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Food Price Shocks, Subsidies and
Monetary Policy: A DSGE Approach
William Ginn† and Marc Pourroy‡
Novembre 2016
- Preliminary Version -
Abstract:
We develop a small open economy DSGE model to
analyze the effects of food price shocks for a
developing economy. The model features realistic
attributes of a low income country such as a large
share of household food consumption; the presence
of “hand-to-mouth” households which have financial
limitations in smoothing consumption; and fiscal
policy aimed at shielding households in response
to food price shocks. The novelty of the paper is
that we analyze how different policy monetary and
fiscal policy responses may affect welfare. Viewed
in this light, we argue that coordinated policies
can, over the short-term, use fiscal coordination
to target a consumer cohort with food subsidies in
the presence of food price shocks improve
aggregate welfare.
Key Words: Monetary Policy, Fiscal Policy, Commodities, DSGE
Model
JEL Codes: E52, E62, O23, E31, E32
† William Ginn, PhD Candidate, Friedrich-Alexander-
Universität Erlangen-Nürnberg. Wil-
‡ Marc Pourroy, Université de Poitiers, [email protected]
- 2 -
Contents
1 Introduction ............................................... 3
2 Stylized Facts ............................................. 5
2.1 Large share of food expenditures: ....................... 5
2.2 Food Subsidies .......................................... 6
2.3 Financial Access ........................................ 9
3 Literature Review ......................................... 10
3.1 Reflection of Food Subsidies in Developing Economies ... 10
3.2 Monetary Policy ........................................ 12
4 The Model ................................................. 14
4.1 Households ............................................. 16
4.1.1 Ricardian Household................................... 19
4.1.2 Non-Ricardian Household............................... 23
4.2 Firms .................................................. 24
4.2.1 Food Firms:........................................... 25
4.2.2 Manufacturing Firms:.................................. 26
4.3 Fiscal Policy .......................................... 29
4.4 Foreign Economy ........................................ 31
4.5 Monetary Policy ........................................ 32
5 Model Experiments ......................................... 33
5.1 Aggregation ............................................ 35
5.2 Calibration: ........................................... 36
5.3 Baseline Model ......................................... 39
5.4 Fiscal Policy Intervention ............................. 42
5.5 Welfare Analysis ....................................... 45
5.5.1 Aggregate welfare evaluation.......................... 47
5.5.2 Distributional Welfare Evaluation..................... 49
6 Conclusion ................................................ 50
7 References ................................................ 52
8 Appendix .................................................. 55
8.1 Food Prices by Commodity ............................... 55
8.2 Steady State ........................................... 55
8.3 Impulse Response Functions ............................. 57
8.4 Welfare - Aggregate Shocks ............................. 62
- 3 -
[F]ood prices [are] the biggest threat today to the world's
poor… Already 44 million people have fallen into poverty as
a result of rising food prices over the last year… Further
10% rise in the food price index could push 10 million more
people into poverty.
- Robert Zoellick, World Bank President
April 2011
Few policies place good economics so directly at odds with
good politics as subsidies for food and energy.
- Jeffrey Frankel, Harvard University
August 2014
1 Introduction
Dramatic surges in international food commodity prices
relative to the last couple decades, widely acknowledged as
a global food price crisis, have posed major challenges for
policy makers. The impact has been more pronounced in
developing countries, considering food consumption
represents a large share of household expenditures in
developing economies, renewing interest in how central banks
react to exogenous food price shocks in a small open economy.
In response to the rising food prices, many governments had
significant budget outlays to support food price subsidies.
Food price subsidies are a means to which governments can
curb household inflation for food consumption. Many
countries had existing subsidy programs in place before the
- 4 -
onset of the food price shocks to the extent that they are
an entrenched social contract between the government and its
citizens.
The purpose of this paper aspires to capture the main
elements to analyzing policy makers’ intentions when faced
with exogenous food price shocks. To this end, we address
the fiscal challenges and macroeconomic implications of a
representative net-food exporting developing country to
isolate the effects of exogenous food price shocks using a
multi-sector New Keynesian DSGE model in a small open
economy setting. We do this by disentangling the offsetting
effects of surging food prices have on heterogeneous
household (Ricardian vs. non-Ricardian) incomes, while
capturing an additional channel vis-à-vis price subsidy to
dampen the effects of the ensuing price shock, however with
the potential of increasing the financial burden via a
higher debt position.
Only recently, there are a handful of papers to address the
challenges that central banks face whether to target
headline or core inflation based on a high share of food
expenditures and financially constrained household in
emerging markets (see e.g. Anand et al. [2015], Pourroy et
al. [2013] and Anand and Prasad [2010]). Our research adds
an additional channel by incorporating the effects of price
subsidies as a means to cushion global food price shocks in
many countries, which, to our knowledge is the first time
household price subsidies have been used in a DSGE model.
Another feature that distinguishes our study is the model
incorporates capital as an input to the technology process.
- 5 -
This paper is a DSGE in a small open economy setting with
New Keynesian features with respect to food price subsidies
as a means of fiscal intervention. The focus on developing
countries with particular focus on staple foods1 and aspires
to accommodate coordinated macroeconomic stabilization
policies via targeted subsidies to the poor – those mostly
likely affected - over the short-term. We ask three simple
questions:
In the presence of financial frictions, should the
central bank react to core inflation or headline
inflation and does the degree of fiscal intervention
affect this decision?
Are there any welfare distributional effects by
household type?
Can we characterize optimal policy?
2 Stylized Facts
We examine relevant features representing developing and
emerging market economies which allow us to understand the
macroeconomic channels faced by policy makers. Such stylized
facts include: large share of food expenditure, food
subsidies and a sizable portion of the population which is
financially constrained.
2.1 Large share of food expenditures:
Households in developing economies spend a higher share of
expenditures on food than wealthier, developed ones. This is
Engel’s law2 at work, which can be seen in Figure 1. The
average household expenditures share for food in low-income,
1 We abstract from agricultural non-staple foods which do not constitute
as a source of standard diet. Examples include cotton and tobacco. 2 Engel’s law is a theory named after German statistician Ernst Engel
(see Engel [1857]).
- 6 -
middle-income and high-income countries represent 48%, 31%
and 20%, respectively.3
Figure 1 – Food Share & Per Capita Income
0
10
20
30
40
50
60
6 7 8 9 10 11
Per Capita Income
Fo
od
Sh
are
Source: U.S. Department of Agriculture (USDA), Economic Research
Service. The food share excludes alcoholic beverages and tobacco.
Per capita income is shown in logarithm form.
Considering the substantial share of food in developing
economies, significant price swings can have noticeable
effects on real incomes. Anand, Ding, and Tulin [2014] find
evidence that food inflation is a key feature in inflation
expectations and wage growth in India. The authors also find
evidence of large second-round effects that food has on
Indian inflation, partly due to the high share of food in
the consumption basket, concluding policy makers should lean
towards headline CPI as their nominal anchor.
2.2 Food Subsidies
There have been two recent inflationary episodes attributed
to food price shocks of 2007 and 2011. Since the turn of the
century for 2015, food prices have, on average, soared 83%
3 Source: International Comparison Program [2005, the World Bank].
- 7 -
(152%) in real (nominal) terms according to the Food and
Agriculture Organization (FAO; see Figure 2).
Figure 2 – FAO Real Food Price Index (Annual)
Source: FAO of the United Nations. Base year: 2002-2004
weighted averages
In recent years, food prices have been increasingly volatile.
A casual inspection of Figure 2 shows that there are two
notable shocks occurring in 2008 and 2011 based on food
price data relating to five major commodities (cereal,
vegetable oil, meat, sugar and dairy) from the FAO.
Furthermore, the prices for all five commodities increased
roughly in lock-step.4 Many developing countries quickly
reacted through varying means of domestic and international
policies including enacting food subsidies, export taxes,
import duties and bans on certain exports.
As a means to cushion the effects of global food price
shocks, fiscal policies significantly increased food
subsidies. Food subsidies are prevalent in developing
economies. Between 2006 and 2008, the IMF (see IMF [2008])
documents that twenty-eight countries significantly food
subsidies to offset rising food prices with a median cost of
4 See Figure 9 in the Appendix.
50
100
150
200
250
1990 1995 2000 2005 2010 2015
Nominal Real
- 8 -
0.2% of GDP, and circa 20% of those countries ended up
spending in excess of 1% of GDP (Figure 3).
Figure 3 – Change in Food Subsidies (as % GDP: 2006 - 2008)
Source: see IMF [2008b], Figure 10 on pp. 29.
Figure 4 reveals sharp increases in food subsidies in 2008
relative to 2007, coinciding with the same period of the
world food price increase in Figure 2.
Figure 4 – Selected Countries with Food Subsidies (% GDP)
- 9 -
Source: see IMF [2008a], Table 13 (pp. 25)
for countries with food subsidies greater
than 0.5% of GDP.
2.3 Financial Access
An important feature in developing economies is limited
financial access relative to advanced economies. We follow
the New Keynesian literature by incorporating a share of the
population that can be described as hand-to-mouth (also
described in the literature as non-asset holders).5 This
implies the central bank has a limited effect since the
hand-to-mouth household has no access to assets to smooth
consumption. The implication is a broken link for the latter
household between optimizing current relative to future
consumption via the interest rate characterized in the Euler
equation. Thus, the larger the share of non-Ricardian
establishes an important role for fiscal policy which is
complemented by limited financial access. As non-Ricardians
cannot borrow in order to smooth consumption, the government
may do so for them by providing subsistence via a
combination of debt and taxes.
5 See e.g. Gali et al. [2004].
Country
Increase (2007 to
2008)
Subsidies
(2008)
Maldives 2,9 3,6
Timor-Leste 1,5 2,3
Burundi 0,6 2,5
Senegal 0,5 0,5
Costa Rica 0,5 0,5
Egypt, Arab Rep. 0,3 1,8
Morocco 0,2 1,2
India 0,1 0,7
Indonesia 0,1 0,9
Jordan -0,1 1,7
Turkmenistan -0,1 0,6
- 10 -
Figure 5: Financial Access
0
20
40
60
80
100
6 7 8 9 10 11
Per Capita Income
Fin
an
cia
l A
cce
ss
Vertical axis source: World Bank Global Financial Inclusion Database;
account access to a financial institution as percentage adults (15
years or older).
Horizontal axis source: USDA (shown in logarithm form). All data
relates to 2014.
3 Literature Review
We describe briefly the relevant literature on food
subsidies and how the effect of food prices has on a
developing economy, each will be discussed in turn.
3.1 Reflection of Food Subsidies in Developing Economies
By reducing the price a household would pay relative to
market clearing prices, mandated government subsidies are
designed to achieve a number of social, economic and
political goals. Food subsidies may take the form of either
universal subsidies or targeted subsidies. Kramer [1990]
cites a number of objectives, in particular to ensure
adequate nutrition, food consumption and food security for
its citizens as well as a means to transfer income to the
poor (pp. 2).
