1
Exchange Rate Pass-Through to Disaggregated Prices In South
Africa: A VAR Approach
by
Harris Madhuku
Student at
University of Zululand, Economics Department
Email: madhukuharris@gmail,com or [email protected]
Abstract
One important challenge monetary policy crafters face is the effect of exchange rate changes on
inflation. A handful literature in South Africa investigated the effects of exchange rate pass
through (ERPT) to disaggregated prices but most of the analyses are bunched under
macroeconomic data. This paper outline ERPT to different individual prices of goods and
merchandised imports in South Africa using a unique dataset from 1979-2014. The paper
considers product or sector heterogeneity in analyzing the effect of exchange rate changes,
whilst minimizing aggregated bias. . Using actual weights to estimate ERPT, the record high in
the model were food CPI (22.72%) and machinery prices (46.6%) as pass through was seen to
be high in these proxies although not complete.
Key words: Exchange rate pass-through, merchandised imports, inflation
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Contents
Introduction .................................................................................................................................................. 3
Theory ........................................................................................................................................................... 5
Modeling ERPT .......................................................................................................................................... 5
Channels of ERPT ...................................................................................................................................... 6
Exchange Rate Pass -Through (ERPT) in South Africa and the entire continent ....................................... 7
Monetary policy and ERPT ........................................................................................................................ 8
Methodology .............................................................................................................................................. 10
Data and data sources ............................................................................................................................ 11
Unit Roots Tests ...................................................................................................................................... 11
Lag selection criteria ............................................................................................................................... 12
VAR Results................................................................................................................................................. 13
Impulse response functions .................................................................................................................... 13
Variance decomposition analysis............................................................................................................ 15
Conclusion .................................................................................................................................................. 17
Appendix1: VAR regression of the individual prices ........................................................................... 18
Appendix2: Variance decomposition of individual prices................................................................... 19
Appendix3: VAR regression of disaggregated indices............................ Error! Bookmark not defined.
Appendix4: Variance decomposition disaggregated indices .............................................................. 20
References .................................................................................................................................................. 21
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Introduction
One important challenge monetary policy crafters face is the effect of exchange
rate pass through (ERPT) on inflation. Exchange rate pass through is response of
import prices as a results of fluctuations in the exchange rate and through them to other
domestic prices (Aron, Farrell et al. 2014). A handful literature in South Africa
investigated the effects of exchange rate pass through (ERPT) to disaggregated prices
but most of the analyses are bunched under macroeconomic data. This paper outline
ERPT to different individual prices of goods and merchandised imports in South Africa
using a unique dataset from 1979-2014. The paper also considers product or sector
heterogeneity in analysing the effects of exchange rate changes whilst minimising
disaggregate bias in economic analysis.
The adoption of inflation targeting by many developing countries before and after
the 2008 global financial crisis, and its main focus on inflation forecasting and low prices
is the stimulating factor in the ERPT interests especially in South Africa. South Africa
started to officially target inflation in 2000 and the target range was put between 36%(Smal, De Jager et al. 2001). A lot of researches found a positive relationship
between inflation targeting and low inflation (ERPT) especially in developing economies
like Kenya, Malawi, Tanzania, Tunisia, Zimbabwe and South Africa (Jombo, Simwaka et
al.). This was observed when most of the countries that were experiencing high levels of
inflation managed to bring down inflation after embracing the adoption of inflation
targeting as a tool to bring down inflation(Ozkan and Erden 2015). However, (Kaseeram
2012) argued that the private sector inflation expectation in South Africa are always
backward looking or adaptive a thing which can affect the credibility of the SARB the
institution running the Inflation targeting(IT) regime and make it difficult to keep inflation
in the targeted range.
