisfy the 

restrictions of the null hypothesis.4 A small p-value of the 

Wald statistic rejects the null hypothesis that there is no 

feedback to the dependent variable, and a large p-value of 

the Wald statistic implies that the null hypothesis is not 

rejected. A p-value of less than 0.01 indicates rejection 

of the null hypothesis at the 99-percent confidence level, 

whereas a p-value of 0.05 or less indicates rejection of 

the null hypothesis at the 95-percent confidence level. A 

p-value greater than 0.05 suggests acceptance of the null 

hypothesis that there is no Granger causality.

In addition to testing for Granger causality from 

individual indexes to the dependent variable, the analysis 

tested the joint lagged values of variables at stages of 

processing before and after the dependent variable for 

Granger causality. For example, the null hypothesis that 

prices for unprocessed foods and feeds and for finished 

consumer food do not jointly Granger-cause the CPI for 

total food was tested. Table 1 presents the results of the 

Granger causality tests.

The tests indicate that food prices at earlier stages of 

production generally Granger-cause food prices at more 

processed stages of production but that food prices at later 

stages of production do not Granger-cause food prices 

Table 1. Results of the Granger causality tests

VAR-TOTAL: Null hypothesis Chi-square p-value

Dependent variable: PPI for unprocessed foodstuffs and feedstuffs

PPI for finished consumer food = 0 0.070 0.791

CPI for total food = 0 2.083 .149

PPI for finished consumer foods/CPI for total food = 0 2.911 .233

Dependent variable: PPI for finished consumer food

PPI for unprocessed foodstuffs and feedstuffs = 0 25.109 .000

CPI for total food = 0 1.012 .315

Dependent variable: CPI for total food

PPI for unprocessed foodstuffs and feedstuffs = 0 .354 .552

PPI for finished consumer food = 0 23.308 .000

PPI for unprocessed foodstuffs and feedstuffs/PPI for finished consumer food = 0 46.092 .000
Monthly Labor Review • December 2012 21

at earlier stages of production. The tests show that the PPI

for unprocessed foodstuffs and feedstuffs Granger-causes 

the PPI for finished consumer food, the PPI for finished 

consumer food Granger-causes the CPI for total food, and 

the PPI for unprocessed foodstuffs and feedstuffs and the PPI

for finished consumer food jointly Granger-cause the CPI

for total food. By contrast, the CPI for total food does not 

Granger-cause the PPI for finished consumer food, the CPI

for total food does not Granger-cause the PPI for unprocessed 

foodstuffs and feedstuffs, the PPI for finished consumer food 

does not Granger-cause the PPI for unprocessed foodstuffs 

and feedstuffs, and the CPI for total food and the PPI for 

finished consumer food do not jointly Granger-cause the PPI

for unprocessed foodstuffs and feedstuffs.

VAR coefficients are difficult to interpret because of the 

multivariate nature of the models. Accordingly, impulse 

response functions and variance decompositions were 

developed to assist in interpreting VARs. Impulse response 

functions measure the effect of a one-standard-deviation 

perturbation of a variable in a system of equations on 

current and future values of all variables in the system. 

Variance decompositions show the percentage of forecast 

error variance in one variable of the VAR that is explained 

by perturbations to all variables used in the VAR.

5

 Because 

shocks within a VAR are generally not contemporaneously 

independent of each other, a random shock to one 

variable often occurs simultaneously with shocks to 

other variables. To overcome this problem, the residuals 

may be orthogonalized by a Cholesky decomposition 

in which the covariance matrix of the residuals is lower 

triangular. Therefore, a shock to one variable in the system 

contemporaneously affects only variables ordered after 

that variable in the VAR.

6

The residuals of the VAR were orthogonalized by a 

Cholesky decomposition using the following ordering: 

PPI for unprocessed foodstuffs and feedstuffs, PPI for 

finished consumer food, and CPI for total food. This 

ordering was chosen because unprocessed foods and feeds 

are used as inputs to produce finished consumer foods, 

which are then used as inputs to CPI food. In addition, 

the Wald tests that were carried out indicated that the PPI

for unprocessed foodstuffs and feedstuffs Granger-causes 

the PPI for finished consumer food and that the PPI for 

finished consumer food Granger-causes the CPI for food. 

Subsequent to orthogonalization of the residuals, impulse 

response functions and variance decompositions were 

constructed from the VAR coefficients.

