The Income-Distributional Impacts of Canadian Monetary Policy and Commodity-Price Shocks
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The Income-Distributional Impacts of Canadian
Monetary Policy and Commodity-Price Shocks
Carlo Tolentino
Bachelor of Arts (Honours), University of Victoria, 2019
An Extended Essay Submitted in Partial Fulfillment
of the Requirements for the Degree of
MASTER OF ARTS
in the Department of Economics
We accept this extended essay as conforming
to the required standard
Dr. Graham Voss, Co-Supervisor
Department of Economics, University of Victoria
I hereby approve Carlo’s essay as complete. This is in lieu of my
signature.
Dr. Judith Clarke, Co-Supervisor
Department of Economics, University of Victoria
©Carlo Tolentino, 2021
University of Victoria
All rights reserved. This extended essay may not be reproduced in whole or in part,
by photocopy or other means, without the permission of the author.
Abstract This paper examines the income-distributional impacts of commodity-price shocks and monetary shocks by analyzing the impacts of these shocks on income-specific consumer price indices (ISCPI) in Canada. An ISCPI is the price index for the aggregate consumption basket for households within a range of income. I construct ISCPIs using consumer spending micro-data and disaggregated price index data from Statistics Canada, which I convert to income-specific inflation rates (ISIRs). I then estimate exogenous monetary and commodity-price shocks using a Structural Vector Autoregression. Finally, I estimate the impulse response functions (IRFs) of the ISIRs to commodity-price shocks and monetary shocks using the Local Projections Method (Jordà, 2005). I find no statistically significant di↵erence between the IRFs of di↵erent ISIRs to monetary shocks. In contrast, the IRF of the ISIR for middle- income households, as a response to commodity-price shocks, is larger than the IRFs for the ISIRs of low-income and high-income households. I find no statistically significant di↵erence between the IRFs of the ISIR of the bottom-income and top- income households to commodity-price shocks.
1 Introduction
Carolyn Wilkins, The Deputy-Governor of the Bank of Canada, states that
Canadian monetary policy “will be judged against how they a↵ect the distribution of
income and wealth in [Canada]” (Press, 2020, p.1). Monetary policy has distributional
impacts if it heterogeneously a↵ects prices of consumption baskets because of variations
in income. Similarly, commodity-price shocks will have distributional impacts if
it also heterogeneously a↵ects prices of consumption baskets. This essay aims to
analyze how Canadian monetary policy and commodity-price shocks impact the
price of di↵erent Income-Specific Consumer Price Indices (ISCPI). An ISCPI is the
price index of the aggregate consumption basket for households within an income-
percentile range. An income-percentile range is defined as a range of income between
two percentile values of household income. This topic’s premise is that if monetary
and commodity-price shocks a↵ect the prices of goods heterogeneously, and households
of di↵erent incomes consume di↵erent goods, then these macroeconomic shocks have
income-distributional impacts.
I compare three income-percentile ranges of ISCPIs: The bottom 10%, the top
10%, and the ISCPI for those between the 45th and 55th of percentiles of household
income. I convert each ISCPI into income-specific annual inflation rates (ISIR).
Therefore, let ⇡tB denote the income-specific inflation rate for households making
less than the 10th percentile of household income. Let ⇡tM denote the income-
specific inflation rate for households making between the 45th and 55th percentiles of
1
household income. Let ⇡tT denote the income-specific inflation rate for households
making more than the 90th percentile of household income.
I find no statistically significant di↵erence between the responses of the three
ISIRs to monetary shocks. However, I find a statistically significantly di↵erent
response of ⇡tM , from the responses of ⇡tT and ⇡tB , to commodity-price shocks.
The responses of the ⇡tT and ⇡tB to commodity-price shocks are not statistically
significantly di↵erent from each other. More specifically, after two quarters, a one
percentage-point change in commodity-price causes: a 0.032 percentage-point increase
in ⇡tB , a 0.041 percentage-point increase in ⇡tM , and a 0.036 percentage point increase
in ⇡tT . The policy implication of my results show that monetary policy may not
have distributional impacts in Canada. However, my results show that positive
commodity-price shocks may harm middle-income households more than low-income
or high-income households, since they have greater unanticipated price increases in
their consumption basket.
The main literature this essay builds upon is the econometric results of Cravino,
Lan, and Levchenko (2020). Cravino et al. (2020) analyze the distributional impacts
of monetary policy along the income-distribution, using data from the US. In this
essay, I analyze the same research question as Cravino et al. (2020) but using
Canadian data. I also expand on Cravino et al. (2020) by also looking at the
distributional impacts of commodity-price shocks on Canadian households. Cravino
et al. (2020) find that the consumption baskets of high-income and low-income
2households are less price-volatile than middle-income households because middle-
income households consume more goods that are more price volatile, relative to
high-income and low-income households. Cravino et al. (2020) also find that the
impulse responses of the ISCPI for those in the top 1% household income are one-
third smaller than the ISCPI of middle-income1 households as a response to monetary
shocks. One main di↵erence between this essay and Cravino et al. (2020) is that
Cravino et al. (2020) uses the Romer Narrative approach to identify monetary policy
shocks (Romer and Romer, 2004). In contrast to Cravino et al. (2020), I am using
a Structural Vector Autoregression (SVAR) to identify exogenous shocks2 . I use
the same Local Projection Method (Jordà, 2005) to estimate IRFs as Cravino et al.
(2020).