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The relationship between inflation has been extensively researched especially in
the developed countries like USA, Canada, Japan and others and those for the SubSaharan Africa most of them are multi country analyses. One wrong aspect about
bunching all countries in one analysis in country heterogeneity because countries have
different macroeconomic environments, monetary policies and trade policies(Parsley
2012). In South Africa there is quite a number of researches done on ERPT pre and
post the inflation targeting era and some of the most cited papers are from (Jooste and
Jhaveri 2014),(Edwards and Garlick 2008), (Aron, Farrell et al. 2014),(Aron, Macdonald
et al. 2014),(Choudhri and Hakura 2015),(Schaling and Kabundi 2014), (Razafimahefa
2012). All of the researchers were interchanging the tradable prices (Import, export,
consumer and producer prices) on an aggregated perspective meaning that their
analyses were on a macroeconomic level. The agreement of literature on South Africa
is that import prices contribute more to inflation followed by producer prices, export
prices and consumer prices care the level of endogeinity increase as we move down the
chain.
The purpose of this study is to go down to individual prices of certain products
and industrial or sectorial prices and the aspects to be investigated are chemical prices,
energy import prices, merchandised imports, agriculture producer prices, food prices
and machinery import prices. Output gap is also included since it can also contribute to
inflation when the potential output is below the actual output(Parsley 2012). Also one of
the contributions to high or low ERPT is the content of imported elements in a
consumption basket but it has not been fully cleared out which products or sectors are
more prone to high ERPT than others in the basket and that is what this paper is going
to do. The choice of these items to be investigated is motivated by the contribution of
the certain sectors to the South African economy and those which are not represented
here might be because of data availability.
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Theory
Modeling ERPT
The frequently used specification by many researchers on ERPT is normally on
the pricing choices or behavior of prices on imports especially from the microeconomic
point of view. Lets start by taking a simple static profit maximization problem an
exporting firm faces.
Considering a foreign firm exporting its goods to our domestic market or country,
the firm which is exporting solves the following profit maximization problem:
Max π=e-1pq-C(q)…………………………………………………………………………..(1)
Π- represents profits in foreign currency, e – is the exchange rate in terms of units of
domestic currency per unit of forex, p-price of the good in the domestic country, C- is
the cost function and q- denotes quantity.
Then if we solve equation (1) above we get the first order condition of the form:
P =eCqµ…………………………………………………………………………………..(2)
Cq-represent the marginal costs, µ-mark-up of price over the marginal cost.
Equation (2) states that local currency of the commodities can differ as a result of a
change in the exchange rate, changes in the additional cots (MC) and changes in the
price (mark up).
Most importantly, it must be noted that the firm’s mark-up can change without
any changes in the exchange rate. On another note (Bailliu and Fujii, 2004), observed
that demand shocks from the importing country can change mark-up of the exporter.
Also proper care must be taken for changes of other determinants of prices so that
when we want to estimate ERPT we isolate only the effects of the exchange rate
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change on the import prices and other price variables down the chain (Goldberg and
Campa, 2005).
Below is a logged reduced form equation showing the changes of ERPT as other things
like marginal costs and demand conditions change.
Pt = α + λet + βp*t + Φyt + ɛt………………………………………………………………….(3)
P* and y are measurements of the MC of the exporter and the demand condition of the
importer respectively whilst λ is a measure of ERPT itself
Channels of ERPT
Fluctuations in the external value of the rand can have both direct and indirect
effects to the domestic prices in South Africa (Lafleche, 1996). Under depreciation,
finished products imported into the country can be expensive because we will need to
use more of the rand than before. On the other hand, for the industries which are fed by
imported inputs, the inputs will become more expensive and when mark ups are put in
place the final consumer prices will respond by going up. The effect of exchange rate
changes to finished and input imports is more direct.
Indirectly, final consumer prices also can be affected by depreciation of the rand
assuming than when South African firms are exporting, foreign imports will need less of
their money to buy more of the rand and that can increase demand of domestically
produced goods(Savoie-Chabot and Khan 2015). The rise in demand for South African
exports will demand more production and more production demand more labour; rise in
demand for labour will raise wages also raising production costs. On the other side the
expensiveness of the imported products will make people to switch from imported
products to domestically produced products. So the increase in demand versus supply
is inflationary in the short run. However, this expenditure switching cannot take place
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over night but it can take time because of various economic reasons(Aron, Farrell et al.