- 11 -
Fiscal intervention via subsidies is not without
shortcomings. There is an existing body of research, while
ad hoc, to suggest intended subsidies do not always reach
its intended beneficiary (commonly known as targeting
leakage) and excess costs.
Jha and Ramaswami [2010] provide a succinct literature
overview on the relative costs of public and private agents
and ask which of the two would lead to more efficient
allocation of resources. Their findings for the case of
India suggest that the private sector in India is more
efficient in terms of lower costs in trading, marketing
costs and storage costs (Jha and Srinivasan [2004]).
Food subsidies are usually targeted in order to cost
effectively transfer benefits to vulnerable members of
society and reduce or stabilize fiscal outlays for
supporting subsidies (Kramer [1990], pp. 8). Subsidy
programs typically are associated with administrative costs,
that is collecting information on households is not without
costs, reducing the subsidy benefit to the household.6 The
purpose of surveying households is to improve targeting
performance.
According to Coady et al. [2004], “scarce government
resources have encouraged efforts to concentrate resources
on ‘target groups’ of poor households or individuals” (pp.
1). Targeting leakage is an outcome of an inclusion error,
whereby those that are not intended to receive a subsidy
actually enjoy some of the direct benefits. This can be
problematic considering the scarcity of fiscal resources
6 See Coady et al. [2004], Chapter 2.
- 12 -
which may be exacerbated if there are any inefficiencies
from government led intervention.
3.2 Monetary Policy
Over the past few decades, central banks have focused on
controlling for the general rise of prices, a framework
described as inflation targeting. While many central banks
have pursued inflation targeting policies as explicit
objectives, others have targeted inflation indirectly,
commonly referred to as inflation targeting light,
underscoring the importance of low, stable prices. It has
been less clear-cut as to whether central banks should use
core inflation or headline inflation as the inflation
indexation.7 Wynne [1999] argues that core inflation is an
appropriate measure of inflation since volatile components
such as energy and food may be non-monetary in nature (i.e.,
driven by supply shocks). Aoki [2001] showed that targeting
core inflation is optimal by means of stabilizing sticky
prices, since fully-flexible prices are posited as mean-
reverting in the long run. Furthermore, targeting sticky
prices (i.e. core inflation) achieves headline price
stability.
The recent food inflationary episodes have provoked
reconsideration whether inflation indexation should be
anchored on core or headline prices. Walsh [2011] documents
the difference between food and non-food inflation tends to
be higher in developing countries than advanced economies,
which challenges the assumption of inflation indexation on
core inflation in three important ways. Food inflation in
7 Headline inflation is a measure of price changes for all goods while
core inflation is defined inflation excluding the effects of volatile
components (e.g., food and energy).
- 13 -
many developing economies is higher than non-food inflation
even in the long-run, thus excluding food inflation can lead
to a biased, underestimated inflation indexation. Secondly,
food price volatility can be quite persistent and could lead
to higher inflation expectations for food and non-food
prices. Lastly, food inflation may lead to second-round
effects with a higher pass-through to non-food prices for
developing economies than developed ones.
Anand and Prasad [2010] develop a New Keynesian closed
economy DSGE model aimed at understanding optimal monetary
policy when faced by increases in food prices relating to a
productivity shock in the food sector. Anand et al. [2015]
incorporate many of the features of Anand and Prasad [2010],
however incorporate an exporting sector for non-food. The
authors in both papers argue that targeting core inflation
is no longer welfare maximizing in the presence of
incomplete markets characterized with credit-constrained
consumers, an attribute common in many developing and
emerging economies. Further, the authors argue that food
consumption represents a significant portion of household
expenditures and that food inflation may feed into inflation
expectations.
Chang and Catão [2015] develop a DSGE model including a food
sector in a small open economy setting facing an exogenous
price shock. Similar to Anand and Prasad [2010], Chang and
Catão [2015] show that targeting headline inflation can be
welfare improving with volatile food price shocks.
Pourroy et al. [2016] develop a small, open economy in a New
Keynesian setting with tradable and non-tradable food and
non-food composite goods. They find that while non-tradable
food consumption is negligible in developed economies, it is
- 14 -
not the case in developing countries where the share of food
consumption is higher. Thus, the authors argue, central
banks in developing countries should target headline
inflation.
4 The Model
The model is based on an open economy setting, where the
domestic economy is characterized as a developing net food
exporting country. The structure of the model draws on the
recent research by Anand and Prasad [2010], Anand et al.
[2015] and Pourroy et al. [2016]. Anand and Prasad [2010]
and Anand et al. [2015] assumes there are two households;
food sector households, who are financially constrained, and
non-food households which have access to financial markets
able to smooth consumption in the event of productivity
shocks which is treated as a domestic event. Pourroy et al.
[2016] develop a DSGE in a more international setting, where
Ricardians have access to both domestic and foreign assets,
where the latter includes a country risk premium based on
the net foreign asset position. They include an exogenous
shock relating to the world price of food, adding realism in
the food price shocks felt the world over particularly in
2006 and 2011.
There are a couple novelties in our paper. Firstly, this
paper is a blend of Anand et al. [2015] and Pourroy et al.
[2013] in that we assume a fraction of food households are
credit constrained and the domestic economy faces a world
exogenous price shock based on the law of one price.
Secondly, to our knowledge, this is the first paper in the
DSGE literature to address the impacts of subsidies. We
incorporate the effect of food price subsidy has on
household optimization to capture fiscal authority’s actions
- 15 -
to curb inflation. Lastly, to our knowledge, we add, unlike
any of the papers incorporating a food sector, capital as an
input technology, which relates to the non-food sector.
Adding capital allows us to explore investment dynamics as
it relates to potential adverse (i.e., crowding out) effects
that subsidies may have on investment.
The domestic economy is small such that foreign variables
are not affected by the actions of agents in the domestic
economy. Hence, the price of food exports and lending rates
are determined exogenously via a rest of the world setting.
The model incorporates four optimizing agents: households,
firms, a monetary authority and a fiscal authority. In
summary, the model features:
two types of households: Ricardian and non-Ricardian;
• Ricardian members can trade in asset markets
(capital and bonds)
• non-Ricardian members do not hold financial assets
and cannot smooth consumption
two production sectors: a food sector and a
manufacturing sector;
• The food sector can be consumed in the domestic
economy as well as exported abroad at the
prevailing foreign exchange rate based on the law
of one price. Food is therefore representative of
the flexible price sector
• The manufacturing sector is consumed at home.
These firms are monopolistically competitive and
thus characterize the sticky price sector
a fiscal authority, who is charged with adjusting tax
rates and managing government spending, may, with good
intentions, consider offsetting food price shocks.
- 16 -
However in doing so, the government faces a higher
financial burden; and
a monetary authority who is charged with setting a
nominal interest rate as its policy instrument
Figure 6 below formalizes the main model assumptions.
Figure 6 - Model Structure
4.1 Households
There is a continuum of households on the interval [0, 1].
The model incorporates household heterogeneity by having two
Abroad Small Open Economy
Consume Food Non-Food Food Non-Food
Establish fiscal intervention (food subsidy)
Time varying taxes on wages, capital rents, consumption, profits
Conducts Monetary Policy
Sets nominal Interest Rate
Fiscal
Policy
Monetary
Policy
Food Sector Labor
Flexibe Prices
Household
Type
Firm
Technology
Asset
Markets
Sticky Prices
Capital
Industrial Sector Labor
Food Price
Shock
Food Sector Manufacturing Sector
Ricardian
Industrial household
Bonds (domestic, foreign)
Capital
No assets
non-Ricardian
Food household
- 17 -
consumer types, which draws on the work of Gali et al.
[2004]. To this end, a share of 1 − 𝜆 represent the neo-
classical Ricardian household ( 𝔯 ), who is able to smooth
consumption via trading in both financial (i.e., bonds) and
physical (i.e., capital) asset markets. The rest of the
households 𝜆 are labeled non-Ricardian (𝔫), who do not have
access to trade in asset markets. The distinction by
household type is quite important, particularly in
developing and emerging economies with opaque financial
markets. To simplify notation for the household, let 𝑖 ∈ (𝔯, 𝔫).
Household member i is assumed to have the same consumption
preferences for both food (𝐶𝑖,𝑡𝐹) and manufacturing (𝐶𝑖,𝑡
𝑀) goods,
combined in a CES basket:
𝐶𝑖,𝑡 = [𝜑1
휃(𝐶𝑖,𝑡𝐹 )
휃−1
휃 + (1 − 𝜑)1
휃(𝐶𝑖,𝑡𝑁 )
휃−1
휃 ]
휃
휃−1
(1)
where 𝜑 denotes the share of food consumption and 휃
represents the intertemporal elasticity of substitution
between food and manufacturing goods. The CES basket implies
the following consumption price index (CPI) per unit of
consumption:
𝑃𝑡 = [𝜑(𝑃𝑡𝐹)
1−휃+ (1 − 𝜑)(𝑃𝑡
𝑁)1−휃
]
11−휃
(2)
𝑃𝑡𝐹 and 𝑃𝑡
𝑁 denote the price of food and non-food goods,
respectively. The price of the food basket is liquid in the
sense it is traded on a global commodity price index. We
assume global food prices (𝑃𝑡𝐹⋆) sold domestically follows the
“law of one price” based on the prevailing exchange rate (𝑠𝑡):
𝑃𝑡𝐹 = 𝑠𝑡𝑃𝑡
𝐹⋆ (3)
- 18 -
Equation (2) reflects market clearing prices. It does not
necessarily reflect fiscal intervention to shield households
from food price shocks. Many countries implemented measures
to mitigate the effects of rising food prices. According to
an IMF [2008] report, a sample of 11 countries included both
general and targeted subsidies (pp. 22, 24). Similar to
Aissa and Rebei [2012], we introduce a simple way of
capturing the effects of fiscal intervention via subsidizing
food prices in the event of higher food price shocks as
follows:
�⃑⃑� 𝑖,𝑡𝐹
= 𝜅𝑖�⃑⃑� 𝑖,𝑡−1
𝐹+ (1 − 𝜅𝑖)𝑃𝑡
𝐹 (4)
Food prices denoted with �⃑⃑� 𝑖,𝑡𝐹 represent an adjusted price
subsidy depending on the intensity of 𝜅𝑖 . Equation (4) is
similar to price stickiness, where the difference between
the market prevailing food price less the subsidized food
price by consumption is subsidized. The parameter 𝜅𝑖
represents the degree of government intervention (0 ≤ 𝜅𝑖 ≤ 1)
by household type. As 𝜅𝑖 approaches unity (zero) translates
to household i effectively paying the steady state price
(market clearing price). Any fiscal intervention results in
an increase in debt and taxes (discussed below). Therefore,
household i faces the following price index:
�⃑⃑� 𝑖,𝑡 = [𝜑 (�⃑⃑� 𝑖,𝑡𝐹)1−휃
+ (1 − 𝜑)(𝑃𝑡𝑀)
1−휃]
11−휃
(5)
Equation (5) implies that market clearing prices are not
identical to those faced by the household, depending on the
intensity of 𝜅𝑖.