A paper that uses Canadian data to analyze monetary policy’s distributional
impacts in Canada is Kronick & Villarreal (2019). Kronick & Villarreal (2019) uses
the same method as Cravino et al. (2020) and the same Canadian data that I
am using in constructing ISCPIs. However, Kronick & Villarreal (2019) focus on
analyzing how low inflation a↵ects inequality and how inequality a↵ects monetary
transmission. Using an SVAR technique, Kronick & Villarreal (2019) find that
expansionary monetary policy increases income inequality in Canada, as measured
by the GINI Index (Gini, 1921). Secondly, Kronick & Villarreal (2019) find that
1
The middle-income households in Cravino et al. (2020) are households who are between the
th
40 and 60th percentile of household income
2
I am not able to do narrative approach in this essay because of time-constraints in writing this
essay. To my knowledge, only one paper has analyzed monetary shocks in Canada using a narrative
approach (Champagne & Sekkel, 2018). A further discussion on the narrative approach is in Section
6
3the estimated inflation response to monetary shocks could be overestimated if the
estimation does not account for inequality. Like, Cravino et al. (2020), my focus
is on the di↵erence in the responses ISCPIs to macroeconomic shocks, rather than
overall inequality.
While Cravino et al. (2020) and this essay focus on a consumer’s entire consumption
basket, Kim (2019) looks at monetary policy’s e↵ect among the same product category
with variations in quality. Kim (2019) finds that high-quality products are more price
rigid than low-quality products in the same product category, such as milk-based
drinks. Kim (2019) finds that consumers with higher incomes tend to buy higher-
quality products than low-income consumers. Therefore, Kim (2019) concludes that
an expansionary monetary shock will benefit high-income consumers more than
low-income consumers. Conversely, Kim (2019) finds that contractionary monetary
shocks will harm high-income consumers more than low-income consumers.
Generally, Kim (2019) and Cravino et al. (2020) both find that monetary shocks
has significant distributional impacts in the US, particular between the middle-
income Americans and high-income Americans; In contrast, I find that Canadian
Monetary shocks has no significant distributional impact between middle-income
Canadians and high-income Canadians. A potential explanation why monetary
shocks has greater impact in the US, in contrast to Canada, may be due to the wider
income-gap between the middle-income Americans and high-income Americans. Saez
& Zucman (n.d.) find that in 2019, a median-income person in American earns about
4$48,000 USD per year, while an American in the 99th percentile of income earns about
$580,000 USD per year. In Canada, Statistics Canada (n.d.D) finds that in 2018, the
median-income Canadian earns about $36,000 CAD a year while a Canadian in the
99th percentile of income earns about $250,000 CAD a year. Although the exchange
rate between the Canadian and US dollar is not a perfect one-to-one exchange, there
is still a substantial di↵erence between the top 1% of earners in the US compared to
the top 1% of earners in Canada; This di↵erence in income could result in di↵erences
in consumption baskets, which leads to di↵erences in reaction to monetary shocks.
My essay contributes to the literature on the distributional impacts of monetary
policy and commodity-price shocks in Canada; More specifically, my paper analyzes
the impact of these macroeconomic shocks on the price of income-specific consumption
baskets, which, to my knowledge, has not been analyzed in Canada.
This essay proceeds as follows: Section 2 introduces the data. Section 3.1
explains the Structural Vector Autoregression (SVAR) for identifying exogenous
shocks. Section 3.2 explains the Local Projection Method (LPM) empirical strategy
for estimating the IRFs of the ISIRs. Section 4 presents and discusses key results
from the SVAR procedure. Section 5 discusses the results of the LPM. Section 6
concludes this essay with a discussion and o↵ers potential extensions to this essay.
Appendix I presents an additional set of figures and tables not included in the main
body of this essay. Appendix II presents the rest of the IRFs from the SVAR not
discussed in Section 4.
52 Data
2.1 Construction of the Income-Specific CPIs
An Income-Specific CPI, for those in an income-percentile range p, at time t, is
defined as
n
X
CP Ipt = wip Xit (1)
i
Where wip denotes the expenditure weights for item category i for the income-
percentile range p, Xit is the price index for category i at time t, and n is the number
of product categories included. I construct the expenditure category weights, wip 3 ,
as
ip
wip = Pn (2)
i ip
Where ip is the total expenditure in category i for those in the pth income-percentile
range. Note that the denominator is the total expenditure of the categories included,
not total expenditure in the survey (since I have omitted some categories), and not by
total income since the average propensity to consume di↵ers among di↵erent income
groups.
Therefore, constructing the ISCPI requires finding the income cuto↵s for each
income-percentile range, constructing the expenditure weights, and combining the
3
The expenditure weights are time-invariant because I only have data for 2017. Ideally, if
consumer spending data was available for every time-period, expenditure category weights would
be indexed by time.
6expenditure weights with a price index. I use the 2017 version of the Survey of
Household Spending (SHS) from Statistics Canada (Statistics Canada, 2019a) and
Table-18100004 from Statistics Canada (n.d.A), henceforth ”CPI dataset,” to construct
the ISCPIs.
The CPI dataset has price indices for di↵erent item categories, which is a table
of 330 monthly series of consumer price indices for di↵erent categories of goods
and services, with monthly observations from 1941-01 to 2020-07. However, not all
categories have observations for every date. I only use a sample length from 1989-1
to 2020-3. The CPI dataset is not seasonally adjusted and contains price indices at
di↵erent levels of aggregation, from “All-Items” to “Non-durable goods” and to finer
levels like “Butter.”
