FUNDAÇÃO GETULIO VARGAS
ESCOLA DE ECONOMIA DE SÃO PAULO
GUILHERME AUGUSTO RIBEIRO
COMMODITY PRICE SHOCKS AND ECONOMIC POLICY: AN
ASSESSMENT OF THE BRAZILIAN CASE
São Paulo
2021
COMMODITY PRICE SHOCKS AND ECONOMIC POLICY: AN
ASSESSMENT OF THE BRAZILIAN CASE
Dissertação apresentada à Escola de Econo-mia de São Paulo como pré-requisito à ob-tenção de título de mestre em Economia de Empresas.
Orientador: Pierluca Pannella.
São Paulo
2021
Ribeiro, Guilherme Augusto.
Commodity price shocks and economic policy: an assessment of the Brazilian case / Guilherme Augusto Ribeiro. - 2021.
60 f.
Orientador: Pierluca Pannella.
Dissertação (mestrado CMEE) – Fundação Getulio Vargas, Escola de Economia de São Paulo.
1. Mercadorias. 2. Preços - Determinação. 3. Política monetária. 4. Política tributária. 5. Econometria. I. Pannella, Pierluca. II. Dissertação (mestrado CMEE) – Escola de Economia de São Paulo. III. Fundação Getulio Vargas. IV. Título.
CDU 339.172
Ficha Catalográfica elaborada por: Isabele Oliveira dos Santos Garcia CRB SP-010191/O Biblioteca Karl A. Boedecker da Fundação Getulio Vargas – SP
COMMODITY PRICE SHOCKS AND ECONOMIC POLICY: AN
ASSESSMENT OF THE BRAZILIAN CASE
Dissertação apresentada à Escola de Econo-mia de São Paulo como pré-requisito à ob-tenção de título de mestre em Economia de Empresas.
Data de aprovação:
Banca examinadora:
Prof. Dr. Pierluca Pannella FGV-EESP (Orientador)
Prof. Dr. Marcel Bertini Ribeiro FGV-EESP
Prof. Dr. Samer Shousha
Division of International Finance, Federal Re-serve Board
Agradecimentos
Ao meu orientador, muito obrigado por todo apoio ao longo desse período tão importante. Foi essencial ter contado com seus conhecimentos, suas intuições e comentários sempre edificantes e generosos. Aos membros da banca, agradeço imensamente pelas valorosas observações e críticas apresentadas.
Aos queridos amigos que fiz ao longo desses anos. Obrigado por tudo, Fernanda, Laura, Marcondes, Richard, Rafael, Vanessa e, apesar dos pesares, Tomaz. Essa jornada certamente teria sido muito mais difícil se não compartilhada com vocês!
Aos amigos do Pas nas Redes, por toda resenha futebolística e não-futebolística que alivia os nossos dias.
A Gabi, por estar ao meu lado o tempo todo, dividindo todas as alegrias e todas as dores. É um prazer e um privilégio estar acompanhado de uma pessoa tão especial.
À minha família, que me deu toda a sustentação e o incentivo para que eu chegasse até aqui. Meus pais, Carlos e Meire, minha irmã, Beatriz, muito, muito obrigado!
O presente trabalho foi realizado com apoio da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Código de Financiamento 001.
Ao longo das últimas duas décadas, flutuações nos preços internacionais de commodities e mudanças na condução da política econômica foram ambas responsabilizadas pela trajetória da economia brasileira. Neste artigo, avaliamos a importância dos choques de preços de commodities e suas interações com as políticas monetária e fiscal. Construímos e estimamos um modelo de pequena economia aberta com três setores, rigidez nominal, uma combinação de agentes Ricardianos e não-Ricardianos, e um governo seguindo regras de política monetária e fiscal. Em contraste com artigos que negligenciam rigidezes nominais e o papel do governo, encontramos uma pequena participação dos choques de preços de
commodities na variância do PIB. Mostramos que a presença de uma política reativa
e a modelagem explícita da produção de commodities são cruciais para explicar essa diferença. Quando cancelamos esses elementos, a contribuição dos choques de preços de
commodities para a variância do PIB chega a 19.64%. A análise de bem-estar sugere
que, em resposta a choques no setor de commodities, uma combinação de política mais contra-cíclica e estabilizadora da dívida pública gera ganhos de bem-estar em relação à regra fiscal estimada.
Palavras-chave: Choques de preços de commodities, Pequena economia aberta, Econo-metria Bayesiana, Política monetária, Política fiscal.
Abstract
Over the last two decades, swings in international commodity prices and shifts in the conduction of domestic economic policy were both deemed responsible for the developments of the Brazilian economy. In this paper, we assess the importance of commodity price shocks and their interactions with monetary and fiscal policies. We build and estimate a three-sector SOE model featuring nominal rigidities, a combination of Ricardian and non-Ricardian households, and a government following a monetary and a fiscal rule. In contrast to papers neglecting nominal disturbances and the role of government, we find that commodity price shocks play a small role in explaining the GDP variance. We show that the presence of counteracting policy and the explicit modeling of commodity production are crucial to explain this difference. When we mute these elements, the contribution of commodity price shocks to GDP variance rises from 1.45% to 19.64%. A welfare analysis suggests that, in response to commodity shocks, a mix of a more counter-cyclical and debt-stabilizing policy is welfare-improving relative to the estimated fiscal rule.