Each household i has perfect foresight on the underlying
price changes they face at the time they occur, thus chooses
- 19 -
the consumption bundle that minimizes expenditure. Household
i derives demand for each good variety as follows:
ℒ𝑖,𝑡 = �⃑⃑� 𝑖,𝑡𝐹𝐶𝑖,𝑡
𝐹 + 𝑃𝑖,𝑡𝑀𝐶𝑖,𝑡
𝑀
+ 𝜆𝑖,𝑡 [𝐶𝑡 − [𝜑1휃(𝐶𝑖,𝑡
𝐹 )휃−1휃 + (1 − 𝜑)
1휃(𝐶𝑖,𝑡
𝑀)휃−1휃 ]
휃휃−1
] (6)
The first order conditions for food and non-food are
summarized below:
𝐶𝑖,𝑡𝑀 = (1 − 𝜑)(
𝑃𝑖,𝑡𝑀
�⃑⃑� 𝑖,𝑡)
−휃
𝐶𝑖,𝑡 (7)
𝐶𝑖,𝑡𝐹 = 𝜑(
�⃑⃑� 𝑖,𝑡𝐹
�⃑⃑� 𝑖,𝑡)
−휃
𝐶𝑖,𝑡 (8)
4.1.1 Ricardian Household
Ricardian households represent optimizing agents, both
inter-temporally and intra-temporally. Ricardian households
supply labor specifically to the manufacturing sector,
consume and take portfolio decisions on how much to invest.
These households derive utility from consumption ( C𝔯,t ) and
labor effort (𝑁𝔯,𝑡).
𝑈𝔯,𝑡 = 𝔼𝑡 {∑𝛽𝑡
∞
𝑡=0
(1
1 − 𝜌C𝔯,t
1−𝜌 − 𝜓𝑁𝔯,𝑡
1+𝜒𝔯
1 + 𝜒𝔯
)} (9)
where 𝛽𝑡 represents the subjective discount factor (0< 𝛽𝑡 < 1);
𝜒𝔯 is the intra-temporal elasticity of substitution of labor
supply (𝜒𝔯> 0); and 𝜓 denotes the disutility of labor supply
(𝜓 > 0).
Physical and financial assets are solely owned by the
Ricardian household. Financial assets include domestic (B𝔯,t)
- 20 -
and foreign ( B𝔯,t⋆) bond holdings, which pays a return of
(1 + it−1) and St(1 + it−1⋆ ) , respectively. Consumption, wages,
capital rents and profits are endogenously taxed at time-
varying rates 𝜏𝑡𝑐 , 𝜏𝑡
𝑤 , τ𝔯,tk and τ𝔯,t
Π , respectively. The
representative Ricardian agent faces the following
intertemporal budget constraint:
St(1+it−1⋆ )Θ(ℬ𝑡)B𝔯,t−1
⋆
P⃑⃑ 𝔯,t+
(1+it−1)B𝔯,t−1
P⃑⃑ 𝔯,t+
(1−τ𝔯,tw )W𝔯,tN𝔯,t
P⃑⃑ 𝔯,t+ ((1 − τ𝔯,t
k )r𝔯,tut
𝑀+ δτ𝔯,t
k −
a[ut𝑀]) k
𝔯,t−1
𝑀
−StBt,j
⋆
P⃑⃑ 𝔯,t−
Bt,j
P⃑⃑ 𝔯,t− (1 + 𝜏𝑡
𝑐)C𝔯,t − I𝔯,t𝑀 − (1 − τ𝔯,t
Π )Π𝔯,t𝑀 (10)
where Θ(ℬ𝑡) is a country risk premium; ut𝑀 is capital
utilization with a physical cost of capital a[ut𝑀]; and profit
is denoted Π𝔯,t𝑀.8
We assume the manufacturing sector is capital intensive
(contrary to the food sector, which is based on labor as the
only firm technology). The capital stock includes capital
( k𝔯,t𝑀
) and investment ( I𝔯,t𝑀
). Capital is subject to a
depreciation rate denoted δ and evolves according to the
following capital stock constraint:
k𝔯,t𝑀 = (1 − δ)k𝔯,t−1
𝑀 + [1 − Ψ(I𝔯,t𝑀
I𝔯,t−1𝑀 )] I𝔯,t
𝑀 (11)
where δ ∈ (0,1) and investment adjustment costs are denoted by
Ψ(I𝔯,t𝑀/I𝔯,t−1
𝑀 ). Consistent with Christiano, Eichenbaum and Evans
[2005], investment adjustment costs and capital utilization
costs take the following functional form:
Ψ(I𝔯,t𝑀
I𝔯,t−1𝑀 ) =
ψ
2(
I𝔯,t𝑀
I𝔯,t−1𝑀 − 1)
2
(12)
8 Note that profit is solely attributed to the Ricardian household since
they are the owners of the manufacturing firm. Secondly, profit is taxed
similar to Schmitt-Grohé and Uribe [2004a]. Profit is derived as
Π,t𝑀 = k𝔯,t
𝑀 − r𝔯,t𝑀u𝔯,t
𝑀k𝔯,t𝑀 − W𝔯,t
𝑀N𝔯,t𝑀.
- 21 -
a[ut𝑀] = 𝜖1(ut
𝑀 − 1) +𝜖2
2(ut
𝑀 − 1)2 (13)
The representative Ricardian household maximizes utility as
in equation (9) subject to its resource constraint (10) and
capital constraint (11) with respect to C𝔯,t, B𝔯,t, B𝔯,t⋆, k𝔯,t
𝑀, I𝔯,t
𝑀,
ut𝑀 and N𝔯,t . This can be more formally expressed in the
following Ricardian optimization criteria:
ℒ𝔯,𝑡𝑈 = 𝔼𝑡 ∑𝛽𝑡
∞
𝑡=0
{1
1 − 𝜌C𝔯,t
1−𝜌 − 𝜓𝑁𝔯,𝑡
1+𝜒𝔯
1 + 𝜒𝔯
+ Λ𝔯,𝑡 (St(1 + it−1
⋆ )Θ(ℬ𝑡)B𝔯,t−1⋆
P⃑⃑ 𝔯,t+
(1 + it−1)B𝔯,t−1
P⃑⃑ 𝔯,t+
(1 − τ𝔯,tw )W𝔯,tN𝔯,t
P⃑⃑ 𝔯,t
+ ((1 − τ𝔯,tk )r𝔯,tut + δτ𝔯,t
k − (𝜖1(ut𝑀 − 1) +
𝜖2
2(ut
𝑀 − 1)2) k𝔯,t−1𝑀 −
StBt,j⋆
P⃑⃑ 𝔯,t
−Bt,j
P⃑⃑ 𝔯,t− (1 + 𝜏𝔯,𝑡
𝑐 )C𝔯,t
− I𝔯,t𝑀 − (1 − τ𝔯,t
Π )Π𝔯,t𝑀)
+ Q𝔯,𝑡 ((1 − δ)k𝔯,t−1𝑀 + [1 − Ψ(
I𝔯,t𝑀
I𝔯,t−1𝑀 )] I𝔯,t
𝑀 − k𝔯,t𝑀)} (14)
where Λ𝔯,t and Q𝔯,t represent the shadow value on the Ricardian
budget constraint and the Lagrangian multiplier related to
installed capital, respectively. We describe the first order
conditions below ex post allowing for a change of variables
by setting q𝔯,𝑡
=Q𝔯,t
Λ𝔯,t as the marginal value of installed capital
in terms of replacement costs which is commonly known as
Tobin’s Q.9
∂ℒ𝔯,tU
∂C𝔯,t: Λ
𝔯,t
=C𝔯,t
−𝜌
P⃑⃑ 𝔯,t(1 + τ𝔯,tc )
(15)
∂ℒ𝔯,tU
∂B𝔯,t: Λ
𝔯,t
= β𝔼t[Λ𝔯,t+1(1 + it+1)] (16)
9 See e.g. Fernández-Villaverde and Rubio-Ramírez [2006].
- 22 -
𝜕ℒ𝔯,𝑡𝑈
𝜕B𝔯,t⋆ : Λ
𝔯,𝑡
= β𝔼t [Λ𝔯,t+1(1 + 𝑖𝑡+1⋆ )Θ(ℬ𝑡)
𝑆𝑡+1
𝑆𝑡] (17)
𝜕ℒ𝔯,𝑡𝑈
𝜕k𝔯,t𝑀 : q
𝔯,𝑡
= β𝔼t {Λ𝔯,t+1
Λ𝔯,t[(1 − τ𝔯,t
k )r𝔯,t + δτ𝔯,tk − (𝜖1(ut
𝑀 − 1) +𝜖2
2(ut
𝑀 − 1)2
+ (1 − δ)q𝔯,𝑡+1
]} (18)
𝜕ℒ𝔯,𝑡𝑈
𝜕I𝔯,t𝑀 : q
𝔯,𝑡(1 − Ψ(
I𝔯,t𝑀
I𝔯,t−1𝑀 ) − Ψ′ (
I𝔯,t𝑀
I𝔯,t−1𝑀 ) I𝔯,t
𝑀)
+ 𝛽𝔯,𝑡𝔼t {Λ𝔯,t+1
Λ𝔯,t[q
𝔯,𝑡+1
I𝔯,t+1𝑀 2
I𝔯,t𝑀 Ψ′(
I𝔯,t𝑀
I𝔯,t−1𝑀 )]} = 1 (19)
𝜕ℒ𝔯,𝑡𝑈
𝜕ut𝑀
: (1 − τ𝔯,tk )r𝔯,t = 𝜖1 + 𝜖2(ut
𝑀 − 1) (20)
𝜕ℒ𝔯,𝑡𝑈
𝜕N𝔯,t: 𝜓𝑁𝔯,𝑡
𝜒𝔯 = Λ𝔯,𝑡
(1 − τ𝔯,tw )W𝔯,t (21)
Equation (15) represents the marginal utility of consumption.
Equations (15) and (21) together represent the inter-
temporal optimization relating labor supply decisions with
the marginal rate of consumption and real net wage.
Equations (16) and (17) represents the Euler equations for
domestic and foreign bonds. In equilibrium, equations (16)
and (17) have the same return, which characterizes the
standard uncovered interest rate parity (UIP) condition.
Note the marginal utility of income and inter-temporal
equations are a function of the distorted price as implied
by utility maximization. This implies that fiscal
intervention affects inflation faced by the Ricardian
household type.10
10 Inflation is defined by household type i as π⃑⃑ ,t = �⃑⃑� 𝑖,𝑡/�⃑⃑� 𝑖,𝑡−1.
- 23 -
The term Θ(ℬ𝑡) is a country risk premium that depends on the
net asset liquid position. We follow Benigno [2001] and
Schmidt-Grohe and Uribe [2003] and assume the interest rate
is a function of the world interest rate (𝑖𝑡𝑤) with a country
risk premium Θ(ℬ𝑡) , where the latter depends on the net
foreign asset position.