The Survey of Household Spending (SHS) from Statistics Canada (Statistics
Canada, 2019a) contains household spending and household income data. The SHS
encompasses all provinces and territories of Canada and is a representative sample
of Canada. The survey has two components, the “Interview” and the “Diary.” A
sample of 12,492 responded to the Interview component, then a sub-sample of those
who did the Interview responded to the Diary. The Diary has a sample size of 4012
respondents, which has finer expenditure categories compared to the Interview. The
Interview collection method involves a questionnaire asking the respondents to recall
their expenditure within a specific period (i.e. last month, last three months, etc.).
In contrast, the Diary requires a respondent to journal their expenditure within a
7two-week time frame. The SHS data collection occurs throughout the year, so the
SHS respondents do not report their spending all in the same time-frame. The
survey reports annual income and annual expenditure; therefore, reported values are
annualized when survey respondents answer a question with less than a 12 month
recall period.
I only use the Diary component for this essay as it is a more detailed spending
dataset. Statistics Canada has a user guide for the SHS, further explaining the
dataset in more detail (2019b). The SHS also comes with a document titled “Expenditure
category hierarchy,” which explains the spending categories and the hierarchy of
categories and subcategories within the Interview and Diary (Statistics Canada,
2019c).
The SHS orders the spending categories in six levels. Table 1 in Appendix I
reports a sample from each category to illustrate the disaggregation in each level.
I mostly work with level 3 category expenditures, occasionally using level 2 or 4
because certain categories in the Diary could not be matched with the CPI dataset.
Table 2 in Appendix I shows the categories I use and their labels in both the Diary
and CPI dataset. I match the labels from the Diary to the CPI dataset in creating the
ISCPIs. Given that the Diary and CPI dataset both came from the same statistical
agency, I was able to find similar labels between the CPI dataset and the Diary,
which I am assuming that similar labels across the dataset are referring to the same
goods. I omit four categories because they did not match well between the two
8datasets: “Pet expenses,” “Garden supplies and services,” “Games of Chance,” and
“Miscellaneous expenditures.”
I use the total household income reported in the SHS to calculate the income
cuto↵ values in constructing the ISCPIs; These values are reported in Table 3 in
Appendix I.
I then combine the expenditure weights with the CPI dataset using equation (1) to
construct the ISCPIs. The frequency of ISCPIs is originally at a monthly frequency,
which I convert to a quarterly series by averaging over the quarter. For each ISCPIs,
I apply the natural log, take the fourth seasonal di↵erence and multiply by 100,
which ultimately creates an annualized ISIR from 1990Q1 to 2020Q1. I denote the
annualized ISIR as ⇡tp , where p denotes the income-percentile range. Specifically,
let ⇡tB denote the income-specific inflation rate for those making less than the 10th
percentile of household income. Next, let ⇡tM denote the income-specific inflation
rate for those making between the 45th and 55th percentiles of household income.
Finally, let ⇡tT denote the income-specific inflation rate for those making more than
the 90th percentile of household income. Figure 1 depicts the time-series graph of
the ISIRs and shows that the ISIRs are indeed heterogeneous.
9Figure 1: Time-series Plot of the Income-Specific Inflation Rates.
2.2 Data for the Structural Vector Autoregression
The CPI dataset also contains a monthly series for the all-item CPI. I use the
all-item CPI from 1989-01 to 2020-03, converting into a quarterly series by averaging
over the quarter. I take the natural log and the fourth seasonal di↵erence of the
all-item CPI and multiply it by 100, which creates the annualized inflation rate in
Canada, from 1990Q1 to 2020Q1. I denote the Canadian inflation rate as ⇡tall .
Similarly, I use a monthly series of the all-commodities price index from Statistics
Canada (n.d.B) from 1989-01 to 2020-03. I convert the all-commodities price index
10to a quarterly series by averaging over the quarter. Again, I apply the natural log
and the fourth seasonal di↵erence of the all-commodities price index and multiply
the series by 100, which I denote as dlCt .
Next, I use a quarterly series that measures the Canadian output gap using an
extended multivariate filter, from 1990Q1 to 2020Q1 from the Bank of Canada (n.d.),
which I denote as CANt . I also create a measure of the US output gap by using a
quarterly series of the US Real GDP (seasonally adjusted annual rate) from the
U.S. Bureau of Economic Analysis (n.d), which I take the natural log of the series,
applying the Hodrick-Prescott Filter (Hodrick and Prescott, 1997) with a smoothing
parameter of 1600, and then multiplying the series by a 100. I denote the series for
the US output gap as U St .
Finally, I also use a monthly series of the 7-day average annualized overnight
rate in Canada from Statistics Canada (n.d.C) from 1989m9 to 2020m3. I convert
the overnight rate series into a quarterly series by averaging over the quarter, which
I denote as it . Figure 1 in Appendix I displays it in levels, which appears to be
trending. I test for the presence of a unit-root using the Augmented Dickey-Fuller
test (Dickey and Fuller, 1979), in which I fail to reject the presence of a unit root. I
take the first di↵erence of it to induce stationarity. I denote the annualized overnight
interest rate, in first di↵erences, as it . The series it spans from 1990Q1 to 2020Q1.
In summary, I have a quarterly series from 1990Q1 to 2020Q1 of the variables
11listed in Table 1. Table 1 summarizes the notation of each variable and provides a
description. Figure 2 in Appendix I shows the time-series plots of dlCt , U St , it ,
⇡tall , and CANt .