2014).
Choice of currency can also affect the amount of exchange rate passed through
to domestic prices. Choudhri and Hakura (2012), argued that pass through can be high
if we have locally produced goods being sold in foreign currency or paying for imports
using the producer currency or foreign currency (PCP). Their argument states that
paying in foreign currency can be more sensitive to exchange rate changes that when
the goods are being paid using our local currency (LCP). Firms paying using local
currency can be those firms which are in a contract in terms of pricing with foreign firm
or a branch of a multinational company operating in our economy. However, these
pricing decisions are also affected by things like menu costs, demand conditions and
competitiveness in the domestic market. On the other hand firms can use pricing to
market and this has been seen as something with low pass through results. Also
importing from countries with a fixed exchange rate regime can result in low to zero
pass through as compared to those with flexible exchange rate regimes.
Exchange Rate Pass -Through (ERPT) in South Africa and the entire continent
The general phenomenon in the empirical findings is that pass-through between
zero and not complete. This mean that if a country is struck by a 10% depreciation and
no adjustment to prices is done (zero pass-through) or prices are adjusted by a less
than proportionate percentage (incomplete pass-through) like 5%.
In most country specific studies in Africa, pass through is found to be low and in
some cases even zero. Using a VECM model, (Anguyo 2008) found that ERPT to prices
in Uganda is low and consistent with other findings from others. (Devereux and Yetman
2003) based on a single equation approach find low ERPT for Ghana and this was also
confirmed by (Frimpong and Adam 2010) who then used an unrestricted VAR to find
also low ERPT in Ghana. (Choudhri and Hakura 2015) also reported low pass through
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for countries like Zimbabwe, Malawi, Ghana and found modest pass through for
countries like Kenya, Cameroon and Zambia. However, although pass through is
assumed to be low and sometimes zero, there are some studies where it was found to
be very high for example(Sanusi 2010) who found ERPT very high for Ghana counting
to 79%. (Kiptui, Ndolo et al. 2005) on a study for Kenya found ERPT to import prices
counting 70%.
Coming to South Africa a wide range of studies were done getting conflicting
findings since some found ERPT low whilst others getting it extremely high. Studies like
(Edwards and Garlick 2008), (Aron, Farrell et al. 2014), (SARB, 2002), (Bhundia, 2002),
(Nell, 2000), (Karoro, Aziakpono et al. 2009), (Nogueira 2006) found high ERPT in
South Africa ranging between 50% to 85%. However, (Gopinath, Itskhoki et al. 2007),
(Mihaljek and Klau 2008), (Choudhri and Hakura 2015) found ERPT reading a range of
7%-35%. Unfortunately for all these studies for South Africa was sector specific or
product specific but some of the studies recommended the disaggregation process
whilst others pointing food inflation as the major source of inflation in the consumption
basket.
Monetary policy and ERPT
Exchange rate changes can have a material impact on inflation in the long run if
necessary and sufficient action is not done by the monetary policy authorities but
ultimately inflation depends with the monetary policy (Savoie-Chabot and Khan 2015).
To manage in keeping inflation down especially countries that adopted inflation
targeting, all stake holders in the country must believe that the central bank have the
ability to do so(Aron, Macdonald et al. 2014). The SARB is making this realistic by
visiting universities in the country and explain the stance of the central bank in trying to
keep prices down. Also it meets up with the business community at provincial level to
discuss and present its functions and objective so that citizens can believe in the
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mandate of the central bank. This can help in the long-run to keep expectations within
the range and this is an important aspect in the contact of the monetary policy.