Keywords: Commodity price shocks, Small Open Economy, Bayesian econometrics,
Figura 1 – Impulse responses to a 1% commodity price shock. . . 42
Figura 2 – Impulse responses to a 1% risk-premium shock. . . 46
Figura 3 – Fiscal policy welfare analysis: debt-stabilization v.s. counter-cyclicality. 49
Figura 4 – Monetary policy welfare analysis. . . 51
Figura B.0.1–Impulse responses to a 1% commodity productivity shock. . . 58
Figura B.0.2–Fiscal policy welfare analysis: debt-stabilization v.s. counter-cyclicality. 59
Lista de tabelas
Tabela 1 – Calibrated Parameters . . . 36
Tabela 2 – Estimated parameters: priors and posteriors . . . 39
Tabela 3 – Estimated parameters: priors and posteriors (continuation) . . . 40
Tabela 4 – Forecast error variance decomposition (FEVD) - baseline estimation. . 43
1 INTRODUCTION . . . 11
2 MODEL . . . 14
2.1 Households . . . 15
2.1.1 Consumption-savings problem of a Ricardian Household . . . 16
2.1.2 Wage setting problem of a Ricardian Household . . . 18
2.1.3 Non-Ricardian households . . . 20
2.2 Firms . . . 20
2.2.1 Retail firms . . . 21
2.2.2 Commodity sector . . . 22
2.2.3 Wholesale tradable firms . . . 22
2.2.3.1 Input choice . . . 23
2.2.3.2 Price setting to the domestic market . . . 24
2.2.3.3 Price setting to the foreign market . . . 24
2.2.4 Wholesale non-tradables firms . . . 24
2.2.4.1 Input choice . . . 25 2.2.4.2 Price setting . . . 25 2.2.5 Wholesale Importers . . . 26 2.2.6 Final good . . . 27 2.3 Government . . . 27 2.3.1 Fiscal Policy . . . 27 2.3.2 Monetary policy . . . 29 2.4 Foreign Economy . . . 30
2.5 Stochastic processes of shocks . . . 30
2.6 Equilibrium . . . 31
3 ESTIMATION . . . 33
3.1 Data and shocks . . . 33
3.2 Calibration . . . 34
4 EMPIRICAL RESULTS . . . 38
4.1 The commodity price shock. . . 40
4.2 Business cycle drivers . . . 43
4.3 The risk-premium shocks . . . 45
5 WELFARE ANALYSIS . . . 47
5.1 Fiscal policy . . . 47
5.2 Monetary policy . . . 50
6 CONCLUSION . . . 52
REFERÊNCIAS . . . 53
APÊNDICE A – PRICE-SETTING PROBLEMS . . . 55
A.1 Price-setting problems in domestic currency . . . 55
A.2 Price-setting problem in foreign currency . . . 56
1 Introduction
Over the last two decades, the big picture of the Brazilian economic outlook coinci-ded with the large cyclical movements of international commodity prices as well as with the shifts in the conduction of monetary and fiscal policies. It is rather common to attribute the period of economic and social prosperity from the early 2000s until the early 2010s to a virtuous combination of a historically long and intense ascending phase of international commodity prices with the success in the implementation of stabilization policies. From 2001 until 2011, Brazil experienced an average increase in the international prices of its commodities exports in the order of 159%1. In parallel, the successful implementation of an inflation targeting regime in conjunction with a system of primary result targets allowed for the stabilization of inflation and public debt around comfortable levels for Brazilian standards, enabling a decade of sustained growth, with an average GDP per capita growth rate of 2.8% per year. In the same vein, the economic slowdown after 2010, which culminated in the largest recession of the country’s history, also coincided with the reversal of international commodity prices and deleterious flexibilizations in the conduction of monetary and fiscal policies. In contrast to the previous prosperous period, commodity prices fell on average 36%, whereas GDP per capita decreased at an average yearly rate of 0.4% between 2012 and 2019.
Motivated by this recent historical background, the present work aims to assess the importance of commodity price shocks and their interactions with monetary and fiscal policy tools for the Brazilian economy. Towards this end, we build and estimate using Bayesian techniques a three-sector (commodities, tradables2 and non-tradables) Small Open Economy (SOE) model featuring nominal rigidities and a government block that captures the functioning of the Brazilian inflation targeting regime and the system of primary result targets. Unlike previous studies neglecting nominal rigidities and the role of government, the estimated model attributes small participation of commodity price shocks in the variance decomposition of GDP (1.45%). This is explained by the presence of counteracting policy, the explicit modeling of commodity production, and a wider set
1 According to IMF’s Commodity Export Price Index. 2 Non-commodity tradable goods.
Capítulo 1. Introduction 12
of shocks. In simulations addressing each of these dissimilarities to RBC models, the contribution of commodity price shocks to GDP variance increases, reaching 19.64%.
This paper relates to the vast literature investigating the role of foreign shocks to SOEs’ business cycles. Since the seminal contribution ofMendoza (1995), mounting evidence over the impacts of foreign shocks to the business cycle dynamics of SOEs was developed, pointing, in general, towards sizeable participation in the volatility of aggregate variables.3 More recently, the efforts of many researchers was concentrated on commodity price shocks as business cycle drivers. Especially when analyzing Emerging Market Economies (EMEs), authors find a significant contribution of innovations in the international commodity prices exported by these countries in the variance decomposition of output, consumption, and investment. The results range from 20 to 40 percent of the business cycle fluctuations attributed to commodity price shocks.
Fernández, Schmitt-Grohé e Uribe(2017) estimate SVARs for a set of 138 countries and find that, on average, one-third of output variance in this sample is due to commodity price shocks. Shousha (2016) estimates a Panel SVAR for a restricted set of emerging economies and concludes that commodity price shocks account for 23% of the variance of output.4 Both papers do not consider fiscal and monetary responses, which is also a common factor among papers evaluating the importance of commodity price shocks to business cycle fluctuations through the estimation of RBC models. In special, we highlight
Fernández, González e Rodriguez (2018) whose estimates suggest that 27.5% of GDP variance in Brazil is attributed to commodity price shocks. In a model estimated for the Argentinian economy,Drechsel e Tenreyro (2018) find a 37.9% participation of commodity price shocks in GDP variance.
Overall, the aforementioned literature, which we henceforth refer to as “RBC-SOE literature”, contributes to the widely accepted view that EMEs are heavily vulnerable to foreign conditions. However, neither of these papers considers the presence of counter-cyclical economic devices which might mitigate the importance of external shocks.5 The goal of this paper is to fill this gap.
3 See e.g.Kose(2002) andUribe e Yue(2006).
4 Namely, the set of emerging economies considered contains Argentina, Brazil, Chile, Colombia, Peru,
and South Africa.
5 This idea is present e.g. in the concluding remarks of Shousha (2016) and Fernández, González e
This paper also relates to the literature on welfare analysis of SOEs’ fiscal responses (Garcia, Restrepo e Tanner (2011), Ojeda-Joya, Parra-Polania e Vargas (2016), Medina e Soto (2016), García-Cicco e Kawamura (2015)) and monetary responses (Dib (2008),
Garcia e González (2013), Garcia e González (2014), Hevia e Nicolini (2014), Catão e Chang(2013), Lama e Guzman(2010)) to commodity shocks. In particular, our model structure is closer toDib (2008), which is the only one among these papers to encompass nominal price and wage rigidities, active monetary and fiscal authorities, as well as a three-sector structure with explicit modelling of the commodity production. Moreover,
García-Cicco e Kawamura (2015) and Lama e Guzman (2010) are primarily concerned with Dutch Disease effects and thus consider learn-by-doing externality in the tradable sector and financial frictions, which is outside the scope of this paper.
The welfare analysis of fiscal policy suggests that a mix of a more counter-cyclical and debt-stabilizing policy is welfare-improving relative to the estimated rule representing the Brazilian system of primary result targets. Our analysis is similar to the ones conducted by Garcia, Restrepo e Tanner (2011) and Ojeda-Joya, Parra-Polania e Vargas (2016), who compute welfare effects of commodity shocks given a system of structural surplus.6 Concerning the welfare analysis of monetary policy, our results follow the principle sum-marized by Ragan (2005). Exchange rate variations originated in shocks that directly affect demand for domestic goods (e.g. commodity price shocks) are stabilizing and thus should not be confronted by the monetary authority. On the other hand, exchange rate fluctuations originated in shocks that do not directly affect demand for domestic goods (e.g. risk-premium shocks) are destabilizing. Hence, in this case, putting some weight on real exchange rate variations in the monetary rule increases the performance of the monetary policy. This prediction is corroborated byGarcia e González (2013) and also appears in our model.