Θ(ℬ𝑡) = 𝑒−𝜈(ℬ𝑡−ℬ̅) (22)
The parameter 𝜈>0 and ℬ𝑡 = 𝑆𝑡Bt,j⋆ /�⃑⃑� 𝑡. The parameter v is scalar
denoting a country risk premium elasticity on the net
foreign asset position. In this setting, the Ricardian
household pay a risk premium above the world interest rate
on foreign bond holdings in the event the net foreign
position is negative. Otherwise, households receive a lower
remuneration as net lenders.
Equation (18) is the first order condition of marginal
product of capital net of taxes. Notice if there is no
investment adjustment costs (i.e., Ψ(I𝔯,t𝑀/I𝔯,t−1
𝑀 )=0), equation (19)
is equivalent to q𝔯,𝑡=1 which implies Tobin’s Q is equal to
the replacement cost of capital.11
4.1.2 Non-Ricardian Household
Non-Ricardian agents are synonymous with the “rule of thumb”
household common in the literature. The non-Ricardian
household thus has the following utility function:
𝑈𝔫,𝑡 =1
1 − 𝜌C𝔯,t
1−𝜌 − 𝜓𝑁𝔫,𝑡
1+𝜒𝔫
1 + 𝜒𝔫
(23)
11 See e.g. Fernández-Villaverde and Rubio-Ramírez [2006].
- 24 -
The budget constraint for this representative non-Ricardian
agent evolves where these agents only consume their current
income as follows:12
(1 + 𝜏𝔫,𝑡𝐶 )𝐶𝔫,𝑡 =
𝑊𝔫,𝑡
�⃑⃑� 𝔫,𝑡𝑁𝔫,𝑡 (24)
Contrary to most DSGE models, we relax the assumption of
having a labor tax collection on non-Ricardian wages. Low
income countries typically have a large share of informal
workers, which can be characterized as low wages and low tax
collection. Thus, we assume food sector wages are not taxed.
Utility maximization, given there are no taxable wages,
yields the normal intra-temporal labor supply optimality
conditions:
∂ℒ𝔫,tU
∂C𝔫,t: Λ
𝔫,t
=C𝔯,t
−𝜌
�⃑⃑� 𝔫,𝑡(1 + τ𝔫,tc )
(25)
𝜓𝑁𝔫,𝑡
𝜒𝔫 = Λ𝔫,𝑡𝑊𝔫,𝑡 (26)
4.2 Firms
There are two types of production firms in the domestic
economy: a food sector and manufacturing sector. The
production sectors are modeled using a constant return to
scale technology. The firm production in the manufacturing
sector is based on labor and capital, whereas the food
sector is solely based on labor technology. Food firms
operate in perfectly competitive markets and hence take
market clearing prices as given (i.e., flexible price
sector). Domestic food production may also be exported. The
12 See e.g. Campbell and Mankiw [1991] and Gali et al. [2007].
- 25 -
law of one price is assumed to hold at all times for this
good.
We allow for staggered prices in the manufacturing sector à
la Calvo [1983] (i.e., sticky price sector). The
manufacturing sector is based on labor and capital inputs
and is a non-traded good.
Similar to Anand et al. [2015], we allow for two types of
wages: 𝑊𝔫,𝑡𝐹
and 𝑊𝔯,𝑡𝑀
for food and manufacturing wages,
respectively. Labor is not mobile, i.e. only Ricardians are
associated with the manufacturing sector while non-
Ricardians relate to the food sector.
4.2.1 Food Firms:
Food firms (𝑌𝑡𝐹) optimally allocate labor resources from the
non-Ricardian household (𝑁𝔫,𝑡𝐹) using a constant return to
scale technology.
𝑌𝑡𝐹 = 𝐴𝑡
𝐹𝑁𝔫,𝑡𝐹 (27)
where 𝐴𝑡𝐹 represents productivity which follows an AR(1)
stochastic process. Food firms minimize the expected costs
subject to the production technology:13
𝑚𝑖𝑛𝑁𝔫,𝑡𝐹 (
𝑊𝑡𝐹
𝑃𝑡)𝑁𝔫,𝑡
𝐹 + 𝑚𝑐𝑡𝐹(𝑌𝑡
𝐹 − 𝐴𝑡𝐹𝑁𝔫,𝑡
𝐹 ) (28)
where 𝑚𝑐𝑡𝐹 can be interpreted as the nominal marginal cost
for the respective firm. Assuming an interior solution, the
first order condition yields:
13 The cost minimization follows Walsh [2010], see pp. 334.
- 26 -
𝑚𝑐𝑡𝐹 =
𝑊𝔫,𝑡𝐹
𝑃𝑡𝐴𝑡𝐹 (29)
The food sector operates in a competitive market whereby
domestic firms cannot price-discriminate. Thus, the marginal
cost and market clearing price level of food are synonymous
(i.e., 𝑚𝑐𝑡𝐹 = 𝑃𝑡
𝐹). Furthermore, we assume the law of one price
holds. This implies the following parity condition:
𝑊𝔫,𝑡𝐹 = 𝐴𝑡
𝐹𝑃𝑡𝐹 = 𝐴𝑡
𝐹𝑆𝑡𝑃𝑡𝐹⋆ (30)
where 𝑆𝑡𝑃𝑡𝑇⋆ is the domestic value of the world food price at
the prevailing foreign exchange rate.
4.2.2 Manufacturing Firms:
The non-tradable manufacturing technology is based on
capital and labor, which follows the standard Cobb-Douglas
form.
𝑌𝑡𝑀 = 𝐴𝑡
𝑀 (ut𝑀𝑘
𝔯,𝑡−1
𝑀)𝛼
(𝑁𝔯,𝑡𝑀)
1−𝛼 (31)
where 0 < 𝛼 < 1 is the share of capital. 𝐴𝑡𝑀 represents food
sector productivity that follows an AR(1) stochastic process.
Manufacturing labor is supplied by the Ricardian household.
The manufacturing sector solves pricing via a two-stage
process. The first stage consists of minimizing cost in
order to maximize profit based on perfectly competitive
factor markets which is generalized as follows:
min𝑁𝔯,𝑡
𝑀 ,�̂�𝔯,𝑡−1𝑀
𝑤𝔯,𝑡𝑀𝑁𝔯,𝑡
𝑀 + 𝑟𝑡𝑀�̂�𝔯,𝑡−1
𝑀+ 𝑚𝑐𝑡
𝑀 [𝑌𝑡𝑀 − 𝐴𝑡
𝑀 (�̂�𝔯,𝑡−1𝑀
)𝛼
(𝑁𝔯,𝑡𝑀)
1−𝛼] (32)
- 27 -
Note that we have made a change of variable for capital to
simplify notation: ut𝑀𝑘𝔯,𝑡−1
𝑀= �̂�𝔯,𝑡−1
𝑀.Assuming an interior solution,
cost minimization yields the following marginal products for
the optimal choice of labor and capital:
𝑁𝔯,𝑡𝑀 = (1 − 𝛼) ⋅ 𝑚𝑐𝑡
𝑀𝑌𝑡
𝑀
𝑤𝔯,𝑡𝑀
(33)
�̂�𝔯,𝑡−1𝑀
= 𝛼 ⋅ 𝑚𝑐𝑡𝑀
𝑌𝑡𝑀
𝑟𝑡𝑀
(34)
Where 𝑚𝑐𝑡𝑀 represents marginal costs for the representative
manufacturing sector producer. The previous two equations
yield the relative factor demands and nominal marginal cost
function:
�̂�𝔯,𝑡−1𝑀
𝑁𝑡𝑀 =
𝛼
(1 − 𝛼)
𝑤𝔯,𝑡𝑀
𝑟𝑡𝑀
(35)
𝑚𝑐𝑡𝑀 =
1
(1 − 𝛼)1−𝛼
1
𝛼𝛼
(𝑤𝔯,𝑡𝑀)
1−𝛼(𝑟𝑡
𝑀)𝛼
𝐴𝑡𝑀 (36)
Unlike the food sector, the manufacturing sector operates in
a monopolistic competitive environment. In the second stage
we incorporate stickiness a la Calvo [1983], such that each
manufacturing firm faces an exogenous probability 𝜙𝑀
> 0 of
not being able to re-optimize its price and hence retain the
price charged from the previous period. This can be
expressed in the following optimization process:
𝑚𝑎𝑥𝑃𝑗,𝑡
𝑀𝔼𝑡 ∑𝜙
𝑀𝑠
∞
𝑠=0
𝛯𝑡+𝑠 {(𝑃𝑗,𝑡
𝑀
𝑃𝑡+𝑠𝑀 − 𝑚𝑐𝑡+𝑠
𝑀 )𝑌𝑗,𝑡+𝑠𝑀 } (37)
subject to sector specific demand:
𝑌𝑗,𝑡𝑀 = (
𝑃𝑗,𝑡𝑀
𝑃𝑡𝑀)
−𝜖
𝑌𝑡𝑀 (38)
- 28 -
We set the pricing kernel equal to the Ricardian owners’
valuation Ξt+s = Λ𝔯,t+s/Λ𝔯,t , i.e. the marginal utility of
consumption. Inserting the demand into the maximization
process above simplifies optimization from a constrained
maximization to an unconstrained one:
max𝑃𝑗,𝑡
𝑀𝔼𝑡 ∑𝛽𝑠𝜙
𝑀𝑠
∞
𝑠=0
Ξt+s {(𝑃𝑗,𝑡
𝑀
𝑃𝑡+𝑠𝑀 (
𝑃𝑗,𝑡𝑀
𝑃𝑡𝑀)
−𝜖
− (𝑃𝑗,𝑡
𝑀
𝑃𝑡𝑀)
−𝜖
𝑚𝑐𝑡+𝑠
𝑀
)𝑌𝑡𝑀} (39)
Note that 𝑃𝑗,𝑡𝑀 is decided in period t and not t+1 since
manufacturing firms choose the optimal price in the current
time which will occur in the next period. The first order
conditions with respect to 𝑃𝑗,𝑡𝑀 yields the well know optimal
price setting equation as follows:
𝑃𝑡𝑀,⋆
𝑃𝑡𝑀 =
𝜖
𝜖 − 1
𝔼𝑡 ∑ 𝛽𝑠𝜙𝑀𝑠 𝛯𝑡+𝑠𝑌𝑡+𝑠
𝑀 𝑚𝑐𝑡+𝑠𝑀∞
𝑠=0 (𝑃𝑡+𝑠
𝑀
𝑃𝑡𝑀 )
𝜖
𝔼𝑡 ∑ 𝛽𝑠𝜙𝑀𝑠 𝛯𝑡+𝑠𝑌𝑡+𝑠
𝑀 𝑚𝑐𝑡+𝑠𝑀∞
𝑠=0 (𝑃𝑡+𝑠
𝑀
𝑃𝑡𝑀 )
𝜖−1 (40)
Note that if prices are completely flexible (i.e., 𝜙𝑀=0),
equation (36) simplifies to 𝑃𝑡
𝑀,⋆
𝑃𝑡𝑀 =
𝜖
𝜖−1𝑚𝑐𝑡
𝑀 . We work with the
condition of symmetric prices where 𝑃𝑡𝑀,⋆ = 𝑃𝑡
𝑀, implying
marginal cost would be equivalent to the inverse mark-up,
i.e. 𝑚𝑐𝑡𝑀 =
𝜖−1
𝜖.