One observation from (Kaseeram 2012) point out the behavior of the private
agents in South Africa as he only identified them as always adaptive or backward
looking since they believe that inflation in the next period will be greater than what is
there today. This can have an impact on the pricing decisions made in the country, if
there is an exchange rate shock in the form of a depreciation (1) agents can see it as
temporary (2) can also see it as something that will be staying for some time. Only
agents who believe in the credibility of the monetary policy authorities will see the shock
as temporary and cannot adjust their mark ups in any way (low or zero pass-through)
and those who doubt or who are adaptive will see it as something to stay and they can
quickly adjust their prices (high pass-through).
An observation from (Savoie-Chabot and Khan 2015) points out that, monetary
policy through the authorities should react to shocks that affect aggregate demand in
the country. These shocks can be seen manifesting from the output gap and they are
key to the contact of the monetary policy. Central banks with high credibility always
succeed to put inflation and as a result of that low pass through will prevail (Mishkin,
2009).
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The diagram below show the relationship between inflation and nominal exchange rate
in South Africa:
Fig: 01
CPI and exchange rate(1995-2015)
140
120
100
80
60
40
20
0
1995
1998
2001
2005
CPI
2009
2012
2015
exchange rate
Source: STATS SA
Methodology
In terms of estimation approach, the unrestricted Vector autoregressive (VAR) approach
was used. We estimate an unrestricted VAR to track down impulse responses and
variance decomposition on inflation in South Africa just like, (Jombo, Simwaka et al.),
(Bonato and Billmeier 2002, Frimpong and Adam 2010) in their papers for country
specific papers.
The simplest form of a VAR is the reduced VAR model, where each variable will be a
linear function of its own past values and the past values of the other variables in an
equation. A VAR in its reduced form of order p in levels of the variables can be
expressed as shown below:
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𝑿𝒕 = 𝑨𝒚𝒕 + ∅𝟏 𝑿𝒕−𝟏 + . . . + ∅𝒊 𝑿𝒕−𝟏 + . . . +∅𝒑 𝑿𝒕−𝒑 + 𝜺𝒕
Where Yt is a (n X 1) vector of constant variables, ∅ is a (n X n) vector of
autoregressive coefficients to be estimated and ɛt is a (N X 1) vector of white noise.
The variables in the model were ordered in a way to make sure that those variables like
output gap and exchange rate were put first so as for them to affect the rest of the other
variables in the models whilst they do not get affected by the other variables. Also the
orthogonalisation (diagonalise the variance-covariance) in the unrestricted VAR help to
interpret the correlation among other variables in a causal manner, meaning that
causality is more pronounced than correlation. Also the computing of the cholesky
factorization of the model’s covariance matrix was done as borrowed from (Lütkepohl
1993).
Data and data sources
We use yearly data downloaded from the South African Reserve Bank (SARB),
STATS SA website and Quantec. Data were downloaded in excel form and then
imported into EViews. All data was transformed into log form and some to percentages
since our interpretation of results was to be done in percentages. All the variables were
downloaded as indices except output gap (the difference between actual and potential
output) (NEER, food cpi, ppi agriculture, energy prices, machinery prices, chemical
prices, merchandised import prices and output gap).
Unit Roots Tests
Each variable was tested for stationarity using the Augmented Dickey Fuller (ADF) tests
to show if the variables are stationary in the levels or after they are differenced. The
results of the unit root tests indicated that all the variables got to be stationary after they
were differenced once I(1) except output gap which was stationary in levels I(1).
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Table1. Augmented Dickey-Fuller Unit Root Test
VARIABLE
LEVEL
FIRST DIFFERENCE
ADF
ADF
COMMENT
Output gap
-4.1899
-
I(0)
Lneer
-1.2529
-4.4502
I(1)
Lchemical
-0.2087
-4.1258
I(1)
Lfood_cpi
-2.6967
-4.9918
I(1)
Lmechandised_imports
-3.0062
-6.5018
I(1)
LPPI_agriculture
-2.5166
-5.9080
I(1)
LMachinery prices
-3.6133
-3.9090
I(1)
Energy prices
-3.0339
-5.3990
I(1)
Lag selection criteria
In determining the number of lags to include in the model to regress the disaggregated
indices, we used the VAR lag order election criterion and then picked the Akaike
Information criteria (AIC) to determine our lag length. In the AIC, the lag with the
smallest value will be taken into consideration and in this condition 3 lags were used as
indicated by the table below.