The remaining of this paper develops as follows: Section 2 outlines the model; Section 3describes estimation procedure and the data set adopted; Section 4 presents and discusses the main results of model estimation; Section5 performs welfare evaluations of fiscal and monetary policies; Section 6concludes.
6 Systems of structural surplus are currently adopted by countries heavily dependent on commodity
exports revenues, such as Chile and Colombia. In a nutshell, these systems consist of rules that attach the government spending to a long-run level of international prices of commodities exported by the country. The objective is to make fiscal policy more acyclical, avoiding drastic reversals in government spending that could be caused by large shifts in commodity prices.
14
2 Model
The model combines features of the RBC-SOE literature focused on commodity price shocks (Shousha(2016),Fernández, González e Rodriguez(2018),Drechsel e Tenreyro
(2018)) with traditional elements of New Keynesian models. Namely, building on Dib
(2008), we consider the rich productive structure of a three-sector model with nominal rigidities as well as monetary and fiscal policies. Labor and capital are employed in the production of commodities, tradable and non-tradable goods. Moreover, nominal rigidities are introduced in price and wage-setting.
Commodities are inputs for the production of tradable goods and their prices are determined exogenously in the foreign markets. That is, we assume that the Law of One Price (LOP) holds even in the short run for commodity goods and their production is perfectly competitive. Tradable goods, on the other hand, are subject to nominal rigidities. Monopolist firms set different prices for domestic and foreign markets, so we have an incomplete pass-through on exports of tradables. Non-tradable goods are also produced by monopolists and can only be consumed domestically. Finally, imported goods encompass incomplete pass-through by the action of monopolist importers, which differentiate a homogeneous good bought abroad. The final good, used for household consumption, investment, and government consumption, consists of an aggregation of tradables, non-tradables, and imported goods.
The government manages both fiscal and monetary policies. Inspired on Castro et al. (2015), the fiscal rules aim to describe the functioning of the Brazilian primary surplus targeting regime, introduced in 1999. Moreover, the monetary policy rule mimics the inflation targeting regime, implemented in the same year. Even though the real exchange rate stabilization is not an official objective in the conduction of the Brazilian Central Bank (BCB) monetary policy, we include deviations of this variable in the monetary rule for welfare analysis purposes. Nevertheless, as Section 4 shows, our estimates find no evidence that the BCB uses the nominal interest rate as an instrument to stabilize the real exchange rate.
to nominal rigidities. They are owners of firms and allocate the income from labor and profits between consumption, investment in productive capital, domestic bonds, and bonds denominated in foreign currency. Moreover, we introduce a fraction of non-Ricardian households. That is, agents who are not owners of firms nor can access the credit markets and therefore must consume their current net income from labor. Aside from being a realist feature of the Brazilian economy, the introduction of this class of agents - often referred to as “hand-to-mouth” agents - is a common practice in the literature on fiscal policy rules. Different from an economy exclusively inhabited by traditional Ricardian households, the presence of non-Ricardians enables the path of primary results to produce real effects and has non-trivial consequences for welfare results.
In the subsections below, the model is described in detail.
2.1
Households
The domestic economy is inhabited by a continuum of infinitely-living households indexed by h ∈ [0, 1]. The discounted present value of lifetime utility at period t is defined as Ut(h) ≡ Et ∞ X `=0 β` " ζC,t Ct(h)1−σ 1 − σ − ζH,t Ht(h)1+χ 1 + χ # , [2.1]
where σ > 0 is the inter-temporal elasticity of substitution of consumption; χ > 0 is the inverse of the Frisch labor elasticity; Ct(h) denotes household h’s consumption of
a composite of tradable, non-tradable and imported goods; ζC,t and ζH,t are stationary
preference shocks to consumption and leisure, respectively. Both shocks evolve following a simple AR(1) process.
The household supplies hours of labor to commodity, tradable and non-tradable sectors, indexed by X, T and N , respectively. The variable Ht(h) that enters (2.1) is a
composition of hours supplied to each of these sectors:
Ht(h) = HX,t(h) 1+η η + H T ,t(h) 1+η η + H N,t(h) 1+η η 1+ηη , [2.2]
Capítulo 2. Model 16
2.1.1
Consumption-savings problem of a Ricardian Household
A fraction 1 − λN R of the households of the economy is Ricardian. That is, these
agents have access to credit markets and allocate inter-temporally their expected flow of income between consumption and savings in order to maximize their expected present value of utility (2.1) subject to an inter-temporal budget constraint. Ricardian household
h acquires income from three sources: i) supplying hours of its labor Hi,t(h) at nominal
hourly wage Wi,t(h) to sectors i = X, T, N ; ii) renting capital Ki,t(h) at nominal rental
price RK
i,t to sectors i = X, T, N ; iii) receiving their share of nominal profits from the firms
they own Di,t(h), i = X, T, N, F .
Savings can take the form of three kinds of assets. A Ricardian household h can invest in productive capital Ii,t(h) in sectors i = X, T, N . They can also access the domestic
and foreign credit markets. A one-period domestic bond Bt−1(h) acquired in period t − 1
by household h pays the gross nominal interest rate Rt−1 in t. The foreign asset Bt−1∗ (h)
acquired by household h in period t − 1 is denominated in foreign currency and pays in t the international nominal gross interest rate R∗t−1 times the country risk-premium Θt−1.
The country risk-premium is increasing in the aggregate foreign net deb-to-GDP ratio −BY,t∗ ≡ −tB∗t
PtYt.
1 This assumption gives rise to the so-called balance-sheet effect as described by Céspedes, Chang e Velasco(2004), i.e. an increase in country-risk premium following a nominal exchange rate depreciation (↑ t), once it increases the value of domestic
liabilities denominated in foreign currency. Moreover, as suggested by Schmitt-Grohé e Uribe(2003), this is a technical device that ensures stationarity to SOE models. In addition, following the recent RBC-SOE literature (e.g.Shousha (2016), Drechsel e Tenreyro (2018) and Fernández, González e Rodriguez (2018)), we consider the empirical regularity of a negative relation between a country’s commodity export prices and risk-premium in foreign markets in a reduced form:
Θt= Θ exp h −θB∗(B∗ Y,t− B ∗ Y) − θp∗X(p∗X,t− p ∗ X) i ζΘ,t, [2.3]
where ζΘ,t is a stationary shock to the country risk-premium and the parameters θB∗, θp∗
X >
0 define the sensitivity of the country risk-premium to deviations from steady state of aggregate foreign net debt-to-GDP ratio and international real commodity prices, respectively.
1 B∗
The intertemporal budget constraint of a Ricardian household h is given by: Pt CtR(h) + It(h) + Bt(h) Rt +tB ∗ t(h) R∗tΘt = X i=T ,N,X
Hi,tR(h)Wi,t(h) + Ki,t(h)RKi,t
+ Bt−1(h) + tBt−1∗ (h) + X i=T,N,F Di,t(h) − Tt, [2.4]
where It(h) ≡ IX,t(h)+IT ,t(h)+IN,t(h) denotes total capital investment made by household h and Tt is a net lump-sum tax.