Chart 1 presents the accumulated impulse response 

functions of one-standard-deviation shocks to the three 

variables in the system. Standard error bands (dashed 

red lines) were constructed with the use of the software 

program EVIEWS 5.0 to represent the statistical significance 

of the impulse response functions. The impulse responses 

were found to be significant at the 95-percent confidence 

level when both standard error bands were simultaneously 

above or below zero on the y-axis.

The impulse response functions show that changes in 

prices are passed forward through the three stages of food 

production. In all cases, price shocks at earlier stages of 

food production lead to statistically significant changes in 

prices at later stages of food production. For example, a onestandard-deviation (2.4-percent) unanticipated increase in 

the PPI for unprocessed foodstuffs and feedstuffs leads to a 

0.7-percent increase in the PPI for finished consumer food. 

More than half of the impact of the unprocessed-food 

shock on the PPI for finished consumer food occurs in the 

same month as the shock, and the full impact is reached 

after 4 months. A one-standard-deviation (2.4-percent) 

unanticipated increase in the PPI for unprocessed foodstuffs 

and feedstuffs leads to a 0.17-percent increase in the CPI

for total food. Approximately a quarter of the impact of 

the unprocessed-food shock occurs in the same month as 

the shock, and the full impact is reached after 6 months. 

Likewise, a one-standard-deviation (0.58-percent) increase in the PPI for finished consumer food results in a 

0.21-percent rise in the CPI for total food. By contrast, 

the impulse response functions do not suggest that price 

changes are passed backward through the stages of food 

production: in no instances does an unanticipated change 

to an index at a later stage of food production lead to a 

statistically significant change to an index at an earlier 

stage of food production.

Table 2 presents the variance decompositions for the 

stage-of-processing food indexes after 12 months. Like the 

impulse response functions, the variance decompositions 

imply that price shocks are passed forward, and not 

backward, through the stages of food production.

Table 2 shows that 11.35 percent of the forecast error 

variance in the CPI for total food can be attributed to 

shocks to the PPI for unprocessed foodstuffs and feedstuffs 

while 23.93 percent is attributable to finished consumer 

food. Alternatively, less than 0.5 percent of the forecast 

error variance in the PPIs for unprocessed foodstuffs and 

feedstuffs and for finished consumer food can be explained 

by shocks to CPI food.

In sum, the Granger causality tests, impulse response 

functions, and variance decompositions all indicate that 

changes in producer prices for unprocessed foods and 

feeds, as well as changes in producer prices for finished 

consumer food, are transmitted forward to prices for 
Food Price Transmission

22 Monthly Labor Review • December 2012

 Chart 1. Accumulated impulse response functions from VAR-TOTAL

 CPI for total food

0.04

.03

.02

.01

.00

–.01 1 2 3 4 5 6 7 8 9 10 11 12

 PPI for finished consumer food 

0.04

.03

.02

.01

.00

–.01 1 2 3 4 5 6 7 8 9 10 11 12

PPI for unprocessed foodstuffs and feedstuffs

0.04

.03

.02

.01

.00

–.01 1 2 3 4 5 6 7 8 9 10 11 12

Shock to—

 1 2 3 4 5 6 7 8 9 10 11 12

0.0035

.0030

.0025

.0020

.0015

.0010

.0005

.0000 1 2 3 4 5 6 7 8 9 10 11 12

0.0035

.0030

.0025

.0020

.0015

.0010

.0005

.0000 1 2 3 4 5 6 7 8 9 10 11 12

0.0035

.0030

.0025

.0020

.0015

.0010

.0005

.0000

CPI for 

total 

food

PPI for 

unprocessed 

foodstuffs

and

feedstuffs

0.010

.008

.006

.004

.002

.000

–.002 1 2 3 4 5 6 7 8 9 10 11 12

0.010

.008

.006

.004

.002

.000

–.002

 1 2 3 4 5 6 7 8 9 10 11 12

0.010

.008

.006

.004

.002

.000

–.002

 1 2 3 4 5 6 7 8 9 10 11 12

PPI for 

finished 

consumer 

food 

Response 

of—

consumer food. The tests also suggest that price changes 

for foods are not passed backward through the stages of 

food production.