Table2: Akaike Information Criteria (AIC)
VAR Lag Order Selection Criteria
Endogenous variables: YT LNEER LMCH_IMP LPPI_AGRIC FD_CPI
Exogenous variables: C
Date: 06/20/16 Time: 17:05
Sample: 1 37
Included observations: 34
Lag
LogL
LR
FPE
AIC
SC
HQ
0
1
2
3
-185.7774
0.742094
21.38536
53.90989
NA
307.2085*
27.92912
34.43774
0.051452
3.92e-06*
5.61e-06
4.77e-06
11.22220
1.721053
1.977332
1.534712*
11.44666
3.067842*
4.446445
5.126149
11.29875
2.180347*
2.819370
2.759495
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
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AIC for individual price indices
VAR Lag Order Selection Criteria
Endogenous variables: LNEER LCHEMC LMCHIN ENGY
Exogenous variables: C
Date: 06/20/16 Time: 12:51
Sample: 1 36
Included observations: 33
Lag
LogL
LR
FPE
AIC
SC
HQ
0
1
2
-90.40410
61.13745
75.52958
NA
257.1614*
20.93401
0.003589
9.80e-07*
1.13e-06
5.721461
-2.493179*
-2.395732
5.902855
-1.586204*
-0.763178
5.782494
-2.188009*
-1.846427
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
VAR Results
Impulse response functions
After the estimating an unrestricted VAR, impulse response functions and Variance
decompositions were computed in order to analyse the effects of ERPT to prices
(Inflation). In order to quantify ERPT, variance decompositions were used as borrowed
from (Karoro, Aziakpono et al. 2009) and (Hussain Academy You tube videos, 2013).
The results of the exchange rate impulse under the Unrestricted VAR are shown in the
table 2 below and they show the impact of one standard deviation shock, defined as an
exogenous, unexpected, non-permanent depreciation or appreciation in the exchange
rate with a 95% confidence level on domestic prices (inflation) and output gap(Jombo,
Simwaka et al.). The middle solid line showing in every graph is the estimated response
while the dotted lines mean a two standard error confidence band around the estimated
variable(Sims 1986). The rest of the analysis was done using the variance
decompositions since they quantify the effects of shocks in percentages a thing which is
in line with the idea of the paper.
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Figure 2: Responses to Exchange rate shocks
Response to Cholesky One S.D. Innovations ± 2 S.E.Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of LNEER to YT
Response of YT to LNEER
.2
8
.1
4
.0
0
-.1
-4
-.2
-8
2
4
6
8
10
2
4
6
8
10
Response to Cholesky One S.D. Innovations ± 2 S.E.Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of LNEER to LMCH_IMP
Response of LMCH_IMP to LNEER
.2
.08
.1
.04
.0
.00
-.1
-.04
-.2
-.08
2
4
6
8
10
2
4
6
8
10
Response to Cholesky One S.D. Innovations ± 2 S.E.Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of LPPI_AGRIC to LNEER
Response of LFD_CPI to LNEER
.10
.10
.05
.05
.00
.00
-.05
-.05
-.10
-.15
-.10
2
4
6
8
10
2
4
6
8
10
Response to Cholesky One S.D. Innovations ± 2 S.E.Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of LCHEMC to LNEER
Response of ENGY to LNEER
.12
6
.08
4
.04
2
.00
0
-.04
-.08
-2
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
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15
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of LMCHIN to LNEER
.10
Response of LNEER to LNEER
.15
.05
.10
.05
.00
.00
-.05
-.05
-.10
-.10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
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Variance decomposition analysis
As discussed in the methodology, we estimated the unrestricted VAR model
using the AIC to determine lag length of the Variables. The results of the estimates of
the short-run and long-run ERPT using different indices of different variables are shown
at the end (back) of this paper.