Table 1: Summary of Variables
Variable Notation Description of Variable
dlCt All-Commodities Price Index in logs and fourth-seasonal-di↵erences
U St US Output Gap
CANt Canadian Output Gap
it Overnight Rate in Canada in first-di↵erences
⇡tall Canadian Annual Inflation Rate
⇡tB Income-specific Annual Inflation Rate for households making less
than the 10th percentile of household income
⇡tM Income-specific Annual Inflation Rate for households making
between the 45th and 55th percentile of household income
⇡tT Income-specific Annual Inflation Rate for households making more
than the 90th percentile of household income
123 Empirical Strategy
3.1 Identifying Monetary Shocks
To identify exogenous monetary shocks I use the following Structural Vector
Autoregression (SVAR)
2 32 3 2 3 2 32 3
a 0 0 0 0 dlCt b c c12 0 0 0 dlCt 1
6 11 76 7 6 1 7 6 11 76 7
6 76 7 6 7 6 76 7
6a21 a22 0 0 07 6 7 6 7 6 07 6 U St 1 7
6 7 6 U St 7 6b2 7 6c21 c22 0 0 76 7
6 76 7 6 7 6 76 7
6a 07 6 7 6 7 6 c35 7 6CANt 1 7
7 6
6 31 a32 a33 0 7 6CANt 7 = 6b3 7+6c31 c32 c33 c34 7+
6 76 7 6 7 6 76 7
6 7 6 all 7 6 7 6 7 6 all 7
6a41 a42 a43 a44 0 7 6 ⇡t 7 6b4 7 6c41 c42 c43 c44 c45 7 6 ⇡t 1 7
4 54 5 4 5 4 54 5
a51 a52 a53 a54 a55 it b5 c51 c52 c53 c54 c55 it 1
2 32 3 2 3
d d 0 0 0 dlCt 2 ✏
6 11 12 76 7 6 1t 7
6 76 7 6 7
6d21 d22 0 0 07 6 7 6 7
6 7 6 U St 2 7 6✏2t 7
6 76 7 6 7
6d 76 7 6 7
6 31 d32 d33 d34 d35 7 6CANt 2 7 + 6✏3t 7 (3)
6 76 7 6 7
6 7 6 all 7 6 7
6d41 d42 d43 d44 d45 7 6 ⇡t 2 7 6✏4t 7
4 54 5 4 5
d51 d52 d53 d54 d55 it 2 ✏5t
In matrix notation, the SVAR is
AXt = B + CXt 1 + DXt 2 + ✏t (4)
where Xt is a vector containing the endogenous variables. The matrix A is the
parameters for the contemporaneous relationships among the endogenous variables.
The matrices C and D are the matrices of parameters for the vector autoregression
for the first and second lags of the endogenous variables. The Hannan–Quinn
information criterion (Hannan & Quinn, 1979) and Akaike information criterion
13(Akaike, 1981) indicate the SVAR should have two lags. Vector B consists of
constants, and vector ✏t consists of the structural shocks.
Since the SVAR aims to identify exogenous monetary shocks, I impose an additional
restriction on the SVAR that the structural shocks are uncorrelated4 .
2 3
2
1 0 0 0 0
6 7
6 7
60 2
0 0 07
6 2 7
6 7
E(✏t ✏t ) = 6
0
60 0 2
3 0 07
7 (5)
6 7
6 2 7
60 0 0 4 07
4 5
2
0 0 0 0 5
The restrictions on matrices A, C, and D impose that the previous period’s
and current values of the Canadian domestic variables do not impact commodity-
prices or the US output gap. However, the SVAR allows for the current period’s
commodity-price and the US output gap, as well as its lags, to influences the current
period’s Canadian domestic variables. I justify these restrictions on matrices A, C,
and D using the assumption that Canada is a small-open economy. As a small open
economy, world prices and the US economy are likely to be important external factors
for Canada, a small open economy. In contrast, we can assume that the Canadian
variables do not directly a↵ect the world commodity prices and the US economy.
4
Uncorrelated structural shocks is generally a standard assumption in the SVAR literature, since
it is necessary to identify exogenous shocks. Since the SVAR is just-identified this assumption can
not be tested.
14The lower-triangular restriction on matrix A imposes that variables listed first in
vector Xt (from top to bottom) will contemporaneously impact variables listed after
it; however, variables will not contemporaneously a↵ect variables listed before it.
Therefore, I impose the restriction that the overnight rate will not impact inflation
or the Canadian output contemporaneously. I am assuming that it takes time for the
economy to adjust to monetary policy, hence why the Canadian inflation rate and
Canadian output may not react to changes in the overnight rate contemporaneously.
3.2 Estimating Impulse Responses of Income-Specific Inflation
I estimate the IRFs of the ISIRs to the commodity-price shocks and overnight
rate shocks using the Local Projections Method (LPM) (Jordà, 2005). The LPM
is also the method Cravino et al. (2020) use in estimating IRFs. Since the SVAR
estimates the structural shocks, the LPM allows for a convenient way to extract
the structural shocks and separately estimate the IRFs without estimating another
SVAR which includes the ISIRs. The LPM also has other desirable properties such
as being more robust to misspecification and can be estimated by OLS. (Jordà, 2005).
Let h denote the number of quarters after a shock that occurs at time t. I
estimate the following regression using OLS, h number of times, for each income-
specific inflation rate.
j k
p
X X p
⇡t+h = ↵h + h Shockt + hi Shockt i + hi ⇡t i + eth (6)
i=1 i=1
15where ⇡tp is the ISIR for the pth income-percentile range and Shockt is the structural
shock of interest, which is estimated using equation (4). The coefficient of interest is
h, which gives the impulse response of ⇡tp at the hth period after a monetary shock
occurring at time t.