Producer food to CPI food consumed at home 

and away from home

This section uses two separate VAR models to examine 

whether there are differences in price transmission from 

producer food to consumer food purchased for home 

consumption versus consumer food consumed away from 

home. The first VAR, composed of the PPI for unprocessed 

foodstuffs and feedstuffs, the PPI for finished consumer 

food, and the CPI for food consumed at home, will be 

referred to as VAR-HOME. The second VAR, composed of 

the PPI for unprocessed foodstuffs and feedstuffs, the PPI

Table 2. Variance decompositions from VAR-TOTAL after 12 months

Decomposition variable

Percentage of forecast error due to—

PPI for unprocessed 

foodstuffs and feedstuffs

PPI for finished consumer 

food

CPI for total food

PPI for unprocessed foodstuffs and feedstuffs 99.18 0.32 0.49

PPI for finished consumer food 43.30 56.47 .23

CPI for total food 11.35 23.93 64.72
Monthly Labor Review • December 2012 23

for finished consumer food, and the CPI for food consumed 

away from home, will be referred to as VAR-AWAY.

7

Estimating two separate VARs—one that includes the CPI

for food consumed at home as the final stage and the other 

that instead includes the CPI for food consumed away from 

home as the final stage—allows for a separate examination 

of price transmission effects on food consumed at home 

versus food consumed away from home. As mentioned 

earlier, it might be expected that the price transmission 

effects from producer food to consumer food consumed 

away from home would be less than those to consumer 

food consumed at home, because the former includes the 

service of food preparation as a substantial component. 

One lag of monthly seasonally adjusted data from 

January 1980 through May 2011 was used to estimate the 

two VARs. All data were seasonally adjusted and converted 

to percentage-growth form by taking first differences of 

their natural logarithms. Dickey–Fuller tests that were 

run indicated that all series expressed in percentagegrowth form were stationary. The VAR models were used 

to examine Granger causality among prices at the three 

stages of production. Table 3 displays the results of the 

Granger causality tests.

The results of the Granger causality tests developed 

from VAR-HOME and VAR-AWAY are similar to each 

other and to those from VAR-TOTAL, which includes total 

foods. For both VAR-HOME and VAR-AWAY, Granger 

causality occurs only from indexes at earlier stages of food 

production to those at later stages of food production. 

The Granger causality tests, therefore, do not provide 

strong evidence of differences in price pass-through from 

producer food prices to consumer food prices for food 

Table 3. Results of the Granger causality tests

Variables Chi-square p-value

VAR-HOME: Null hypothesis

Dependent variable: PPI for unprocessed foodstuffs and feedstuffs

Independent variable:

 PPI for finished consumer food = 0 0.109 0.742

 CPI for food at home = 0 1.525 .217

 PPI for finished consumer food/CPI for food at home = 0 2.351 .309

Dependent variable: PPI for finished consumer food

Independent variable:

 PPI for unprocessed foodstuffs and feedstuffs = 0 24.588 .000

 CPI for food at home = 0 .388 .534

Dependent variable: CPI for food at home

Independent variable:

 PPI for unprocessed foodstuffs and feedstuffs = 0 .962 .327

 PPI for finished consumer food = 0 28.884 .000

 PPI for unprocessed foodstuffs and feedstuffs/PPI for finished consumer food = 0 60.369 .000

VAR-AWAY: Null hypothesis

Dependent variable: PPI for unprocessed foodstuffs and feedstuffs

Independent variable:

 PPI for finished consumer food = 0 .542 .462

 CPI for food away from home = 0 2.120 .145

 PPI for finished consumer food/CPI for food away from home = 0 2.948 .229

Dependent variable: PPI for finished consumer food

Independent variable:

 PPI for unprocessed foodstuffs and feedstuffs = 0 26.121 .000

 CPI for food away from home = 0 2.515 .113

Dependent variable: CPI for food away from home

Independent variable:

 PPI for unprocessed foodstuffs and feedstuffs = 0 .518 .472

 PPI for finished consumer food = 0 6.434 .011

 PPI for unprocessed foodstuffs and feedstuffs/PPI for finished consumer food = 0 7.963 .019
Food Price Transmission

24 Monthly Labor Review • December 2012

consumed at home versus food consumed away from 

home.

In addition to playing their role in Granger causality tests, 

the two VARs estimated in this section were used to develop 

impulse response functions and variance decompositions. 

As with VAR-TOTAL in the previous section, the residuals 

were orthogonalized by a Cholesky decomposition with 

the following ordering: PPI for unprocessed foodstuffs 

and feedstuffs, PPI for finished consumer food, and CPI

for food consumed at home (for VAR-HOME) or CPI for 

food consumed away from home (for VAR-AWAY). Chart 

2 presents the accumulated impulse response functions 

developed from the coefficients of VAR-HOME, while 

chart 3 shows the response functions developed from the 

coefficients of VAR-AWAY. 