Capital adjustment is costly. The stock of physical capital in sector i = T, N, X evolves according to the following law of motion:
Ki,t+1 = ζI,tIi,t+ (1 − δ) Ki,t− Ψi
Ki,t+1 Ki,t
!
Ki,t, [2.5]
where ζI,t is a stationary shock to the efficiency of investment, common to all sectors, and
Ψi
K
i,t+1
Ki,t
is a strictly increasing and convex function governing the adjustment cost of capital in sector i. It must satisfy Ψi(1) = 0, so that in steady-state there is no adjustment
cost. In particular, we adopt the conventional functional form: Ψi Ki,t+1 Ki,t ! ≡ ψi 2 Ki,t+1 Ki,t − 1 !2 , ψi > 0.
The consumption-savings problem of a Ricardian household h at period t is to choose a sequencenCR
t+`(h), Ii,t+`(h), Ki,t+`+1(h), Bt+`(h), Bt+`∗ (h)
o∞
`=0, i=X,T ,N in order to
maximize the discounted present value of utility (2.1), subject to the inter-temporal budget constraint (2.4) and the law of motion of capital (2.5). The optimality conditions are given by: λt= ζC,t CtR(h)−σ [2.6] λt Rt = β Et " λt+1 Πt+1 # [2.7] λt R∗tΘt = β E t " λt+1t+1/t Πt+1 # [2.8] 1 + ψi Ki,t+1 Ki,t − 1 ! =β ζI,tEt ( λt+1 λt " RK i,t+1 Pt+1 + 1 ζI,t+1 × 1 − δ + ψi Ki,t+2 Ki,t+1 − 1 ! Ki,t+2 Ki,t+1 − ψi 2 Ki,t+2 Ki,t+1 − 1 !2 . [2.9]
Capítulo 2. Model 18
In the equations above, λt denotes the Lagrange multiplier associated to the
inter-temporal budget constraint, which is equivalent to the marginal utility of consumption. Domestic final good gross inflation rate is denoted by Πt ≡ PPt−1t . Moreover, in equation
(2.9) we combine the first-order conditions with respect to Ii,t(h) and Ki,t(h) to obtain the
sectoral capital Euler equations.2 Combining the log-linearized first-order conditions with respect to domestic (2.7) and foreign (2.8) net assets, one obtains the Uncovered Interest Parity (UIP) relationship linking domestic and international interest rates: ˆRt− ˆRt∗ =
ˆ
Θt+ Et[∆ˆt+1].
2.1.2
Wage setting problem of a Ricardian Household
Each Ricardian household h is the monopolist of its differentiated labor type and thus has the power to set its nominal hourly wage Wi,t(h) to work for firms in sectors i = X, T, N . Given the hourly wages set, a household must supply any amount of labor
services demanded by its employers. Following Erceg, Henderson e Levin (2000), we assume that, for each sector, an employment agency intermediates the relationship between households and firms. That is, the employment agency combines the differentiated labor types through a Dixit-Stiglitz aggregator and then sells the aggregate labor services to firms in competitive input markets for each sector i = X, T, N :
Hi,t = Z 1 0 Hi,t(h) ϑ−1 ϑ dh ϑ−1ϑ , [2.10]
where ϑ > 0 is the elasticity of substitution between differentiated labor types. The sectoral employment agencies solve the following profit maximization problem
max {Hi,t(h)}1h=0 Wi,tHi,t − Z 1 0 Wi,t(h) Hi,t(h) dh s.t. (2.10),
where Wi,t is the aggregate nominal wage index prevailing in sector i = X, T, N . The
solution yields the demand curves faced by household h in the wage setting for each sector:
Hi,t(h) =
Wi,t(h) Wi,t
!−ϑ
Hi,t. [2.11]
Applying (2.11) to (2.10), we retrieve the sectoral wage indexes:
Wi,t = Z 1 0 Wi,t(h)1−ϑdh 1−ϑ1 , [2.12]
The Ricardian households face rigidities as in Calvo (1983) to set their nominal wages to sectors i = X, T, N . Each period, with probability 1 − ϕi, a household h receives
a signal to optimally reset its nominal wage with the employment agency in sector i. With probability ϕi, the household can only update its nominal wage by the current inflation
target, ¯Πt. The probability of receiving a signal is independent of the household’s history.
Thus, in t + `, a Ricardian household h which has last optimally adjusted its sector i’s nominal wage in period t follows the indexation rule
Wi,t+`R (h) = ΓWi,t+`Wi,tR(h), where
ΓWi,t+` ≡ ΓWi,t+`−1Π¯t+`, if ` > 0 and ΓWi,t = 1.
The wage setting problem of a Ricardian household h to sector i = X, T, N is characterized below. It chooses ˜Wi,tR(h) in order to maximize utility subject to the intertemporal budget constraint and the demand for its differentiated labor type over the expected window of indexation. Considering only the relevant terms, this problem is equivalent to maximizing the difference between the utility arising from extra real labor income and the disutility of labor:
max ˜ WR i,t(h) Et ∞ X `=0 (β ϕi)` λt+`ΓWi,t+` ˜ WR i,t(h) Pt+` Hi,t+`R (h) − ζH,t HR t+`(h) 1+χ 1 + χ , subject to Hi,t+`R (h) = Γ W i,t+`W˜i,tR(h) Wi,t+` !−ϑ Hi,t+`.
After some straightforward algebra, the first order condition yields the following expression for the optimal nominal wage in sector i = X, T, N :
˜ WtR(h) = ϑ ϑ − 1 Et P∞`=0(β ϕi)`ζH,tHt+`R (h) χ−η+11 HR i,t+`(h) 1 η ΓW i,t+` −ϑ Wϑ i,t+`Hi,t+` Et P∞`=0(β ϕi)`λt+`ΓWi,t+` 1−ϑ Wi,t+`ϑ−1Hi,t+`Pt+`−1 .
The expression above can be rewritten recursively, as in Dib (2008), so that the optimal real wage in sector i is given by
˜ wRi,t(h) ≡ ˜ WR i,t(h) Pt = ϑ ϑ − 1 f1 i,t f2 i,t , [2.13]
Capítulo 2. Model 20
where f1
i,t and fi,t2 are auxiliary variables defined as fi,t1 = ζH,tHtR(h) χ− 1 η+1HR i,t(h) 1 ηH i,twi,tϑ + β ϕiEt h ¯ Π−ϑt+1Πt+1ϑfi,t+11 i [2.14]
fi,t2 = λtHi,twi,tϑ + β ϕiEt
h ¯
Π1−ϑt+1 Πt+1ϑ−1fi,t+12
i
. [2.15]
In the symmetric equilibrium, each Ricardian household receiving a signal to adjust its wage in sector i = X, T, N chooses the same optimal wage: ˜WR
i,t(h) = ˜Wi,tR. Therefore,
the law of motion of the average sectoral wage set by Ricardian households is given by:
Wi,tR1−ϑ = ϕi ¯ ΠtWi,t−1R 1−ϑ + (1 − ϕi) ˜ Wi,tR1−ϑ. [2.16]
2.1.3
Non-Ricardian households
Non-Ricardian households have no access to credit markets, do not own the firms, and cannot invest in capital. Therefore, they simply consume their real disposable income from labor: CtN R = X i=X,T ,N WN R i,t Pt Hi,tN R ! − Tt Pt , [2.17] where WN R
i,t and Hi,tN R denote the wage set and hours worked by non-Ricardian households
in sector i.