The control variables are j number of lags of the shock of interest, denoted by
Shockt j , and k number of lags of the ISIR, denoted by ⇡t k . The number of lags
for the shock of interest and ISIR are chosen to ensure that the residuals are a
approximately a white-noise series.
Essentially, estimating equation (6) using LPM involves first estimating
j k
X X
⇡tp = ↵0 + 0 Shockt + 0i Shockt i + p
0i ⇡t i + et0 (7)
i=1 i=1
and storing the estimated coefficient b0 ; then applying the lead operator to the
dependent variable and estimating
j k
p
X X p
⇡t+1 = ↵1 + 1 Shockt + 1i Shockt i + 1i ⇡t i + et1 (8)
i=1 i=1
which iterates h numbers of times, yielding b0 = [ b0 , ..., bh ]. Plotting b over time
produces the IRFs graphs of the ISIR to the shock of interest.
I specify the control variables of LPM for the overnight rate shock as j = 6 and
k = 6. I specify the the control variables of LPM for the commodity-price shock
16as j = 2 and k = 6. Again, j and k are selected to ensure that the residuals
of the LPM are approximately a white-noise series. In choosing the appropriate
control variables, I estimate a regression of aggregate inflation against overnight rate
shocks and commodity-price shocks, and inspecting the residuals ex post. Table
4 in Appendix I shows the correlogram of the residuals from regressing aggregate
inflation against overnight rate shocks, six lags of overnight rate shocks, and six
lags of aggregate inflation. Table 5 in Appendix I shows the correlogram of the
residuals from regressing aggregate inflation against commodity price shocks, two
lags of commodity-price shocks, and six lags of aggregate inflation.
Finally, let b standard error of the estimated coefficient5 . I construct the 90%
confidence interval (CI) for the LPM IRFs using
CIh = bh ± 1.65 ⇤ ch (7)
5
Since the structural shocks are generated regressors, the standard errors may be incorrectly
estimated (Pagan, 1984). A potential extension to this paper could re-estimate the standard errors
using simulation methods.
174 Results of the Structural Vector Autoregression
In this section, I discuss the key results of the SVAR. I particularly present the
IRFs of the Canadian domestic variables to the overnight rate shocks and commodity-
price shocks. I then compare the results of the SVAR to other papers that estimate
shocks through di↵erent SVAR methods. Appendix II contains the rest of the IRFs
not discussed in this section.
In macroeconomic theory, a central bank can increase interest rates to lower
economic output and ultimately lower inflation. Figure 2 depicts the reaction of ⇡tall
and CANt to a one standard deviation shock to it . The results are as follows: A
one standard deviation shock to it causes a peak fall of -0.079 percentage-point
to the CANt two quarters after the shock, and a peak fall of -0.062 percentage-
point to ⇡tall three quarters after the shock. Papers that use a structural model
to identify monetary shocks also find a negative response of output and inflation to
overnight rates shocks, such as Bhuiyan (2012), Cushman (1997), and Raghavan et al.
(2016). For example, Cushman (1997) estimates an SVAR for the Canadian economy
using the US macroeconomic variables (such as output, industrial production and
the federal funds rate) as a source of exogenous shocks to the Canadian economy.
Cushman (1997) finds that a contradictory monetary shock causes a slight decrease
in Canadian output and Inflation. Raghavan et al. (2016) use a structural Vector
Autoregressive Moving Average (SVARMA) with oil-price shocks and the US federal
funds rate as external shocks to the Canadian economy. Raghavan et al. (2016) find
18that a positive shock to the Canadian overnight rate causes output and inflation to
decline. Similarly, using a Bayesian SVAR, Bhuiyan (2012) also finds that Canadian
monetary shocks cause a decrease in Canadian output and inflation.
Commodities are a major component of Canada’s economic output; hence we can
expect a positive shock to commodity-prices should be expansionary to the Canadian
(and the US) economy. Figure 3A depicts the reaction of the other variables in the
SVAR to a one standard deviation shock to dlCt . The result are as follows: A one-
standard-deviation shock to the dlCt causes a 0.1992 percentage-point increase in
U St after a quarter, a 0.3492 increase to CANt after two quarters, a 0.4120 increase
in ⇡tall , and a 0.0632 increase to it after one quarter. Figure 3B depicts the reaction
of dlCt to shocks to itself, which shows that dlCt will increase in the first year, but
its reaction is quite muted afterwards. Martel (p.9, 2008) also finds that “an energy
price shock implies a sharp increase in the price of energy, but this e↵ect is somewhat
muted thereafter.” Martel (2008) finds that oil-price shocks cause a positive increase
in Canadian output and inflation rate. Raghavan et al. (2016) also find that oil-price
shocks cause a positive increase in US Output, Canadian output, Canadian inflation
and Canadian interest rates.
19Figure 2: The Impact of it Shocks to the Canadian Variables
Note: The impulse variable is a one standard deviation shock to it . The gray area
represents a 65% confidence interval.
20Figure 3A: The Impact of dlCt Shocks
Note: The impulse variable is a one standard deviation shock to the dlCt . The gray
area represents a 65% confidence interval.
21Figure 3B: The IRF of dlCt to dlCt Shocks.
Note: The impulse is a one standard deviation shock to dlCt . The gray area
represents a 65% confidence interval.
225 Results of the Local Projections Method
My main objective in this paper is to examine the distributional impacts of
commodity-price shocks and overnight rate shocks. Figure 4 shows the IRFs of each
ISIR, with 90% confidence intervals, to overnight rate shocks. I use a 90% confidence
interval, rather than the 65% confidence interval, for the LPM IRFs since the LPM
estimates the IRFs using OLS, which I expect to be a more efficient estimator in
comparison to an SVAR. Figure 5 shows the IRFs of the three ISIR to overnight rate
shocks in the same graph.