In contrast to the Granger causality tests presented 

in table 3, the impulse response functions suggest that 

there are substantial differences in how price changes 

are transmitted from producer food to consumer food 

consumed at home versus consumer food consumed 

away from home. A comparison of the impulse response 

functions in charts 2 and 3 shows that unanticipated 

price changes in the PPI for unprocessed foodstuffs and 

feedstuffs significantly affect the CPI for food consumed 

at home but do not significantly affect the CPI for food 

consumed away from home. In addition, the impulse 

response functions indicate that unanticipated changes to 

the PPI for finished consumer food significantly affect both 

the CPI for food consumed at home and the CPI for food 

consumed away from home but that the effect is much 

Response 

of—

 Chart 2. Accumulated impulse response functions from VAR-HOME

0.04

.03

.02

.01

.00

–.01

0.04

.03

.02

.01

.00

–.01

0.04

.03

.02

.01

.00

–.01

PPI for 

unprocessed

foodstuffs

and

feedstuffs

PPI for unprocessed foodstuffs and feedstuffs PPI for finished consumer food CPI for food consumed at home

Shock to—

 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

0.010

.008

.006

.004

.002

.000

–.002

0.010

.008

.006

.004

.002

.000

–.002

0.010

.008

.006

.004

.002

.000

–.002

PPI for 

finished 

consumer 

food

 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

0.005

.004

.003

.002

.001

.000

0.005

.004

.003

.002

.001

.000

0.005

.004

.003

.002

.001

.000

CPI for

food

consumed

at home

 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
Monthly Labor Review • December 2012 25

 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

0.04

.03

.02

.01

.00

–.01

–.02

0.04

.03

.02

.01

.00

–.01

–.02

0.04

.03

.02

.01

.00

–.01

–.02

0.010

.008

.006

.004

.002

.000

–.002

0.010

.008

.006

.004

.002

.000

–.002

0.010

.008

.006

.004

.002

.000

–.002

0.005

.004

.003

.002

.001

.000

–.001

0.005

.004

.003

.002

.001

.000

–.001 1 2 3 4 5 6 7 8 9 10 11 12

0.005

.004

.003

.002

.001

.000

–.001

PPI for unprocessed foodstuffs and feedstuffs PPI for finished consumer food CPI for food consumed away from home 

CPI for 

food 

consumed 

away 

from 

home

PPI for 

finished 

consumer food

PPI for 

unprocessed 

foodstuffs and 

feedstuffs

Response 

of—

Shock to—

Chart 3. Accumulated impulse response functions from VAR-AWAY

stronger for food consumed at home. A one-standarddeviation (0.58-percent) shock to the PPI for finished 

consumer food leads to a 0.29-percent increase in the CPI

for food consumed at home, but to only a 0.05-percent 

increase in the CPI for food consumed away from home. 

Furthermore, the shock to finished consumer food has an 

immediate effect on the CPI for food consumed at home, 

and the full impact of the shock occurs after 4 months. 

The shock to finished consumer food, by contrast, does 

not initially affect the CPI for food consumed away from 

home, and the full effects of the shock are not realized for 8 

months. The impulse response function analysis, therefore, 

supports the hypothesis that changes to producer food 

prices are transmitted more strongly to consumer prices 

for food consumed at home than to consumer prices for 

food consumed away from home.

Table 4 presents the variance decompositions of VARHOME and VAR-AWAY. Like the impulse response 

functions, the variance decompositions suggest that the 

price transmission effects from producer food to consumer 

food are much stronger for food consumed at home than 

for food consumed away from home.

The variance decompositions in table 4 show that 13.33 

percent of the forecast error variance in the CPI for food 

consumed at home can be attributed to unanticipated 

changes to the PPI for unprocessed foodstuffs and feedstuffs 

while 24.65 percent is attributable to the PPI for finished 

consumer food. Alternatively, the variance decompositions 

indicate that only 0.46 percent of the forecast error 

variance in the CPI for food consumed away from home 
Food Price Transmission

26 Monthly Labor Review • December 2012

Table 4. Variance decompositions

Decomposition variable

Percentage of forecast error due to—

PPI for unprocessed 

foodstuffs and feedstuffs

PPI for finished consumer 

food CPI for food at home

VAR-HOME

PPI for unprocessed foodstuffs and feedstuffs 99.36 0.30 0.34

PPI for finished consumer food 43.02 56.86 .11

CPI for food at home 13.33 24.65 62.02

VAR-AWAY

PPI for unprocessed foodstuffs and feedstuffs 99.05 .17 .77

PPI for finished consumer food 43.73 55.90 .38

CPI for food away from home .46 2.11 97.43

can be explained by unexpected changes to the PPI for 

unprocessed foodstuffs and feedstuffs while 2.11 percent 

is explainable by the PPI for finished consumer food. The 

vast majority (97.43 percent) of the forecast error variance 

in the CPI for food consumed away from home is due to 

unanticipated changes in that variable itself.