For the variables under consideration the paper overwhelmingly reject complete
ERPT into all the variables (merchandised imports, PPI agric, machinery prices,
chemical prices, energy prices and food prices) for both Short-run (SR) and Long-run
(LR). That result is in line with previous findings about ERPT in South Africa. The results
of this paper could not confirm that SR pass through is greater than LR for most of the
prices except because there is mixed behavior of prices when it comes to that issue
with others having high SR pass and others high LR pass through.
It has been observed from the results that under the variance decompositions
computed from the model, a shock to the nominal exchange rate lead to a 38.8 %
fluctuation in the machinery prices for the SR and 46.6% in the LR. This means that
machinery prices respond too much immediately after the shock and slow down as time
goes by. Also impacting the machinery prices are the chemical prices, bringing in 7.01%
fluctuations in the LR.
Estimates of Food cpi shows almost zero pass through of 0.047% in the SR and
22.27% in the LR. This is confirmed by a lot of suspicions from other papers as it was
always assumed that food prices are prone to exchange rate changes because of the
composition of import aspects in its basket. However, producer prices from the
agriculture sector lead to a fluctuation in food prices by 38% (SR) and 24% (LR). This
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can be confirmed by theory since all the food processors feed from the production of the
Agriculture sector a sector which contributes a significant percentage to the South
African economy. Also an impulse to machinery prices makes the nominal exchange
rate to fluctuate by 25% in the LR a very big contribution to volatility of the exchange
rate.
Chemical prices’ results show that, an impulse or shock to the exchange rate can
lead to a 9.49% change in the in the chemical prices in the South Africa with a LR
estimation of 12.90%. Producer prices in the agriculture sector don’t show to be
vulnerable if an exchange rate shock hits the economy as expected from all other
producer prices. In the SR the producer prices in the agriculture sector in South Africa
respond by 0.95% whilst the long-run estimation sits at 21.13%. This is a sign of low
almost zero ERPT in the agriculture sector prices in the SR and it boost after some time
or with a lag.
Taking a look at the Merchandised imports in South Africa, also they don’t show
much volatility since after a shock to the exchange rate only a paltry of 1.77 % is passed
through to the merchandised imports for the SR phenomenon. In the LR 4.27% pass
through is identified and again it doesn’t confirm with theory since aggregate import
prices have a high tolerance to ERPT. This means that in the basket for imported
elements, merchandised imports do not contribute much to the total pass through. Food
prices are seen contributing 9.08% in the SR and 10.08% in LR meaning that
merchandised are significantly affected by food prices more than the exchange rate
changes does to them.
From the literature energy prices were assumed to be one of the highest
contributors to inflation in different countries as outlined by (Sanusi 2010). However,
from the look of our results, energy prices are showing the lowest pass through in the
model as compared to all considered variables. A paltry of 1.09% is passed on to
energy prices after an exchange rate shock hits the economy in the SR with the LR
estimations counting only 0.68% for South Africa. The assumption to this maybe of the
type of market energy belongs to. Remember the types of markets and number of
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players in an industry determines low or high pass through. However, chemical prices
are showing a huge contribution to the fluctuations in the energy prices, bringing 25% in
the SR and long-run estimations shooting to 64.44% for the LR phenomenon.
Regarding the hypothesis that developing countries have higher ERPT in
comparison to developed nations, as proposed by (Campa and Goldberg 2005), (Ozkan
and Erden 2015), (Nogueira 2006) and others, this paper found mixed results. Also
researches in South Africa before found results that are not conclusive when it comes to
estimates of ERPT in the country. Since this paper use disaggregated data and
individual product prices in trying to track the estimation of ERPT, the conclusion is that,
there are still other goods or sectors which are contributing much to inflation in South
Africa for example, machinery prices, food prices and chemical prices.