For simplicity, following Medina, Soto et al. (2007) and Castro et al. (2015), we assume that non-Ricardian households simply set their wages equal to the average wage set by Ricardian households, i.e. Wi,tN R= Wi,tR. This implies that Wi,t = Wi,tR and thus the law
of motion proposed in (2.16) also applies to aggregate sectoral wages over all households. That is, Wi,t1−ϑ = ϕi ¯ ΠtWi,t−1 1−ϑ + (1 − ϕi) ˜ Wi,t 1−ϑ .
Moreover, since Ricardian and non-Ricardian households face the same demand schedules for labor services, having WN R
i,t = Wi,tR means that hours supplied by non-Ricardians are
equal to the average of hours supplied by Ricardian households, i.e. HN R
i,t = Hi,tR.
2.2
Firms
Domestic production takes place in three steps. First, labor and capital are employed in the production of three kinds of goods: a commodity homogeneous good YX,t, tradable
YT ,t(j) and non-tradable varieties YN,t(j) , j ∈ [0, 1]. The commodity good is used as input
in the production of tradable varieties or exported. Second, retail sectoral firms bundle the varieties into tradable and non-tradable composite goods, Yd
T,tand YN,t, respectively.3 Third
and last, a representative firm combines tradable, non-tradable, and imported composite goods to produce the final good Zt, used as investment, household, and government
consumptions.
In opposition to retail firms, we call “wholesale firms” the monopolists producing tradable and non-tradable varieties. The same logic applies to importers. That is, in parallel to the domestic productive structure, there are wholesale importers, which sell varieties of imported goods YF,t(j), j ∈ [0, 1], and retail importers, which bundle these
varieties into the composite imported good YF,t. We begin our detailed description of the
productive structure from retail firms.
2.2.1
Retail firms
The production by sectoral retail firms of composite tradable, non-tradable, and imported goods are analogous. Competitive retail firms in sector s ∈ {T, N, F } buy varieties and combine them to produce a composite sectoral good according to technology
Ys,t= Z 1 0 Ys,t(j) θ−1 θ dj θ−1θ ,
where T, N and F indexes denote tradable, non-tradable and import sectors, respectively. Moreover, θ > 0 denotes the elasticity of substitution between varieties.
Each variety is bought at the price Ps,t(j) set by its wholesale monopolist producer.
The cost minimization problem of retail firms yields the demand curves faced by each wholesale firm. Letting Ps,t denote the price of the sectoral composite good, we have:
Ys,t(j) =
Ps,t(j) Ps,t
!−θ
Ys,t, j ∈ [0, 1], s ∈ {T, N, F }. [2.18]
Applying (2.18) to the aggregation technology of retail firms, we obtain the expres-sion for sectoral price indexes:
Ps,t= Z 1 0 Ps,t(j)1−θdj 1−θ1 , s ∈ {T, N, F } . 3 The superscript d in Yd
Capítulo 2. Model 22
Next, we characterize the commodity producers as well as wholesale firms in the tradable, non-tradable, and import sectors.
2.2.2
Commodity sector
Commodity producers are competitive and take as given the international commo-dity price denominated in foreign currency PX,t∗ , i.e. we adopt the traditional assumption that our economy cannot influence the international commodity prices. Firms hire labor
HX,t and rent capital KX,t to produce according to technology YX,t= AX,tKX,tαXH
1−αX
X,t , [2.19]
where αX ∈ [0, 1] is the share of capital in commodity production and AX,t is a stationary
productivity shock to the commodity sector.
Commodity production can be consumed domestically, as inputs in the tradable sector, or internationally. The nominal price PX,t∗ received by commodity firms is the same in both markets. Given sectoral hourly wages, WX,t and capital rental price RKX,t the profit
maximization problem of such firms resumes to max {HX,t,KX,t} h tPX,t∗ YX,t− WX,tHX,t− RKX,tKX,t i . Pt,
subject to the production technology (2.19). The first-order conditions related to optimal input choices are given by
rX,tK = αXRERtp∗X,t YX,t KX,t [2.20] wX,t = (1 − αX) RERtp∗X,t YX,t HX,t , [2.21] where RERt ≡ t Pt∗ Pt, p ∗ X,t ≡ P∗ X,t P∗ t , wX,t ≡ WX,t Pt and r K X,t ≡ RK X,t
Pt denote the real
exchange rate, the real price of commodities in foreign currency, the sector X’s real wage, and real rental price of capital sector X, respectively.
2.2.3
Wholesale tradable firms
There is a continuum j ∈ [0, 1] of monopolist that use labor, HT ,t(j), capital, KT ,t(j), and commodities, YX,tT (j), as inputs to produce according to
YT ,t(j) = AT ,tKT ,t(j)αT HT ,t(j)γT YX,tT (j)
where αT, γT ∈ [0, 1] denote, respectively, the shares of capital and labor in the tradable
production and AT ,t is a stationary productivity shock common to all firms in tradable
sector.
The supply of a wholesale tradable firm j is in part consumed domestically, Yd T,t(j),
and in part exported, Yex T ,t(j): YT ,t(j) = YT ,td (j) + Y
ex
T ,t(j). [2.23]
We assume local currency pricing. That is, firm j sets PT,t(j), in domestic currency,
for the domestic market and PT ,t∗ (j), in foreign currency, for the foreign market. Both pricing processes are subject to nominal frictions as inCalvo (1983). Assuming a separate pricing schedule in foreign currency with nominal rigidities is a way to break with the LOP (in the short run) and to allow for incomplete pass-through in tradable exports, following
empirical evidence.
For the ease of exposition, we present the profit maximization problem of wholesale tradable firms in three parts: input choice and price settings for domestic and foreign markets.
2.2.3.1 Input choice
The cost minimization problem of a firm j is given by min KT ,t(j),HT ,t(j),YX,tT (j) rKT ,tKT ,t(j) + wT,tHT ,t(j) + RERtp∗X,tY T X,t(j) + ξT,t h YT ,t(j) − AT ,tKT ,t(j)αT HT ,t(j)γTYX,tT (j) 1−αT−γTi.