We find it convenient to express (36) recursively, which
simplifies to 𝜖 ⋅ 𝑓1,𝑡
= (𝜖 − 1) ⋅ 𝑓2,𝑡 where:
𝑓1,𝑡
= Ξt𝑌𝑡𝑀𝑚𝑐𝑡
𝑀 + 𝛽𝑠𝜙𝑀𝑠 𝔼𝑡 (
𝑃𝑡+1𝑀
𝑃𝑡𝑀 )
𝜖+1
𝑓1,𝑡+1
(41)
𝑓2,𝑡
= Ξt𝑌𝑡𝑀 + 𝛽𝑠𝜙
𝑀𝑠 𝔼𝑡 (
𝑃𝑡+1𝑀
𝑃𝑡𝑀 )
𝜖
𝑓2,𝑡+1
(42)
- 29 -
We can express manufacturing prices evolving as a weighted
average of the fraction of manufacturing firms which
optimized its price and those that did not optimize prices
(which are stuck at charging prices from the previous
period):
𝑃𝑡𝑀 = [(1 − 𝜙
𝑀𝑠 )(𝑃𝑡
𝑀,⋆)1−𝜖
+ 𝜙𝑀𝑠 (𝑃𝑡−1
𝑀 )1−𝜖
]
11−𝜖
(43)
We define the market clearing manufacturing price inflation
(𝜋𝑡𝑀) by dividing (39) by 𝑃𝑡−1
𝑀:14
𝜋𝑡𝔪 = [(1 − 𝜙
𝑀𝑠 ) (
𝑃𝑡𝑀,⋆
𝑃𝑡−1𝑀 )
1−𝜖
+ 𝜙𝑀𝑠 ]
11−𝜖
(44)
Lastly, we define the New Keynesian Phillips Curve (NKPC) in
log-linear terms as follows:15
𝜋𝑡𝔪 =
(1 − 𝜙𝑀𝑠 )(1 − 𝛽𝜙
𝑀𝑠 )
𝜙𝑀𝑠 ((1 − 𝛼)�̂�𝑡
𝑀 + 𝛼 log �̂�𝑡𝔪 − �̂�𝑡
𝔪 − (1 − 𝛼)log(1 − 𝛼)
− 𝛼 log(𝛼)) + 𝛽Ε(𝜋𝑡+1𝔪 ) (45)
The NKPC above shows that manufacturing inflation depends on
real marginal costs, which is an outcome of price setting
decisions made by firms.
4.3 Fiscal Policy
The government’s inter-temporal budget constraint evolves as
follows:
14 See Gali [2008], Chapter 3 pp. 62. 15 This draws on Gali [2008], Chapter 3.
- 30 -
𝐵𝑡𝐺 + St𝐵𝑡
𝐺⋆ − (1 + 𝑖𝑡−1)𝐵𝑡−1𝐺 − St(1 + it−1
⋆ )Θ (Stℬ𝑡
𝐺⋆
𝑃𝑌,𝑡𝑌𝑡)𝐵
𝑡
𝐺⋆
= (1 + 𝜉)�⃑� 𝑡 − 𝜏𝔫,𝑡𝐶 𝐶𝔫,𝑡 −
𝜏𝑡𝑐C
𝔯,t− τ𝔯,t
w𝑊𝔯,t𝑀𝑁𝔯,t
𝑀 − τ𝔯,tk rtut
𝑀k𝔯,𝑡−1𝑀 − τ𝔯,t
k Π𝔯,t𝑀 (46)
In equation (45), the representative fiscal agent finances a
stream of food price subsidies (�⃑� 𝑡) via a variety of sources,
of which include both domestic (𝐵𝑡𝐺) and foreign (St𝐵𝑡
𝐺⋆) debt
and tax revenues. In this setting, we follow Forni and
Pisani [2010] and assume that public debt relates to only
domestic bonds held by the Ricardian household.
There are eight instruments in (45) – price subsidy outlays
defined by household type; domestic and foreign debt; and
time varying taxes on consumption, labor wages, capital
rents and profits. We simplify the model similar to Medina
and Soto [2007] and Medina et al. [2008] by assuming
government debt is denominated in foreign currency. This
reduces our instruments to seven, where we therefore need at
least six instruments for tractability.
The first instrument - food price subsidies - are determined
simply by the product of the respective household’s food
price spread (depending on the intensity and segmentation of
𝜅𝑖) and consumption units for household i, i.e. (𝑃𝑡𝐹 − �⃑⃑� 𝑡
𝐹,𝑖)𝐶𝑖,𝑡
𝐹.
Fiscal revenues come from net debt and taxes.16 In addition,
we incorporate a small deadweight cost (𝜉) in equation (45),
which represents an inefficiency for the government to
intervene.17
In the absence of intervention, the price
16 Note that the government budget constraint is modelled in a way which
abstracts from concessional debt and official development assistance. 17 We loosely follow Gertler and Karadi [2011] in their approach. The
aforementioned authors incorporate a dead-weight cost as a means to
capture government intervention in terms of credit policy. Their main
message, which we apply in our model, is that the government, when it
decides to intervene, is less efficient than the private sector.
- 31 -
spreads by household i collapses to zero and hence there is
no deadweight cost.
�⃑� 𝑡 = (𝑃𝑡𝐹 − �⃑⃑� 𝑡
𝐹,𝔫)𝐶𝑡
𝐹,𝔫 + (𝑃𝑡𝐹 − �⃑⃑� 𝑡
𝐹,𝔯) 𝐶𝑡
𝐹,𝔯 (47)
For purposes of ensuring stability, a Ponzi scheme is ruled
out, i.e. both the consumer budget constraint and a debt
ceiling will always bind. In this setup, two categorical tax
instruments may respond positively to deviations in the
debt-to-output ratio steady state level:18
τi,tc = �̅�𝑖,𝑐 + 𝜌
𝑖,𝑘(τi,c,t−1
c − �̅�𝑖,𝑐) + (1 − 𝜌𝑖,𝑐
) 𝜙𝑖,𝑐
[𝐵𝑡
𝑃𝑡𝑌𝑡−
�̅�
𝑃𝑌̅̅ ̅̅] (48)
τ𝔯,tV = τ̅𝔯
V + 𝜌𝔯V(τ𝔯,t−1
V − τ̅𝔯V) + (1 − 𝜌
𝔯V)𝜙
𝔯V [
𝐵𝑡
𝑃𝑡𝑌𝑡−
�̅�
𝑃𝑌̅̅ ̅̅] (49)
for V ∈ (w, k, Π), which relate to the marginal tax rates on
labor wages, capital rents and profits, respectively. As 𝜙𝔯V
approach zero, the fiscal response will be financed by debt.
On the other hand, for a balanced budget rule if 𝜙𝔯V > 0
ensures a feedback response and to hence ensure solvency.
4.4 Foreign Economy
We set the balance of payment (𝑇𝐵𝑡) equation as simply the
value of exports less the difference on the foreign asset
position including the net interest provision.
StB𝔯,t⋆ = St(1 + it−1
⋆ )B𝔯,t−1⋆ + 𝑇𝐵𝑡 (50)
𝑇𝐵𝑡 = 𝑃𝑡𝐹(𝑌𝑡
𝐹 − 𝐶𝑡𝐹) (51)
18 See e.g. Stähler and Thomas [2012] DSGE model developed by Banco de
España and Deutsche Bundesbank staff in order to address fiscal policy
simulations. Similar to the authors, we incorporate government revenues
that adjust to changing leverage, thereby ensuring stability.
- 32 -
Equation (49) above represents the aggregate net liquid
position on foreign bond holdings (B𝔯,t⋆).
19 The second equation
(50) above shows that the trade balance depends on the
variation of the domestic value of food exported abroad
based on domestic absorption.
4.5 Monetary Policy
The central bank closely follows a Taylor-like Rule to set
changes in short-term interest rates in response to changes
in prices:20
(1 + it
1 + i̅) = (
1 + it−1
1 + i̅)αi
[(𝑌𝑡
Y̅)α𝑌
(π𝑡
𝑋
π̅)
α𝑋
]
(1−αi)
(52)
The central bank conducts interest rate smoothing as 0 < αi ≤
1. The policy weights with respect to deviations away from
output gap and the inflation target are assigned by α𝑌 and
α𝑋, respectively, where X ∈ (𝔪, 𝔥, 𝔡, 𝔬), representing a policy
reaction on stabilizing:
Core inflation: defined as sticky price inflation
𝜋𝑡𝔪 = 𝑃𝑡
𝑀/𝑃𝑡−1𝑀
;
Market clearing headline inflation: defined as market
prices 𝜋𝑡𝔥= 𝑃𝑡/𝑃𝑡−1 which captures sticky and volatile
(food) price changes;
Distorted headline inflation 𝜋𝑡𝔡 = 𝑃𝑡
𝔡/𝑃𝑡−1𝔡
where 𝑃𝑡𝔡 is the
weighted average price level for household i, i.e.
�⃑⃑� 𝑡𝔡= (1 − 𝜆)�⃑⃑� 𝑡
𝔯+ 𝜆�⃑⃑� 𝑡
𝔫; and
Optimal inflation: similar to Anand et al. [2015], the
optimal inflation rate is defined as the weighted value
19 See Medina and Soto [2007]. 20 The Taylor rule builds on the seminal work of Taylor [1993].
- 33 -
(𝜛) of core and market clearing headline inflation that
maximize welfare 𝜋𝑖,𝑡𝔬 = 𝜛𝑖𝜋𝑖,𝑡
𝑀 + (1 − 𝜛𝑖)𝜋𝑖,𝑡𝔥
Notice the value of 𝜛𝑖 depends on household i, which will
allow us to investigate distributional effects. Further, we
constrain the weighted parameter 0≤ 𝜛𝑖 ≤1. Further, note that
steady state market clearing inflation ( π̅) is identical to
that of the distorted inflation steady state.
The above analysis will be used to conduct welfare analyses
regarding whether price subsidies to offset price
consumption inflation are welfare improving regarding
Ricardian and non-Ricardian households using a second-order
welfare approximation.
5 Model Experiments
We are now at a point to address three questions presented
in the introduction:
In the presence of financial frictions, should the
central bank react to core inflation or headline
inflation (incorporating a food price shock) and does
the degree of fiscal intervention affect this decision?
Are there any welfare distributional effects by
household type?
Can we characterize optimal policy?
To answer these questions we conduct three experiments with
regard to different fiscal intervention intensities of
whether to subsidize food price shocks. In the first
experiment, we describe the model in the absence of fiscal
subsidies, which we refer to as the Baseline model (Model I).