THIS ARTICLE HAS PRESENTED estimated VAR

models for studying price transmission through three stages 

of food production, the final stage of which is consumer 

food. The issue examined by the article was whether price 

transmission from producer food to consumer food differed 

for consumer food purchased for home consumption versus 

food consumed away from home.

The analysis began by estimating a VAR with three 

variables: the PPI for unprocessed foodstuffs and feedstuffs, the PPI for finished consumer food, and the CPI

for total food. The VAR was used to test for Granger 

causality and to construct impulse response functions 

and variance decompositions. The Granger causality tests, 

impulse response functions, and variance decompositions 

all indicated that price changes are transmitted forward 

through the stages of food production, but not backward. 

For example, the impulse response functions suggested 

that a one-standard-deviation (2.4-percent) unanticipated 

increase in the PPI for unprocessed foodstuffs and feedstuffs 

leads to a statistically significant 0.7-percent increase in the 

PPI for finished consumer food and a statistically significant 

0.17-percent increase in the CPI for total food and that 

a one-standard-deviation (0.58-percent) increase in the 

PPI for finished consumer food results in a statistically 

significant 0.21-percent rise in the CPI for total food. In 

no instances did an unanticipated change in a stage-ofprocessing food index lead to a statistically significant 

change in an index at an earlier stage of food production.

The analysis then estimated two separate VARs: one that 

included the CPI for food consumed at home as the final 

stage and the other that instead included the CPI for food 

consumed away from home as the final stage. Estimating 

these two VARs allowed for a separate examination of price 

transmission effects on food consumed at home versus 

food consumed away from home. The impulse response 

functions and variance decompositions constructed from 

the VARs suggest that there are substantial differences 

in price transmission from producer food to consumer 

food consumed at home versus that consumed away from 

home. Specifically, the impulse response functions indicate 

that an unanticipated change to the PPI for unprocessed 

foodstuffs and feedstuffs leads to a statistically significant 

increase in the CPI for food consumed at home but does 

not significantly affect the CPI for food consumed away 

from home. In addition, a shock to the PPI for finished 

consumer food significantly affects both the CPI for food 

consumed at home and the CPI for food consumed away 

from home, but the effect is much lower on the latter. 

A one-standard-deviation (0.58-percent) shock to the 

PPI for finished consumer food causes a 0.29-percent 

increase in the CPI for food consumed at home but just a 

0.05-percent increase in the CPI for food consumed away 

from home. The variance decompositions tell a similar 

story: on the one hand, 13.33 percent of the forecast 

error variance in the CPI for food consumed at home 

can be attributed to unanticipated changes to the PPI for 

unprocessed foodstuffs and feedstuffs while 24.65 percent 

is attributable to the PPI for finished consumer food; on 

the other hand, only 0.46 percent of the forecast error 

variance in the CPI for food consumed away from home 

can be explained by unexpected changes to the PPI for 

unprocessed foodstuffs and feedstuffs while 2.11 percent 

is explainable by the PPI for finished consumer food.
Monthly Labor Review • December 2012 27

Notes

1 William H. Greene, Econometric Analysis (Upper Saddle River, NJ, 

Prentice Hall, 1997); see especially pp. 815–816.

2 David A. Dickey and Wayne A. Fuller, “Distribution of the 

Estimators for Autoregressive Time Series with a Unit Root,” Journal

of the American Statistical Association, vol. 74, 1979, pp. 427–431. Also 

in John Dinardo and Jack Johnston, Econometric Methods (New York, 

McGraw Hill, 1996); see especially pp. 224–225.

3 Philip Hans Franses, Time Series Models for Business and Economic 

Forecasting (Cambridge, U.K., Cambridge University Press, 1998).

4 Greene, Econometric Analysis, p. 161.

5 Dinardo and Johnston, Econometric Methods, pp. 289–301.

6 Ibid.

7 The CPI program prices food away from home bimonthly in most 

CPI geographical areas. Therefore, the effects of a shock to a PPI foods 

index on the foods-away-from-home index may have a 1-month lag 

compared with the effects on the food-at-home index, which the CPI

program prices monthly everywhere.