The optimal input choices are pinned down by the following first-order conditions:
rT,tK = αT ξT ,t YT,t(j) KT ,t(j) [2.24] wT ,t= γT ξT,t YT ,t(j) HT ,t(j) [2.25] RERtp∗X,t= (1 − αT − γT) ξT ,t YT,t(j) YT X,t(j) [2.26] Combining the conditions above, we obtain the expression for the real marginal cost in the tradable sector, which is equal to the Lagrange multiplier and common to all wholesale firms: mcT,t = ξT ,t= rK T ,t αT !αT wT,t γT !γT RERtp∗X,t 1 − αT − γT !1−αT−γT . [2.27]
Capítulo 2. Model 24
2.2.3.2 Price setting to the domestic market
Each period t, with probability 1 − φT, a wholesale firm j receives a signal to
optimally reset its nominal price to the domestic market ˜PT ,t(j). With probability φT, it
must adjust following an indexation rule ΓT ,t that simply updates its current nominal
price according to the inflation target ¯Πt. The optimal price chosen by wholesale firm j in
period t is given by the expression:4 ˜ PT,t(j) = θ θ − 1 Et P∞`=0(β φT)`λt+`mcT ,t+`Γ−θT ,t+`PT ,t+`θ YT,t+`d Et P∞`=0(β φT)`λt+`Γ1−θT ,t+`PT ,t+`θ YT ,t+`d P −1 t+` .
Since marginal costs and sectoral demand conditions constraining the price-setting are common to all wholesale firms, in symmetric equilibrium, each firm j able to optimally reset its price chooses ˜PT ,t(j) = ˜PT ,t. Thus, the law of motion of domestic price of tradables
is given by PT,t1−θ = φT ¯ ΠtPT ,t−1 1−θ + (1 − φT) ˜PT,t1−θ. [2.28]
2.2.3.3 Price setting to the foreign market
The problem is analogous to the price setting to the domestic market. Now, since the price is denominated in foreign currency, the indexation rule Γ∗T,t updates current prices by foreign inflation Π∗t. The optimal price chosen by wholesale firm j in period t is given by the expression:5
˜ PT,t∗ (j) = θ θ − 1 Et P∞`=0(β φ ∗ T)`λt+`mcT,t+`Γ∗T ,t+` −θ PT ,t+`∗ θYex T ,t+` Et P∞`=0(β φ∗T)`λt+`t+`Γ∗T ,t+` 1−θP∗ T ,t+` θYex T ,t+`P −1 t+` .
Again, in symmetric equilibrium, each firm j able to optimally reset its price chooses ˜PT ,t∗ (j) = ˜PT,t∗ . Thus, the law of motion of the price of tradables to the foreign market is given by
PT,t∗ 1−θ = φ∗T Π∗tPT,t−1∗ 1−θ+ (1 − φ∗T) ˜PT ,t∗ 1−θ. [2.29]
2.2.4
Wholesale non-tradables firms
There is a continuum j ∈ [0, 1] of wholesale monopolist firms that hire labor,
HN,t(j) and rent capital, KN,t(j), as inputs to produce using the following technology: YN,t(j) = AN,tKN,t(j)αNHN,t(j)1−αN , [2.30]
4 For details, see AppendixA.1. 5 For details, see AppendixA.2.
where αN ∈ [0, 1] denotes the share of capital in non-tradables production and AN,t is a
stationary productivity shock common to all wholesale firms in non-tradable sector. By definition, non-tradable goods cannot be traded abroad. Therefore, the entire supply of a wholesale firm j must be commercialized domestically at price PN,t(j), in
domestic currency. The pricing process is subject to nominal frictions as inCalvo (1983). For the ease of exposition, we present the profit maximization problem of non-tradable firms in two parts: input choice and price setting.
2.2.4.1 Input choice
The cost minimization problem of a wholesale firm j is given by: min KN,t(j),HN,t(j) rN,tK KN,t(j) + wN,tHN,t(j) + ξN,t h YN,t(j) − AN,tKN,t(j)αNHN,t(j)1−αN i .
The optimal input choices are pinned down by the following first-order conditions:
rN,tK = αNξN,t YN,t(j) KN,t(j) [2.31] wN,t = (1 − αN) ξN,t YN,t(j) HN,t(j) . [2.32]
Combining the conditions above, we obtain the expression for the real marginal cost in the non-tradable sector, which is equal to the Lagrange multiplier and common to all wholesale firms:
mcN,t = ξN,t = rK N,t αN !αN wN,t 1 − αN 1−αN . [2.33] 2.2.4.2 Price setting
Each period t, with probability 1 − φN, a wholesale non-tradable firm j receives a
signal to optimally reset its nominal price ˜PN,t(j). With probability φN, it must adjust
following an indexation rule ΓN,t that simply updates its current nominal price according
to the inflation target ¯Πt. The optimal price chosen by wholesale firm j in period t is given
by the expression:6 ˜ PN,t(j) = θ θ − 1 Et P∞`=0(β φN)`λt+`mcN,t+`Γ−θN,t+`PN,t+`θ YN,t+` Et P∞`=0(β φN)`λt+`Γ1−θN,t+`PN,t+`θ YN,t+`Pt+`−1 .
Capítulo 2. Model 26
Since marginal costs and sectoral demand conditions constraining the price-setting are common to all non-tradable wholesale firms, in symmetric equilibrium, each firm j able to optimally reset its price chooses ˜PN,t(j) = ˜PN,t. Thus, the law of motion of the
price of non-tradables is given by
PN,t1−θ = φN ¯ ΠtPN,t−1 1−θ + (1 − φN) ˜PN,t1−θ. [2.34]
2.2.5
Wholesale Importers
There is a continuum j ∈ [0, 1] of monopolist wholesale importers that buy a homogeneous good abroad and differentiate it to sell in the domestic market at price
PF,t(j) in domestic currency. For simplicity, we assume that the homogeneous good
bought from abroad is the foreign final good, which costs tPt∗ in domestic currency. This
assumption has the advantage that the real marginal cost to wholesale importers is simply given by the real exchange rate.
As in tradable and non-tradable productive sectors, price setting is subject to nominal rigidities as inCalvo (1983). Each period, with probability 1 − φF, a wholesale
importer j receives a signal to reset its nominal price ˜PF,t(j). With probability φF, it must
adjust following an indexation rule ΓF,t that simply updates its current nominal price
according to the inflation target ¯Πt. The optimal price chosen by wholesale firm j in period t is given by the expression:7
˜ PF,t(j) = θ θ − 1 Et P∞`=0(β φF)`λt+`RERt+`Γ−θF,t+`PF,t+`θ YF,t+` Et P∞`=0(β φF)`λt+`Γ1−θF,t+`PF,t+`θ YF,t+`Pt+`−1 .
Since marginal costs and sectoral demand conditions constraining the price-setting are common to all importers, in symmetric equilibrium, each firm j able to optimally reset its price chooses ˜PF,t(j) = ˜PF,t. Thus, the law of motion of the price of imported goods is
given by PF,t1−θ = φF ¯ ΠtPF,t−1 1−θ + (1 − φF) ˜PF,t1−θ. [2.35]
2.2.6
Final good
The final good is produced competitively by a representative firm combining tradable, non-tradable and imported composite goods according to a CES technology:
Zt = ωT 1 ν Yd T ,t ν−1 ν + ω N 1 ν YN,t ν−1 ν + ω 1 ν F YF,t ν−1 ν ν−1ν [2.36] where ν > 0 denotes the elasticity of substitution between composite goods. Moreover, ωT, ωN and ωF denote, respectively, the shares of tradable, non-tradable and imported goods
in the final good, so that ωT + ωN + ωF = 1.