This implies that all agents face the same price level, i.e.
there is no price distortion (𝜋𝑡 = 𝜋𝑡,𝑖).
- 34 -
Considering the importance of the subsidy debate on
efficiency, we also show the response of the model economy
when fiscal authorities use a targeted approach, i.e. to
subsidize food price shocks only for the households that are
most vulnerable (i.e. non-Ricardian household type in this
model since they are financially constrained). In this
approach, non-Ricardians are unable to save and hence borrow
against food price shocks since food represents a dominant
share of expenditures. We refer to this as a Targeted
subsidy (Model II) experiment.
The last experiment we conduct is similar to Model II,
except the Ricardian household (in addition to the non-
Ricardian household) receives a universal subsidy, either by
legal means or by potentially strong incentive effects of
free-riding behavior (which may result in targeting leakage,
which we refer to Model III. Despite the subsidy targeting
literature, this scenario appears to be quite prevalent than
a more targeted scenario. The IMF [2008] argues that
subsidies were poorly designed. According to McDermott [1992]
food subsidy targeting programs are typically not well
established for two reasons. Firstly, better targeting can
reduce support for the subsidy, thereby reducing the
beneficiaries of the benefit. Secondly, there is a “tradeoff
between better targeting and the increased risk of civil
unrest or demands for wage increases” (see pp. 8).
In summary, we conduct the following experiments:
Model I: Baseline (No Fiscal Policy)
o i.e., no subsidy 𝜅𝔯=𝜅𝔫=0
Model II: Targeted Subsidy
o i.e., non-Ricardian subsidy intervention 𝜅𝔯 = 0; 0 <
𝜅𝔫 ≤1
Model III: Universal Subsidy
- 35 -
o i.e., both households receives subsidy 0 < 𝜅𝔯=𝜅𝔫 ≤1
In the event that fiscal intervention follows either Model I
or Model II, consumption prices faced by both household
types will be equivalent, however the latter model results
in the presence of distorted prices. Model III allows us to
capture the effects of a targeted subsidy program for
society’s most vulnerable. Furthermore, we assume the degree
of interest rate smoothing which is captured in αi is set to
zero in the event of an exogenous food price shock. The
logic of this argument is such that we are capturing a
potential adverse world food price shock on a developing
economy in terms of rule-of-thumb agents, which has strong
implications considering a large share of labor and food
consumption exists in developing economies.
5.1 Aggregation
Market clearing and aggregate variables are defined as
follows:
𝐶𝑡 = (1 − 𝜆)𝐶𝑡𝔫 + 𝜆𝐶𝑡
𝔯 (53)
𝑁𝑡 = (1 − 𝜆)𝑁𝔯,𝑡𝑀 + 𝜆𝑁𝔫,𝑡
𝐹 (54)
kt𝑀 = (1 − 𝜆)k𝔯,t
𝑀 (55)
Bt = (1 − 𝜆)B𝔯,t (56)
B𝔯,t⋆ = (1 − 𝜆)B𝔯,t
⋆ (57)
It𝑀 = (1 − 𝜆)I𝔯,t
𝑀 (58)
GDP is the sum of domestic consumption, food price subsidies,
investment (including capital adjustment costs) and exports.
In the absence of any effect fiscal intervention (i.e. no
- 36 -
efficiency cost 𝜉 as in Model I), GDP can be simplified to
show that domestic food consumption collapses to a simple
representation where both household types face market
clearing prices:
𝑃𝑡𝑌𝑡 = 𝑃𝑡𝐹𝐶𝑡
𝐹 + 𝑃𝑡𝑀𝐶𝑡
𝑀 + 𝑃𝑡𝐼𝑡𝑀 + a[ut
𝑀]It𝑀 + 𝑃𝑡
𝐹𝑇𝐵𝑡𝐹 (59)
However, when the government intervenes via a food subsidy
the market clearing condition results in distorted prices
faced by household i and an inefficiency cost (relating to
Model II and Model III) as follows:
𝑃𝑡𝑌𝑡 = 𝑃𝑡𝐹𝐶𝑡
𝐹 + 𝑃𝑡𝑀𝐶𝑡
𝑀 + 𝜉 ⋅ �⃑� 𝑡 + 𝑄𝑡𝑀𝐼𝑡
𝑀 + a[ut𝑀]It
𝑀 + 𝑃𝑡𝐹𝑇𝐵𝑡
𝐹 (60)
This is equivalent to:
�⃑⃑� 𝑡𝑌𝑡 = �⃑⃑� 𝑡𝐹𝐶𝑡
𝐹 + 𝑃𝑡𝑀𝐶𝑡
𝑀 + (1 + 𝜉) ⋅ �⃑� 𝑡 + 𝑄𝑡𝑀𝐼𝔯,𝑡
𝑀 + a[ut𝑀]k𝔯,𝑡−1
𝑀 + 𝑃𝑡𝐹𝑇𝐵𝑡
𝐹 (61)
This concludes the main “nuts and bolts” of the model.
5.2 Calibration:
The baseline quarterly calibration of the model parameters
can be summarized below in Table 1 below. Similar to Anand
et al. [2015], we assume the share of credit constrained
household ( 𝜆 ) is equal to 40%. We follow Deveraux et al.
[2004] by setting the subjective discount factor ( 𝛽 ) to
0.985 for an emerging market economy. This implies a
quarterly real interest rate equal to 1.5% (i.e., (1 − 𝛽)/𝛽).
Consistent with most papers for developing economies, we set
the risk aversion parameter 𝜌 to 2 (see e.g., Aguiar and
Gopinath [2007]).
The inverse Frisch parameter controlling labor supply
elasticity is distinguished between Ricardian and non-
Ricardian type. There is some contention in the literature
- 37 -
on the value of 𝜒𝑖 between macro- and micro-studies. In the
baseline calibration, we set 𝜒𝔫=𝜒
𝔫=3, a standard value used
in the DSGE literature.
We assume an inelastic substitution, 휃=0.6, between food and
manufacturing goods, which is in line with Anand et al.
[2015]. In the baseline model, we assume no fiscal
intervention, i.e. 𝜅𝔯 , 𝜅𝔫 =0, which is built on the RBC
foundation where the role of food policies plays little role
in explaining short-term frictions over the business cycle.
This implies both debt and taxes ( �̅�) are zero. Considering
the presence of a large share of non-Ricardians and food
expenditure share as well as engrained fiscal policies to
counteract food price shocks, we set the fiscal policy
combination to 𝜅𝔯 =0, 𝜅𝔫 =0.6 to proxy for a targeted policy
(Model II) and 𝜅𝔯=𝜅𝔫=0.6 for a Universal policy (Model III).
A targeted subsidy program implies leverage increases by
0.43% (0.43%) on impact given a food price shock under a
headline (core) inflation targeting regime. Model II and
Model III will require a combination of debt and taxes to
increase in the face of a food price shock.
Similar to Anand et al. [2015], the Calvo price signal (𝜙𝑀)
in the manufacturing sector is assumed to be 0.66. This
implies one-third of manufacturing firms will reset prices
each quarter. Consistent with most of the literature, we
assume a quarterly depreciation rate of 0.025, implying an
annual depreciation of 10%.
We draw on Schmitt-Grohé and Uribe [2003] by setting the
bond adjustment costs to a small number: 휁=0.0009.
- 38 -
We follow Gali et al. [2004] by setting monetary policy
coefficient on the output gap (α𝑌) equal to 0.5. We set the
policy reaction on the inflation targeting regimes we
consider ( α𝑋 ) equal to 2. We incorporate interest rate
smoothing by setting αi=0.7. Furthermore, the aforementioned
monetary policy parameters were used in Anand et al. [2015]
for headline inflation targeting and core inflation
targeting.
Table 1 - Parameter Selection
Population Type
Non-Ricardian; Food Labor Supply 𝜆 0.4
Utility
Discount factor 𝛽 0.985
Inverse of intertemporal elasticity of subst. 𝜌 2
Inverse elasticity of labor supply Ricardian 𝜒𝔫 3
Inverse elasticity of labor supply non-Ricardian 𝜒𝔫 3
Share of food in consumption 𝛾 0.5
Elasticity of substitution: food and non-food 휃 0.6
Industrial Sector
Capital share 𝛼 0.33
Depreciation 𝛿 0.025
Domestic Calvo signal 𝜙𝑀 0.66
Monopoly power 휂𝑀 6
Adjustment Costs
Bond adjustment costs 휁 .0009
Fiscal Policy
Baseline Model I: i.e., no subsidy 𝜅𝔯, 𝜅𝔫 0 0
Targeted Model II: i.e., non-Ricardian subsidy 𝜅𝔯, 𝜅𝔫0.6,0.6
Universal Model III: blanket subsidy 𝜅𝔯, 𝜅𝔫 0,0.
Tax rate �̅� 0
Leverage response (ensures solvency) 𝜙𝜏 0.15
Monetary Policy
Interest Rate Smoothing αi 0.7
Response on output gap α𝑌 0.5
Response on policy rate α𝑋 2
- 39 -
Similar to Anand and Prasad [2010] and Pourroy et al. [2016],
we assume productivity in the food and non-food sector
follows an AR(1) process:
log (𝐴𝑡
𝐹
𝐴𝐹̅̅̅̅) = 𝜌𝐹 log (
𝐴𝑡−1𝐹
𝐴𝐹̅̅̅̅) + 휀𝑡
𝐹
log (𝐴𝑡
𝑀
𝐴𝑀̅̅ ̅̅) = 𝜌𝑀 log (
𝐴𝑡−1𝑀
𝐴𝑀̅̅ ̅̅) + 휀𝑡
𝑀
Similar to Pourroy et al. [2013], we also incorporate shocks
to the global food price and world interest rate.
log (𝑃𝑡
𝐹⋆
𝑃𝐹⋆̅̅ ̅̅̅) = 𝜌𝐹⋆ log (
𝑃𝑡−1𝐹⋆
𝑃𝐹⋆̅̅ ̅̅̅) + 휀𝑡
𝐹⋆
Where 𝜌𝑀, 𝜌𝐹, 𝜌𝐹⋆ ∈ (0,1) and 휀𝑡𝑀, 휀𝑡
𝐹 and 휀𝑡𝐹⋆ are ℕ(0, 𝜎𝑀), ℕ(0, 𝜎𝐹) and
ℕ(0, 𝜎𝐹⋆), respectively.
We follow Deveraux et al. [2004] by assuming an AR(1)
process on the world interest rate set to 0.46.
We use Matlab interfaced with Dynare (version 4.4.3) routine
files for all computations (see Adjemian et al. [2011]).
5.3 Baseline Model
The impulse response functions (IRF) are presented in Figure
7 (below) which compare monetary policy targeting core and
headline inflation. The IRFs relate to monetary policy
responses in the absence of fiscal intervention where
household facing prices are equivalent to market clearing
prices (i.e., Model I). The IRFs display a transitory one
standard deviation orthogonal shock to the global food
prices and are provided in percentage deviations.