Figure 4 indicates that overnight rate shocks have the greatest impact on the
ISIRs at the 15th quarter after the shock, and these impacts are statistically significantly
di↵erent from zero at a 10% significance level. Focusing on the 15th quarter after a
shock to the overnight interest rate, a one percentage-point increase in the overnight
rate decreases: ⇡tB by 0.407 percentage-points, ⇡tM by 0.467 percentage-points, and
⇡tT by 0.429 percentage-points. However, re-estimating the LPM regressions as a
system and testing for coefficient equality shows that the responses of the ISIR to
overnight rate shocks are not statistically significantly di↵erent from each other.
Note that the IRFs from the LPM are di↵erent to the SVAR IRFs in terms of the
time-horizon in which monetary shocks a↵ect inflation; This may be attributed to
the fact that the SVAR contains the additional e↵ects from the fall from output,
while the LPM only contains the lags of the overnight rate and its lags. However,
the result of interest still remains that the reaction of the di↵erent ISIRs are not
23statistically significantly di↵erent from each other.
My results are in contrast to Cravino et al. (2020), who finds an economic and
statistically significant di↵erence between the responses of the top-income household
to the middle-income households. However, Cravino et al. (2020) define middle-
income households as households between the 40th and 60th percentile of household
income and compares it to the top 1% of households in household income; while I
define middle-income households those who are between the 45th and 55th percentile
of household income, and I compare the middle-income households to the top 10%
of households. To be consistent with Cravino et al. (2020), I construct the ISIR for
those between the 40th and 60th percentile of household income, which I denote as
⇡tx , as well as the ISIR of the top 1% of households, which I denote as ⇡ty . Figure
6A shows the IRF of ⇡tx , while Figure 6B shows the ISIR for ⇡ty , and Figure 7 shows
the two IRFs in a single graph. Focusing on the 15th quarter after the overnight
rate shock, I find no statistically significant di↵erence between the IRF of ⇡tx and
⇡ty . These results show that monetary policy may not have distributional impacts,
at least for the percentiles and definitions that I consider.
Figure 8 shows the IRFs of each ISIR, with 90% confidence intervals, to commodity-
price shocks. Figure 9 shows the IRFs of the three ISIR to commodity-price shocks,
in the same graph. Figure 8 indicates that commodity-price shocks have the peak
impact on ISIRs at the 1st quarter after the shock, and these impacts are statistically
significantly di↵erent from zero at a 10% significance level. Therefore, focusing on the
241st quarter after a shock to dlCt , the results show that a one-percentage-point change
in dlCt increases: ⇡tB by 0.032 percentage-points, ⇡tM by 0.041 percentage-points, and
⇡tT by 0.036 percentage-points. Re-estimating the LPM IRFs as a system and testing
for coefficient equality shows that the response of ⇡tM is statistically significantly
di↵erent, at a 1% significance level, to the responses of ⇡tT and ⇡tB , to commodity-
price shocks. I find no statistically significant di↵erence between the response of ⇡tT
and ⇡tB to commodity shocks. My results show that positive commodity shocks may
harm middle-income households more than low-income or high-income households
because they have greater unanticipated price increases in their consumption basket;
A further discussion of these results are in Section 6.
25Figure 4A: IRF of ⇡tB to Overnight Rate Shocks.
Note: The shock is a one percentage point increase in the overnight rate. The green
lines denote a 90% confidence interval.
26Figure 4B: IRF of ⇡tM to Overnight Rate Shocks.
Note: The shock is a one percentage point increase in the overnight rate. The green
lines denotes a 90% confidence interval.
27Figure 4C: IRF of ⇡tT to Overnight Rate Shocks.
Note: The shock is a one percentage point increase in the overnight rate. The green
lines denotes a 90% confidence interval.
28Figure 5: IRF of ⇡tB , ⇡tM and ⇡tT to Overnight Rate Shocks.
29Figure 6A: IRF of ⇡tx to Overnight Rate Shocks.
Note: The shock is a one percentage point increase in the overnight rate. The green
lines denotes a 90% confidence interval.
30Figure 6B: IRF of ⇡ty to Overnight Rate Shocks.
Note: The shock is a one percentage point increase in the overnight rate. The green
lines denotes a 90% confidence interval.
31Figure 7: IRF of ⇡tx and ⇡ty to Overnight Rate Shocks.
32Figure 8A: IRF of ⇡tB to Commodity-Price Shocks.
Note: The shock is a one percentage-point increase in dlCt . The green lines denote
a 90% confidence interval.
33Figure 8B: IRF of ⇡tM to Commodity-Price Shocks.
Note: The shock is a one percentage-point increase in dlCt . The green lines denote
a 90% confidence interval.
34Figure 8C: IRF of ⇡tT to Commodity-Price Shocks.
Note: The shock is a one percentage-point increase in dlCt . The green lines denote
a 90% confidence interval.
35Figure 9: IRF of ⇡tB , ⇡tM and ⇡tT to Commodity-Price shocks.
366 Conclusion
This essay aims to examine the distributional impacts of commodity-price shocks
and monetary shocks along the income-distribution. I construct income-specific
inflation rates (ISIR) using micro-data and price index data from Statistics Canada.