Conclusion
In this paper evidence was presented on exchange rate pass through (ERPT) for
a set of different goods prices in South Africa under the Inflation Targeting (IT) regime.
The question now is whether the regime is helping to keep or bring inflation down and
which sectors to be targeted in order to keep inflation within the targeted range (3-6%).
The results show that some products have low though ERPT confirming that
pass through has decreased in South Africa whilst some are showing moderate to high
ERPT in the very South Africa. This means that more researches must be done at
industrial or sectorial level or even down to individual prices so that the root of high or
low pass through is known where it is coming from.
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Granger Causality
Pairwise Granger Causality Tests
Date: 05/12/16 Time: 06:52
Sample: 1 144
Lags: 2
Null Hypothesis:
Obs
F-Statistic
Prob.
IMP does not Granger Cause REER
REER does not Granger Cause IMP
132
4.62991
4.34233
0.0115
0.0150
PPI does not Granger Cause REER
REER does not Granger Cause PPI
142
0.61863
8.46699
0.5402
0.0003
CPI does not Granger Cause REER
REER does not Granger Cause CPI
142
0.54433
5.07850
0.5815
0.0075
EXPO does not Granger Cause REER
REER does not Granger Cause EXPO
136
7.91511
2.16386
0.0006
0.1190
PETR does not Granger Cause REER
REER does not Granger Cause PETR
142
2.36832
3.48850
0.0975
0.0333
PPI does not Granger Cause IMP
IMP does not Granger Cause PPI
132
0.47262
2.62869
0.6245
0.0761
CPI does not Granger Cause IMP
IMP does not Granger Cause CPI
132
5.37983
4.69469
0.0057
0.0108
EXPO does not Granger Cause IMP
IMP does not Granger Cause EXPO
131
3.97449
4.64011
0.0212
0.0114
PETR does not Granger Cause IMP
IMP does not Granger Cause PETR
132
13.3828
1.54483
5.E-06
0.2173
CPI does not Granger Cause PPI
PPI does not Granger Cause CPI
142
0.83646
10.7496
0.4354
5.E-05
EXPO does not Granger Cause PPI
PPI does not Granger Cause EXPO
136
7.33430
0.14528
0.0010
0.8649
PETR does not Granger Cause PPI
PPI does not Granger Cause PETR
142
4.32083
2.75774
0.0151
0.0670
EXPO does not Granger Cause CPI
CPI does not Granger Cause EXPO
136
4.47734
0.20386
0.0132
0.8158
PETR does not Granger Cause CPI
CPI does not Granger Cause PETR
142
0.71803
6.41332
0.4895
0.0022
PETR does not Granger Cause EXPO
EXPO does not Granger Cause PETR
136
1.45335
15.1737
0.2375
1.E-06
18
19
Appendix2: Variance decomposition of individual prices
19
20
Appendix4: Variance decomposition disaggregated prices
Variance Decomposition of YT:
Period
S.E.
YT
1
2
3
4
5
6
7
8
9
10
4.104391
5.794723
6.362309
6.498195
6.730650
6.995723
7.153660
7.299027
7.364599
7.412176
100.0000
84.66999
81.39282
78.15232
76.86909
73.75269
70.98290
68.20516
67.23695
66.73846
D(LNER)
0.000000
5.545177
8.292574
7.961589
7.633019
7.460483
10.65901
12.89710
12.66892
13.28697
Variance Decomposition of D(LNER):
Period
S.E.
YT
D(LNER)
1
2
3
4
5
6
7
8
9
10
0.119590
0.133105
0.134402
0.138688
0.139887
0.142341
0.144106
0.146969
0.148409
0.149318
1.416541
2.903965
2.850776
2.688177
3.078960
2.976177
3.265806
3.411987
3.347290
3.338243
98.58346
89.96164
89.00036
83.80412
82.54080
80.07332
78.76088
77.60624
76.14308
76.12502
Variance Decomposition of D(LMCHIMP):
Period
S.E.