The final good is used for household consumption, investment and government consumption. It is sold at nominal price Pt and is the numéraire of the economy. The
solution to the cost minimization problem of the representative firm yields the demands for composite goods faced by retail firms:
Ys,t= ωs P s,t Pt −ν Zt, s ∈ {T, N, F }. [2.37]
Applying (2.37) to (2.36), we obtain the expression for the final good price index
Pt= h ωT PT ,t1−ν + ωNPN,t1−ν + ωF PF,t1−ν i1−ν1 . [2.38]
2.3
Government
Government encompasses the fiscal and monetary authorities. Policy rules are designed to capture the main aspects of the functioning of monetary and fiscal policies in Brazil.
2.3.1
Fiscal Policy
This section follows closely the fiscal block proposed by Castro et al.(2015), which aims to describe the modus operandi of the Brazilian regime of primary result targeting, in place since 1999. On the revenue side, each period t, the government collects taxes Tt and
issues new debt in the form of one-period non-contingent bonds Btat gross nominal interest
rate Rt. On the spending side, the government must pay for its nominal consumption PtGt and the outstanding debt Bt−1:
PtGt+ Bt−1 = Bt Rt
Capítulo 2. Model 28
The government non-interest revenues are given exclusively by the lump-sum tax
Tt. For simplicity, we assume that Tt is given by a fixed proportion of nominal GDP plus
a random innovation:
Tt= τ PtYt, +εT ,t, [2.40]
where τ ∈ [0, 1] is the tax rate and εT ,t ∼ N (0, σT2).
By definition, the nominal primary result St is the difference between non-interest
government’s revenues and expenses: St = Tt− PtGt. Using this fact, one obtains the
expression that determines the nominal government spending:
PtGt= Tt− PtYt SY,t, [2.41]
where SY,t denotes the primary result-to-GDP ratio. The fiscal authority manages SY,t
according to: SY,t = ¯SY + ηS SY,t−1− ¯SY + ¯ηS ¯ SY,t− ¯SY + ηY (Yt− Y ) + sGεG,t, [2.42]
where ¯SY,t denotes the target for the primary result-to-GDP ratio in period t, set by the
fiscal authority in period t − 1. The effective primary result in period t is a combination of inertial forces, as captured by the autoregressive parameter ηS ∈ [0, 1), and of the
effectiveness of the government in achieving its target, represented by parameter ¯ηS ∈ [0, 1].
We diverge from Castro et al.(2015) by introducing the term ηY (Yt− Y ), which captures
a contemporaneous response of the fiscal policy to the business cycle, i.e. if ηY > 0,
the execution of the government expenses encompasses some degree of explicit counter-cyclicality concern. As Section5 shows, the value of this parameter, which we estimate to be almost null (see Table2) has important welfare implications.
Equation 2.41 implies that, given that tax revenues are outside of government control, the endogenous adjustment of fiscal policy in order to follow the rule described by equation (2.42) is done by government spending Gt. This means that the innovations εG,t ∼ N (0, σG2) are, in practice, (negative) innovations to Gt. For convenience, we scale εG,t by the steady-state government spending to GDP ratio, sG≡ GY, so that a 1 percent
unexpected shift to government spending shifts the primary result-to-GDP ratio by sG.
The main objective of the primary result targeting regime in Brazil is to stabilize the long-run govern debt-to-GDP ratio. Thus, we assume that the primary result-to-GDP
target for period t + 1 is decided, and announced, in period t considering the current government net debt-to-GDP ratio BY,t ≡ PBtYtt according to
¯ SY,t+1 = ¯SY + κS ¯ SY,t− ¯SY + κB (BY,t− BY) + κY(Yt− Y ) + εS,t¯ , [2.43]
where κS ∈ [0, 1) captures the persistence of the targets set by the fiscal authority. The
parameter κB> 0 measures the degree of responsiveness of the fiscal rule to deviations of
net government debt-to-GDP ratio from its steady-state value. Again, we deviate from
Castro et al.(2015) with the inclusion of the term κY(Yt− Y ), an explicit business cycle
element in the formation of the targets. Differently from its analogous in equation (2.42), however, this adjustment of the fiscal policy to cyclical conditions only takes effect in the subsequent period.8 Finally, ε
¯
S,t ∼ N (0, σS2¯) is an innovation to primary result-to-GDP
target.
Applying identity (2.41) to the government flow budget constraint (2.39) and dividing both sides by the nominal GDP, one obtains the law of motion of net public debt-to-GDP ratio: BY,t = Rt B Y,t−1 Πt Yt−1 Yt − SY,t . [2.44]
2.3.2
Monetary policy
The Brazilian monetary authority follows an inflation targeting regime since 1999. It uses the nominal interest rate Rtas the instrument to pursue aggregate price and activity
stabilities. Even though the real exchange rate stability is not an official objective of the BCB mandate, we include this variable in the Taylor-type rule considering the welfare analysis. Moreover, the effective response of the monetary authority to a commodity price shock depends on the importance it attributes to exchange rate deviations.9 The nominal interest rate is set by the monetary authority according to
Rt R = R t−1 R µR " Π t ¯ Πt !µΠ Yt Y µY RER t RER µ#1−µR exp εR,t, [2.45]
8 This feature captures in a simple form the delayed responses of the fiscal policy to the business cycle
inherent to a democratic system. That is, if there is some degree of counter-cyclicality concern in the conduction of fiscal policy, the majority of adjustments must be incorporated to the budget bill and approved by the Congress before being enacted. Differently from ηY, κY is quantitatively relevant in
our estimation (see Table2).
9 E.g. Garcia e González (2013) identifies relevant responsiveness of monetary authorities to real
exchange rate deviations when estimating NK-DSGE models for several commodity-exporting SOEs (not including Brazil, though). As a result, the IRFs of nominal interest rates to commodity price shocks are negative even though output expands and inflation remains roughly constant because the real exchange rate appreciates.
Capítulo 2. Model 30
where µR∈ [0, 1) pins down the degree of persistence in the nominal interest rate, while µΠ> 1, µY ≥ 0 and µ determine the responses of the monetary authority to deviations
of aggregate inflation from its target and deviations of output and real exchange rate from their steady-states, respectively. 10 Moreover, ε
R,t ∼ N (0, σR2) is the monetary shock.
The inflation target is a predetermined variable. That is, the target for period t + 1 aggregate inflation is determined and announced in period t. For simplicity, following
Smets e Wouters(2003) andAdolfson et al. (2007), it evolves exogenously according to the stochastic process:
¯
Πt+1= (1 − ρΠ¯) ¯Π + ρΠ¯ Π¯t+ εΠ,t¯ , [2.46]
where ρΠ¯ ∈ [0, 1) and εΠ,t¯ ∼ N (0, σΠ2¯) is an innovation to the inflation target.