I estimate the impulse response of these ISIRs, to macroeconomic shocks, using the
Local Projections Method (LPM) (Jordà, 2005). I find no statistically significant
di↵erence between the reaction of the ISIRs among di↵erent income groups to monetary
shocks. In contrast, the reaction of the ISIR of middle-income households is greater
than the reactions of ISIRs of high-income and low-income households to commodity-
price shocks.
To understand why middle-income households are more reactive to commodity-
price shocks, a potential extension could analyze the reaction of the price index of
di↵erent categories of goods to commodity shocks and contrast these reactions with
the weights of each category in di↵erent income-specific consumption baskets. Table
6 in Appendix I shows each category’s weights in constructing the ISIR for each
income-group. Table 6 in Appendix I shows that “vehicle operations” has a higher
weight in the consumption basket of middle-income households in comparison to
low-income and high-income households. One particular sub-category contained in
“vehicle operations” is gasoline consumption. Since gasoline prices may be volatile
and reactive to commodity-price shocks, this may be one of the reasons why middle-
income household are more reactive to commodity-price shocks, in comparison to
37low-income and high-income households.
Since commodity-price shocks and overnight rates shocks are the residuals of
an SVAR, these shocks are therefore generated regressors. As Pagan (1984) points
out, the estimated standard errors for generated regressors are incorrectly estimated.
Therefore, a potential extension to this essay is to correct for the incorrectly estimated
standard errors of the generated regressor through simulation methods. Another
potential extension to this paper is to estimate exogenous monetary shocks for
Canada using a narrative-approach (Romer and Romer, 2004). Monetary shocks
estimated through a narrative-approach is what Cravino et al. (2020) use in estimating
the IRFs of income-specific inflation rates to monetary shock. Identifying monetary
shock through a narrative-approach would require cataloguing press statements from
the Bank of Canada to track the exact date when the Bank of Canada changes the
overnight rate and by how much the Bank of Canada changes the interest rates. A
narrative-approach also circumvents the issues associated with generated regressors
since a separate SVAR is no longer be required to identify exogenous shocks. To my
knowledge, Champagne & Sekkel (2018) is the only paper that apply the narrative-
approach in Canada.
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43Appendix I: Tables and Figures
Table 1: A sample of items from each level in the Diary dataset
Level Diary Code - Expenditure Category Label
1 TC001 – Total current consumption
2 FD001 – Food expenditures
3 FD003 – Food purchased from stores
4 FD100 – Bakery products
5 FD101 – Bread and unsweetened rolls and buns
6 FD102 – Bread
44Table 2: Categories and labels between the Diary and CPI datset
Level Label in the Diary Series Label in the CPI Dataset
3 FD003 - Food purchased from stores Food purchased from stores
3 FD990 - Food purchased from restaurants Food purchased from restaurants
3 SH010 - Owned principal residence & SH040 - Other accommodation Owned accommodation
3 SH003 - Rented principal residence Rented accommodation
3 SH030 - Water, fuel and electricity for principal accommodation Water, fuel and electricity
3 CS001 - Communications Communications
3 CC001 - Child care Child care services
3 HO002 - Domestic and other custodial services (excluding childcare) Housekeeping services
3 HO014 - Paper, plastic and foil supplies Paper, plastic and aluminum foil supplies
2 HF001 - Household furnishings and equipment Household furnishings and equipment
3 HO010 - Household cleaning supplies and equipment Household cleaning products
3 CF001 - Women’s and girls’ wear (4 years and over) Women’s clothing
3 CM001 - Men’s and boys’ wear (4 years and over) Men’s clothing
3 CI001 - Children’s wear (under 4 years) Children’s clothing
45
3 CL007 - Clothing fabric, yarn, thread, and other notions & CL010 - Clothing services Clothing material, notions and services
4 TR003 - Private use vehicles Purchase and leasing of passenger vehicles
4 TR020 - Rented vehicles Rental of passenger vehicles
4 TR050 - Public transportation Public transportation
4 TR030 - Vehicle operations Operation of passenger vehicles
3 PC002 - Personal care products Personal care supplies and equipment
3 PC020 - Personal care services Personal care services
2 HC001 - Health care Health care
3 RE002 - Recreation equipment and related services Recreational equipment and services (excluding recreational vehicles)
3 RE040 - Home entertainment equipment and services Home entertainment equipment, parts and services
3 RE060 - Recreation services Recreational services
3 RV001 - Recreational vehicles and associated services Purchase and operation of recreational vehicles
2 ED002 - Education Education
3 TA005 - Alcoholic beverages Alcoholic beverages
3 TA002 - Tobacco products and smokers’ supplies Tobacco products and smokers’ supplies
Note: The column titled ”Level” refers to the expenditure level of the category in the Diary.Table 3: Income cuto↵s
Percentile Total Household Income (Canadian Dollars)
10 24275
45 67750
55 81500
90 170450
46Table 4: Correlogram of the residuals from regressing inflation against it shocks.
Number
Partial
of Autocorrelation Q-Statistic P-Value
Autocorrelation
Lags
1 -0.008 -0.008 0.0069 0.934
2 0.037 0.037 0.1636 0.921
3 0.032 0.033 0.2847 0.963
4 -0.097 -0.098 1.4091 0.843
5 0.062 0.059 1.8651 0.867
6 -0.044 -0.038 2.0998 0.910
7 0.102 0.106 3.3803 0.848
8 -0.279 -0.298 12.997 0.112
9 0.084 0.118 13.886 0.126
10 0.055 0.044 14.272 0.161
11 0.059 0.119 14.709 0.196
12 0.078 -0.031 15.487 0.216
13 -0.007 0.063 15.493 0.278
14 0.144 0.108 18.207 0.198
15 -0.015 0.061 18.237 0.250
16 -0.062 -0.211 18.754 0.282
17 0.078 0.162 19.577 0.296
18 0.010 0.033 19.590 0.356
19 -0.024 0.015 19.669 0.415
20 -0.015 -0.104 19.700 0.477
Note: The control variables for the regression are six lags of it and six lags of
inflation.