- 40 -
An increase in the world price of food creates inflationary
pressure in the domestic economy on impact. While the
central bank raises the policy rate in response to inflation
for both headline and core inflation targeting regimes, the
reaction of the policy rate is stronger under a headline
inflation targeting regime.
Consumption for the Non-Ricardian households increases at
the time of the food price shock. This is due to their
“hand-to-mouth” property: a rise in food prices means higher
incomes for these households, but since they do not have
access to financial markets they cannot smooth any positive
gain over time as they consume their entire income.
Therefore, the positive food price shock translates into a
rise of Non-Ricardian households consumption. Non-Ricardian
consumption not only increases, but more than offsets the
Ricardian household decrease in consumption, hence leading
to an increase in aggregate consumption.
The trade balance for both regimes is increasing since there
is an appreciation of the exchange rate.
While investment decreases under both a core and headline
inflation targeting regime, the overall investment reduction
is lessened by the latter. This is in part due to a more
stable aggregate demand if the central bank follows a
headline inflation targeting rule. That is, as aggregate
demand increases, targeting headline inflation would require
a stronger policy reaction than a policy targeting core
inflation (see Figure 7). Thus, headline inflation targeting
is a more effective policy choice in terms of stabilizing
output. 21
21 While Anand et al. [2015] do not include investment in their model
(they focus on domestic productivity shocks), our findings are findings
- 41 -
Figure 7: IRF World Food Price Shock (Baseline Model I)
Aggregate Consumption
Consumption of Food
Households
Consumption of Non-Food
Households
Headline Inflation Core Inflation Food Inflation
Interest Rate Saving Exchange Rate
Trade Balance Investment Output
strongly overlap with theirs: headline inflation is a better policy in
terms of stabilizing output.
- 42 -
Legend: — headline inflation targeting; – – core inflation targeting
5.4 Fiscal Policy Intervention
We extend the baseline model to incorporate two additional
experiments, which are designed to represent an isolated
event of higher world food prices face by a developing
economy, where the fiscal authority may decide to intervene
in order to shield certain households from food price shocks.
The IRFs in displayed in Figure 8 (below) shows the three
models representing the three experiments considering the
fiscal intensity combination (i.e., 𝜅𝔯, 𝜅𝔫 ) under monetary
policy reaction on headline inflation.
Irrespective of monetary policy stance of targeting headline
or core inflation (as shown in Figures 11 and 12 in the
Appendix relative to no subsidy as in Figure 7), we find
introducing a food price subsidy is influential at crowding
in consumption for both households (relative to an absence
of having a subsidy).
Consumption for non-Ricardian households increases at the
time of the food price shock, and more so as subsidies
increase. Hence, introducing food price subsides can be an
influential means in crowding in consumption for both
households (relative to an absence of having a subsidy).
However, consumption for Ricardian households may decrease
over time as taxes increase until fiscal debts are repaid.
Note that taxes and public spending are nil in Model I
(there is no subsidy). In the presence of fiscal
intervention as in Models II and III, public spending and
therefore taxes deviate from their steady state in order to
finance the subsidy. This is due to government intervention
- 43 -
to smooth food price volatility. As shown in the Appendix,
at the time of the shock and under similar monetary policy,
the world food price shock translates into an increase of
the domestic food price of 5.6% without subsidy (Model I),
4.7% with a target fiscal policy (Model II) and only 3.2%
with a global subsidy (Model III). This shows the effect of
the smoothing mechanism by means of fiscal intervention. It
translates into similar smaller increase of the consumer
price index faced by households: headline price increase by
2.3% in the absence of a subsidy, but only by 1.4% with a
uniform subsidy (Model III) under an headline inflation
targeting regime.
In addition to reducing household facing inflation with
regard to a world food price shock, food price subsidies,
through fiscal intervention, shifts manufacture producers
from saving to borrowing which can deteriorate the trade
balance.
Net bond holdings (private and government) slightly decrease
the higher the intensity of fiscal intervention. On the one
side, private bonds are reduced, on the other side
government bonds, which are strictly held by the Ricardian
household, increase in order to pay for the food subsidy.
When there is no fiscal intervention, the trade balance is
increasing. However, it falls as when fiscal intervention is
introduced. On the one side, there is a “price effect” such
that a high price of food commodities puts upward pressure
on the trade balance. The rise in the world food price makes
domestic food producers more competitive. On the other side,
fiscal intervention may result in a case of twin deficits:
when public spending over GDP is large, domestic public debt
is large and may even be larger than Ricardian consumers’
- 44 -
willingness to borrow. Hence, Ricardian consumers lend to
domestic government and dissave from abroad, therefore
pushing downward the trade balance.
The reduction in investment, which is only specific to the
manufacturing (sticky price) sector, is lessened by the
intensity fiscal intervention increases in the presence of
food price shocks. This suggests, similar to consumption,
food price subsidies can crowd in private investment
engendered by the effects of increasing aggregate demand.
Figure 4: IRF World Food Price Shock (Headline Targeting)
Aggregate Consumption
Consumption of Food
Households
Consumption of Non-
Food Households
Headline Inflation Core Inflation Food Inflation
- 45 -
Interest Rate Distorted Headline
Inflation Subsidised Food Price
Trade Balance Saving Government Debt
Exchange Rate Marginal Tax Rate (%) Subsidy (in % GDP)
Investment Output
Legend: — Model I; – – Model II; •• Model III
5.5 Welfare Analysis
We conduct conditional welfare analysis of the different
policy options using a second order approximation of the
household welfare. To conduct a policy assessment and
comparative analysis of the different policy options using
numerical simulations of the model.
- 46 -
We define welfare for household type i as follows:
𝑊𝑖,𝑡 = 𝔼𝑡 {∑𝛽𝑛
∞
𝑛=0
𝑈𝑖(C𝑖,t+n, N𝑖,t+n)} |
𝑥0=𝑥
(62)
We can write the welfare equation above in recursive form as
follows:
𝑊𝑖,𝑡 = 𝑈𝑖(C𝑖,t, N𝑖,t) + 𝛽𝑊𝑖,𝑡+1
(63)
This allows us to calculate aggregate welfare which is
defined as the sum of household i welfare weighted by the
respective share of each household:
𝑊𝑡 = (1 − 𝜆)𝑊𝔯,𝑡 + 𝜆𝑊𝔫,𝑡 (64)
We compare welfare for the baseline model with no fiscal
intervention (Model I) for each household, 𝑊𝑖,𝑡, with the two
models based on fiscal intervention (Model II and III) for
four monetary policy regimes.22 The monetary policy regimes
considered include headline inflation, distorted headline
inflation, core inflation and optimal inflation.
We present the results of the welfare evaluation for both
aggregate and heterogeneous welfare based on the fiscal and
monetary policy stance. All models have the same steady
state. As we are analyzing an isolated food price shock23
that occurs for a developing economy, we define welfare
gains as the cumulative consumptions units needed to make
welfare under core inflation targeting equivalent to that of
alternative policy choices.
22 We therefore take as given the Taylor rule including interest rate
smoothing and a reaction to the output gap. 23 We assume an AR(1) coefficient of 0.5 for an exogenous food price
shock in the model.
- 47 -
5.5.1 Aggregate welfare evaluation
We present the aggregate welfare gain in Table 2 based on an
orthogonal food price shock. Core inflation targeting is
taken as a basis to compare alternative welfare policy rules
which include headline and distorted headline. We consider
distorted headline inflation as a leaning against the wind
targeting rule. We also compute the optimal inflation which
is an outcome of maximizing welfare by changing 𝜛, which is
the share of core inflation relative to market clearing
headline inflation.
We rank different fiscal and monetary policies in terms of
welfare. In the welfare tables, we include a “local” and
“global” ranking. The former is defined by ranking the
different monetary policies given a certain fiscal policy.
That is, given a fiscal intervention policy, we assess which
monetary policy regime achieves the highest level of welfare.
In Table 2, we rank headline, distorted headline and core
inflation, where the latter is used as a basis. In Model I,
headline inflation has a higher rank than core inflation.
This is consistent with Model II and Model III, however
distorted headline inflation achieves a higher welfare
ranking than headline for the aforementioned models. The
global ranking suggests that welfare is increasing in the
level of fiscal intensity; hence Model III is preferred to
the other model alternatives.
We have two major findings. Firstly, our results suggest
that aggregate welfare is improving when fiscal policy
intervenes and monetary policy targets distorted headline
inflation followed by headline inflation relative to core
- 48 -
inflation.24 Thus, the results suggest a central bank should
react to food price volatility. Secondly, incorporating the
effect of headline inflation as determined by 𝜛 in the
optimal monetary policy is decreasing in the intensity of
fiscal policy. This is an important, yet intuitive, result:
fiscal policy intervention that shields households,
particularly non-asset holders, from food price shocks
reduces the volatile effects of headline prices in the
optimal inflation target.
Table 2: Aggregate Welfare Gain (Food Price Shock)
Note: The welfare gains are calculated as gains in
consumption units relative to core inflation and are based
on an orthogonal shock to the world price of food.
Consistent with the foregoing welfare based on orthogonal
food price shock, we find that welfare based on exogenous
shocks to aggregate shocks, which we define as shocks to
aggregate productivity25, the world interest rate and the
world food price, is welfare improving when monetary policy
reacts to headline inflation relative to core inflation and
the optimal weight ( 𝜛 ) is decreasing as fiscal intensity
increases.
24 Note that distorted headline inflation is equivalent to headline in-
flation in Model I, i.e. there is an absence of fiscal intervention. 25 To this end, we set manufacturing and food productivity equal with an
AR(1) persistence and standard deviation set to 0.9 and 0.02,
respectively.
Headline
Inflation
Distorted
Headline
Core
Inflation
Optimal
Inflation
Global
Rank
Optimal
Weight ϖ
Welfare 0,013 0,000 0,018 2 0,68
Local Rank 1 2
Welfare 0,012 0,013 0,000 0,015 3 0,36
Local Rank 2 1 3
Welfare 0,015 0,018 0,000 0,016 1 0,30
Local Rank 2 1 3
Model I
(κr=κn=0)
Model II
(κr=0, κn=0.5)
Model III
(κr=κn=0.5)
- 49 -
5.5.2 Distributional Welfare Evaluation
To better understand the consequences of fiscal and monetary
policy combinations have on aggregate welfare, we also
analyze the heterogeneous distributional effects these
policies have on the two household types.
From the perspective of non-Ricardians, welfare is strictly
increasing in the value of fiscal intervention parameter 𝜅𝔫
in the event of a transitory food price shock. The reason
for this is non-Ricardians are unable to smooth consumption,
unlike the Ricardian household, however the government can
do so for non-Ricardians households by borrowing vis-à-vis a
food price subsidy. Furthermore, welfare for non-Ricardians
is also strictly increasing when monetary policy targets
distorted headline inflation relative to core inflation.