YT
D(LNER)
1
2
3
4
5
6
7
8
9
10
0.038945
0.043517
0.044360
0.045898
0.048079
0.048854
0.049179
0.049476
0.049783
0.050188
14.96394
12.97662
13.25418
17.59287
21.31608
22.12544
21.93951
21.88101
21.66831
21.32561
1.772904
1.633442
1.690680
1.898690
1.787201
1.964562
2.140337
2.150423
2.773854
4.270069
Variance Decomposition of D(LPPIAGR):
Period
S.E.
YT
D(LNER)
1
2
3
4
5
6
7
8
9
10
0.057561
0.063627
0.072635
0.079627
0.081958
0.084644
0.087242
0.089631
0.090835
0.091580
0.175428
5.358814
4.230328
3.522002
3.373273
3.476205
3.984236
3.948743
3.864371
3.890990
Variance Decomposition of D(LFD):
Period
S.E.
YT
1
2
3
4
5
6
7
8
9
10
0.044224
0.053793
0.057700
0.063710
0.065861
0.066832
0.067999
0.069789
0.071240
0.071820
0.009609
4.129679
9.344775
13.97533
15.30209
15.87280
15.79115
15.18319
14.60087
14.38186
0.952490
12.27430
16.89791
15.82344
17.99214
16.94809
19.92082
21.18883
20.63088
21.13343
D(LNER)
0.047804
18.79747
20.99373
17.82413
17.51332
17.14255
18.66634
21.64198
22.90435
22.72287
D(LMCHIMP) D(LPPIAGR)
0.000000
0.472919
0.410288
0.558981
0.521976
0.510128
0.532101
0.554302
0.588470
0.643129
0.000000
1.852605
2.417668
4.505978
4.451119
7.714674
7.665613
8.569430
9.876507
9.811621
D(LMCHIMP) D(LPPIAGR)
0.000000
0.427511
0.457273
1.102212
1.083447
1.139025
1.173185
1.127923
1.108783
1.171730
0.000000
6.249621
6.389414
9.229011
9.073441
11.71482
12.49038
13.70109
15.21772
15.03847
D(LMCHIMP) D(LPPIAGR)
83.26316
69.47451
66.90304
62.84713
57.58215
55.78559
55.11073
54.45888
53.81429
52.95035
0.000000
6.832585
6.926917
7.154257
9.636064
10.73820
10.83381
11.33914
11.51708
11.36419
D(LMCHIMP) D(LPPIAGR)
1.695327
1.544689
1.968883
2.738102
2.695367
2.834535
2.911908
2.786655
2.713302
2.878565
97.17676
80.64819
76.76746
74.15338
71.55177
72.62758
68.97091
68.08513
68.62468
67.53462
D(LMCHIMP) D(LPPIAGR)
0.010161
1.029779
0.905108
1.819083
1.908882
2.256106
2.180278
2.111408
2.047282
2.201977
53.37619
38.42755
35.36649
36.61253
35.76338
34.81815
34.09732
32.79052
32.70105
32.71568
D(LFD)
0.000000
7.459306
7.486652
8.821135
10.52480
10.56203
10.16037
9.774010
9.629154
9.519823
D(LFD)
0.000000
0.457268
1.302177
3.176480
4.223347
4.096664
4.309744
4.152758
4.183132
4.326537
D(LFD)
0.000000
9.082843
11.22518
10.50705
9.678506
9.386211
9.975611
10.17054
10.22646
10.08979
D(LFD)
0.000000
0.174001
0.135421
3.763082
4.387454
4.113590
4.212131
3.990641
4.166765
4.562394
D(LFD)
46.55624
37.61552
33.38989
29.76892
29.51233
29.91039
29.26491
28.27289
27.74645
27.97762
Cholesky Ordering: YT D(LNER) D(LMCHIMP) D(LPPIAGR) D(LFD)
20
21
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