47Table 5: Correlogram of the residuals from regressing inflation against dlCt shocks.
Number
Partial
of Autocorrelation Q-Statistic P-Value
Autocorrelation
Lags
1 -0.034 -0.034 0.1400 0.708
2 -0.067 -0.069 0.6814 0.711
3 0.013 0.008 0.7012 0.873
4 -0.091 -0.095 1.6955 0.792
5 0.095 0.091 2.7962 0.731
6 -0.044 -0.053 3.0342 0.805
7 0.057 0.072 3.4407 0.841
8 -0.241 -0.265 10.760 0.216
9 0.051 0.084 11.092 0.269
10 -0.024 -0.104 11.169 0.345
11 -0.134 -0.087 13.485 0.263
12 -0.024 -0.124 13.558 0.330
13 -0.025 0.035 13.642 0.400
14 0.191 0.137 18.513 0.184
15 0.057 0.101 18.956 0.216
16 -0.047 -0.100 19.258 0.255
17 0.072 0.139 19.976 0.275
18 0.056 0.057 20.416 0.310
19 0.039 0.011 20.634 0.357
20 -0.011 -0.064 20.653 0.418
Note: The control variables for the regression are two lags of dlCt and six lags of
inflation.
48Table 6: Weights of each category in each income-specific CPI
Label in the Diary ⇡tB ⇡tM ⇡tT
FD003 - Food purchased from stores 12.41 11.36 8.93
FD990 - Food purchased from restaurants 3.46 4.24 4.72
SH010 - Owned principal residence & SH040 - Other accommodation 11.11 19.72 22.58
SH003 - Rented principal residence 18.19 5.77 1.45
SH030 - Water, fuel and electricity for principal accommodation 5.49 5.10 4.18
CS001 - Communications 5.06 4.52 3.40
CC001 - Child care 0.26 0.65 1.78
HO002 - Domestic and other custodial services (excluding child care) 0.16 0.17 0.52
HO014 - Paper, plastic and foil supplies 0.76 0.66 0.48
HF001 - Household furnishings and equipment 3.40 3.93 4.26
HO010 - Household cleaning supplies and equipment 0.46 0.40 0.30
CF001 - Women’s and girls’ wear (4 years and over) 2.03 2.65 3.10
CM001 - Men’s and boys’ wear (4 years and over) 1.42 1.58 2.08
CI001 - Children’s wear (under 4 years) 0.11 0.18 0.10
CL007 - Clothing fabric, yarn, thread, and other notions & CL010 - Clothing services 0.23 0.18 0.18
TR003 - Private use vehicles 8.24 8.67 9.76
TR020 - Rented vehicles 0.13 0.07 0.27
TR050 - Public transportation 1.78 1.78 3.03
TR030 - Vehicle operations 8.93 10.50 8.71
PC002 - Personal care products 0.85 1.24 1.30
PC020 - Personal care services 0.79 0.97 1.09
HC001 - Health care 4.45 5.27 3.39
RE002 - Recreation equipment and related services 1.01 1.63 1.95
RE040 - Home entertainment equipment and services 0.40 0.32 0.41
RE060 - Recreation services 3.01 3.12 4.91
RV001 - Recreational vehicles and associated services 0.52 0.91 2.20
ED002 - Education 2.73 1.57 2.31
TA005 - Alcoholic beverages 1.42 1.01 0.47
TA002 - Tobacco products and smokers’ supplies 1.17 1.83 2.16
Note: The weights are multiplied by 100.
49Figure 1: Time-series plot of the Overnight Rate
50Figure 2A: Time-series plot of the All-Commodities Price Index.
51Figure 2B: Time-series plot of the US Output Gap.
52Figure 2C: Time-series plot of the Canadian Output Gap.
53Figure 2D: Time-series plot of the Canadian Inflation Rate.
54Figure 2E: Time-series plot of Overnight Interest Rate in First-Di↵erences.
55Appendix II: Other results of the SVAR IRFs
In this section the rest of the IRFs estimated in Section 4.1 is presented. All
IRFs in this section includes a 65% confidence interval, denoted by the shaded grey
area in each of the figures.
Figure 1: The IRF of the Overnight Rate to shocks in the Overnight Rate
Note: The impulse is a one-standard deviation shock to the overnight rate. The gray
area represents a 65% confidence interval.
56Figure 2: The IRFs of the Canadian variables to shocks in Inflation
Note: The impulse is a one standard deviation shock to the Inflation. The gray area
represents a 65% confidence interval.
57Figure 3: The IRFs of the Canadian variables to shocks in the Canadian Output
Gap
Note: The impulse is a one standard deviation shock to the Canadian Output Gap.
The gray area represents a 65% confidence interval.
58Figure 4: The IRF of the US Output Gap to shocks in the US Output Gap
Note: The impulse is a one standard deviation shock to the US Output Gap. The
gray area represents a 65% confidence interval.
59Figure 5A: The Impact of US Output Gap Shocks
Note: The impulse is a one standard deviation shock to the US Output Gap. The
gray area represents a 65% confidence interval.
60Figure 5B: The Impact of US Output Gap Shocks
Note: The impulse is a one standard deviation shock to the US Output Gap. The
gray area represents a 65% confidence interval.
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