Table 3: Non-Ricardian Welfare (Food Price Shock)
Note: The welfare gains are calculated as gains in
consumption units relative to core inflation and are based
on an orthogonal shock to the world price of food.
Our results in Table 4 below suggest a polar case for the
Ricardian household type. From the perspective of the
Ricardian household, the best fiscal policy is to minimize
the degree of fiscal intervention and the best monetary
policy regime is to target core inflation. In the event of
moderate (intense) fiscal intervention (proxied by Model II
Headline
Inflation
Distorted
Headline
Core
Inflation
Optimal
Inflation
Global
Rank
Optimal
Weight ϖ
Welfare 0,060 0,000 0,064 3 0,21
Local Rank 1 2
Welfare 0,040 0,042 0,000 0,040 2 0,00
Local Rank 2 1 3
Welfare 0,034 0,040 0,000 0,034 1 0,00
Local Rank 2 1 3
Model I
(κr=κn=0)
Model II
(κr=0, κn=0.5)
Model III
(κr=κn=0.5)
- 50 -
and Model III, respectively) welfare is improving when
monetary policy targets core (distorted) inflation.
Table 4: Ricardian Welfare (Food Price Shock)
Note: The welfare gains are calculated as gains in
consumption units relative to core inflation and are based
on an orthogonal shock to the world price of food.
We present the distributional welfare based on exogenous
shocks to aggregate productivity in the Appendix (Tables 6
and 7).
6 Conclusion
We develop a DSGE model to show how fiscal and monetary
authorities interventions should be designed to shield
households’ from food price volatility in an emerging
economy. Based on a standard new Keynesian model with two
sectors, heterogeneous agents, sticky prices and limited
assets market participation. The novelty of our approach is
we consider fiscal intervention through the effect of
consumer subsidies. This is a key, realistic feature of
emerging markets considering the prevalence of food price
subsidies observed in fourteen emerging market economies
which are a central component of the pass-through from world
Headline
Inflation
Distorted
Headline
Core
Inflation
Optimal
Inflation
Global
Rank
Optimal
Weight ϖ
Welfare -0,018 0,000 0,000 1 1,00
Local Rank 2 1
Welfare -0,007 -0,006 0,000 0,007 2 0,59
Local Rank 3 2 1
Welfare 0,002 0,003 0,000 0,014 3 0,50
Local Rank 2 1 3
Model I
(κr=κn=0)
Model II
(κr=0, κn=0.5)
Model III
(κr=κn=0.5)
- 51 -
food prices to domestic inflation. In explicitly modeling
food price subsidies we show such a policy can create a
wedge between distorted prices faced by household and market
clearing prices. This allows us to capture key factors to
analyze fiscal and monetary policy simultaneous responses to
food prices volatility.
Our research overlaps with a small, burgeoning literature
providing evidence overturning the conduct of monetary
policy focusing strictly on core inflation for an
aforementioned environment facing financial frictions. We
find that the optimal policy response does not overlook the
effect of headline inflation.
We find that targeting distortive headline inflation
achieves the highest welfare. While this is a leaning
against the wind approach to monetary policy, we consider
this as finding a middle-ground, particularly for Ricardians
(who can smooth consumption over time), in the event of
fiscal intervention. 26
This implies that targeting distorted
inflation results in an interest rate response below
headline inflation target, but higher than core inflation
targeting.
There are distributional effects based on the policy
reaction. In particular, we find the relative importance of
headline inflation increases the higher the intensity of
fiscal intervention. This is an important, yet intuitive,
result: as non-Ricardians are sensitive to changes in food
prices considering a substantial share of expenditures are
attributed to food and their limited financial access to
smooth consumption. The government can thus borrow for non-
26 In the event of no fiscal intervention (Model I), core inflation
achieves the highest welfare (see Table 4).
- 52 -
Ricardians, thereby decreasing non-Ricardians’ vulnerability
to food price shocks. We also find a compositional
distribution mix. Food subsidies, if the government
efficiency is with reason, can not only be welfare improving
for the non-Ricardian household, but also be strong enough
to more than offset than the welfare losses for the
Ricardian household in aggregate.
Lastly, we argue that coordinated fiscal and monetary
policies may be desirable considering the optimal joint
policy reactions are interdependent. This is an important
property considering an inefficient reaction due to
uncoordinated monetary/fiscal policy may potentially
diminish some of the benefits provided by fiscal policy
responses. Therefore, we consider that central bank
independence in developing countries with food prices
subsidies should not be achieved without consideration of
the cost of a lack of monetary and fiscal policy
coordination. The optimal institutional design remains an
open question for future works.
7 References
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8 Appendix
8.1 Food Prices by Commodity
Since the turn of the century, food prices for five major
commodities have generally moved together (see Figure 9
below).
Figure 9: Food Price Index by Commodity
Source: FAO of the United Nations. Base year: 2002-2004
weighted averages for five major commodity price indices:
meat, dairy, cereals, vegetable oils and sugar.
8.2 Steady State
We will define the deterministic steady state of the model
which loosely follows Fernández-Villaverde and Rubio-Ramírez
[2006].27 Prices are set to unity and there is zero price
inflation. To make the three fiscal models comparable, we
normalize bonds to zero, i.e. ℬ̅ = 0 in the steady state. This implies both the marginal tax rates and trade balance are
τ̅i,c = τ̅𝔯V =0 and TB=0, respectively.
27 We apply the equilibrium conditions using standard techniques for non-
linear models e.g. Fernández-Villaverde and Rubio-Ramírez [2006],
Section 4.1.
50
100
150
200
250
300
350
400
1990 1995 2000 2005 2010 2015
Food Price Index Meat Price Index
Dairy Price Index Cereals Price Index
Oils Price Index Sugar Price Index
- 56 -
Λ𝔯 = C𝔯−ρ
Λ𝔫 = C𝔫−ρ
R =1
β
u = 1
r =1
β− 1 + δ
𝑚𝑐𝑀 =𝜖 − 1
𝜖
𝑚𝑐𝑀 =1
(1 − 𝛼)1−𝛼
1
𝛼𝛼(𝑤𝔯
𝑀)1−𝛼(𝑟𝑀)𝛼
𝑌𝑀 =𝛾𝐶𝔫
𝑀 + (1 − 𝛾)𝐶𝔯𝑀
1 − 𝑚𝑐𝑀 𝛼𝛿𝑟𝑀
𝑘𝔯𝑀 = 𝛼 ⋅ 𝑚𝑐𝑀
𝑌𝑀
𝑟𝑀
𝑖𝔯𝑀 = 𝑌𝑀 − 𝛾𝐶𝔫
𝑀 − (1 − 𝛾)𝐶𝔯𝑀
𝑁𝔯𝑀 =
𝑘𝔯𝑀
(𝛼𝑟𝑀)
11−𝛼
𝑊𝔯𝑀 = 𝑚𝑐𝑀1−𝛼 𝑌𝑀
𝑁𝔯𝑀
𝑌𝐹 = 𝛾𝐶𝔫𝐹 + (1 − 𝛾)𝐶𝔯
𝐹
𝑁𝔯𝐹 =
𝑌𝐹
𝐴𝐹
𝑊𝔯𝐹 =
𝑌𝐹𝑝𝐹
𝑁𝔯𝐹
- 57 -
8.3 Impulse Response Functions
Figure 10: IRF World Food Price Shock (Model II)
Aggregate Consumption
Consumption of Food
Households
Consumption of Non-Food
Households
Headline Inflation Core Inflation Food Inflation
Interest Rate Distorted Headline
Inflation Distorted Food Inflation
Trade Balance Saving Government Debt
- 58 -
Exchange Rate Marginal Tax Rate (%) Subsidy (in % GDP)
Investment Output
Legend: — headline inflation targeting; – – core inflation
targeting
- 59 -
Figure 11: IRF World Food Price Shock (Model III)
Aggregate Consumption
Consumption of Food
Households
Consumption of Non-Food
Households
Headline Inflation Core Inflation Food Inflation
Interest Rate Distorted Headline
Inflation Distorted Food Price
Trade Balance Saving Government Debt
- 60 -
Exchange Rate Marginal Tax Rate (%) Subsidy (in % GDP)
Investment Output
Legend: — headline inflation targeting; – – core inflation targeting
- 61 -
Figure 12: IRF World Food Price Shock (Core Targeting)
Aggregate Consumption
Consumption of Food
Households
Consumption of Non-Food
Households
Headline Inflation Core Inflation Food Inflation
Interest Rate Distorted Headline
Inflation Distorted Food Inflation
Trade Balance Saving Government Debt
- 62 -
Exchange Rate Marginal Tax Rate (%) Subsidy (in % GDP)
Investment Output
Legend: — Model I; – – Model II; •• Model III
8.4 Welfare - Aggregate Shocks
Table 5: Aggregate Welfare Gain (Aggregate Shocks)
Note: aggregate shocks, which include perturbations on
aggregate productivity, the world interest rate and the
world price of food. The welfare gains are calculated as
gains in consumption units relative to core inflation.
Table 6: Non-Ricardian Welfare (Aggregate Shocks)
Headline
Inflation
Distorted
Headline
Core
Inflation
Optimal
Inflation
Global
Rank
Optimal
Weight ϖ
Welfare 0,019 0,000 0,022 3 0,67
Local Rank 1 2
Welfare 0,019 0,021 0,000 0,021 2 0,41
Local Rank 2 1 3
Welfare 0,023 0,027 0,000 0,023 1 0,35
Local Rank 2 1 3
Model I
(κr=κn=0)
Model II
(κr=0, κn=0.5)
Model III
(κr=κn=0.5)
- 63 -
Note: aggregate shocks, which include perturbations on
aggregate productivity, the world interest rate and the
world price of food. The welfare gains are calculated as
gains in consumption units relative to core inflation.
Table 7: Ricardian Welfare (Aggregate Shocks)
Note: aggregate shocks, which include perturbations on
aggregate productivity, the world interest rate and the
world price of food. The welfare gains are calculated as
gains in consumption units relative to core inflation.
Headline
Inflation
Distorted
Headline
Core
Inflation
Optimal
Inflation
Global
Rank
Optimal
Weight ϖ
Welfare 0,074 0,000 0,077 3 0,17
Local Rank 1 2
Welfare 0,070 0,073 0,000 0,070 2 0,00
Local Rank 2 1 3
Welfare 0,070 0,077 0,000 0,070 1 0,00
Local Rank 2 1 3
Model I
(κr=κn=0)
Model II
(κr=0, κn=0.5)
Model III
(κr=κn=0.5)
Headline
Inflation
Distorted
Headline
Core
Inflation
Optimal
Inflation
Global
Rank
Optimal
Weight ϖ
Welfare -0,018 0,000 0,000 1 1,00
Local Rank 2 1
Welfare -0,015 -0,014 0,000 0,004 2 0,69
Local Rank 3 2 1
Welfare -0,008 -0,007 0,000 0,010 3 0,59
Local Rank 3 2 1
Model I
(κr=κn=0)
Model II
(κr=0, κn=0.5)
Model III
(κr=κn=0.5)