2.4
Foreign Economy
We assume that the foreign demand for commodity goods is perfectly elastic. That is, for any given international real commodity price in foreign currency p∗X,t, the foreign demand absorbs any volume of home commodity net exports YX,t− YX,tT . Since we do
not explicitly model the economy of the rest of the world, we assume that international real commodity price p∗
X,t, foreign output Yt∗, gross aggregate inflation rate Π∗t and gross
nominal interest rate R∗t follow exogenous AR(1) processes.
By analogy with the domestic economy, we derive the foreign demand for home tradable goods Yex
T,t, which appears in equation (A.5): YT ,tex= ωex
PT ,t∗ Pt∗
!−ν
Yt∗, [2.47]
where ωex is the share of home tradable exports in foreign economy absorption.
2.5
Stochastic processes of shocks
The stationary shocks to preferences, investment efficiency, risk-premium, sectoral productivities and foreign variables follow analogous AR(1) processes:
log(xt) = (1 − ρx) log(x) + ρx log(xt−1) + εx,t, [2.48]
10 As section4shows, the value of zero lies inside the 90% credibility interval of µ
. That is, we do not
find significant evidence that the BCB responds to RER fluctuations using the nominal interest rate as an instrument.
for x = ζC,t, ζH,t, ζI,t, ζΘ,t, AX,t, AT ,t, AN,t, p∗X, Y
∗, Π∗, R∗. As usual, ρ
x ∈ [0, 1) and εx,t ∼ N (0, σx2) is an innovation to exogenous variable x.
2.6
Equilibrium
In symmetric equilibrium, all individuals in the set of Ricardian households ΩRand
all wholesale monopolistic firms make the same optimal decisions. Furthermore, the input markets of capital and labor must clear. Namely, we must have: CR
t (h) = CtR, Bt(h) = Bt, Bt∗(h) = Bt∗, Ii,t(h) = Ii,t, ˜wi,t(h) = ˜wi,t, Hi,t(h) = Hi,t(j) = Hi,t, Ki,t(h) = Ki,t(j) = Ki,t, YX,tT (j) = YX,tT , Ys,t(j) = Ys,t, and ˜ps,t(j) =pes,t, for all h ∈ ΩR, j ∈ [0, 1], i = X, T, N, and s = F, T, N .
As previously discussed in section 2.1.3, in equilibrium, the non-Ricardian hou-seholds set wages equal to the average of wages set by Ricardian houhou-seholds and there-fore also supply their average labor services. In symmetric equilibrium, this means that
wN R
i,t = wRi,t = wi,t and Hi,tN R = Hi,tR = Hi,t, for all i = X, T, N . Aggregating over all
households inhabiting the economy, we have the following expression for the aggregate consumption:
Ct= (1 − λN R) CtR+ λN RCtN R. [2.49]
The market clearing condition for the final good implies that it must be completely absorbed by household consumption, investment and government spending:
Zt = Ct+ It+ Gt. [2.50]
Combining the households’ budget constraint (2.4) with the government budget constraint (2.39), the aggregate consumption (2.49), the market clearing condition for the final good (2.50) and the profit functions of commodity and wholesale firms, we obtain the law of motion of foreign assets to GDP ratio:
BY,t∗ R∗ tΘt = Yt−1 Yt BY,t−1∗ Πt +N Xt Yt , [2.51]
where N Xt denote the country’s real net exports, defined as: N Xt= RERt h p∗X,t YX,t− YX,tT + p∗T ,tYT,tex− YF,t i . [2.52]
Capítulo 2. Model 32
The value added by firms in each sector is the difference between the value of the goods they sell and the intermediate goods used in their productive processes:
YX,tva ≡ RERtp∗X,tYX,t; YT ,tva ≡ pT ,tYT ,td + RERtp∗T ,tY ex T ,t− RERtp∗X,tY T X,t; YN,tva ≡ pN,tYN,t; YF,tva ≡ (pF,t− RERt) YF,t.
And the Gross Domestic Product is obtained as the sum of the value added by firms:
3 Estimation
The model contains 82 parameters, of which 32 are calibrated and 50 are estimated. Following the literature, we fix some parameters prior to estimation using external infor-mation. Due to the highly non-linear structure of the model, the steady-state is solved numerically, as is usual in this kind of three-sector model. Hence, parameters defining the steady-state are not estimated due to the prohibitive computational burden it would entail.1
The remaining parameters are estimated using Bayesian techniques surveyed inAn e Schorfheide (2007). These parameters are related to nominal rigidities, adjustment costs, policy rules, and the stochastic processes of shocks. In the subsections ahead, we describe the data used in the estimation process, the calibration procedure, and the priors adopted.
3.1
Data and shocks
The Bayesian estimation is conducted using a quarterly-frequency data set ran-ging from 2001Q1 to 2019Q4. The period covered encompasses both the ascending and descending phases of the most recent commodity cycle. In total, 17 model variables are used as observables, of which 4 are foreign variables. The considerably large number of observables enables us to overcome identification issues.
The series for GDP, private consumption, and investment, all in real per capita terms, are taken from Brazilian National Accounts, computed by the Brazilian Institute of Geography and Statistics (IBGE). The series of volumes of imports and exports of manufactured goods in per capita terms come from the Brazilian Ministry of Development, Industry and Foreign Commerce (Mdic). The series of total employment rate and average real wage come from surveys produced by IBGE.2 Domestic inflation is measured by the IPCA inflation, computed by IBGE. The series for the domestic nominal interest rate
1 Previous studies adopt the same procedure, e.g.Schmitt-Grohé e Uribe (2018) andDib(2008) 2 During the period covered by the sample, two employment surveys were discontinued: the so-called
"old"(1982-2002) and "new"(2002-2016) Monthly Employment Surveys (PMEs). To overcome this, we adopt the same procedure asCastro et al. (2015), i.e. the current Continuous National Household Survey (PNAD-C) is interpolated with the previous ones by taking its earliest level and multiplying by the rates of change captured by the PMEs.
Capítulo 3. Estimation 34
(Selic rate), the inflation target, the real exchange rate, and the primary result-to-GDP ratios are published by the BCB. The series of primary result-to-GDP ratio targets are extracted from the Budgetary Guideline Bills (LDOs), annually approved by the Brazilian Congress. Series of Fed fund rates, as well as US CPI inflation, are taken from Federal Reserve (FED). The series of the volume of world imports is provided by the Netherlands Bureau for Economic Policy Analysis (PBC). Last but not least, the series of Brazilian commodity export price index is elaborated by the International Monetary Fund (IMF). The data treatment previous to model estimation follows closely the procedures proposed in Castro et al. (2015). All annualized series are properly converted to quarterly frequency. First log-difference and demeaning is applied to the trending observables corresponding to model variables Yt, Ct, It, YT,tex, YF,t, Ht, wt and Yt∗. The gross nominal
inflation and interest rates corresponding to Πt, ¯Πt, Π∗t, Rt, and R∗t as well as RERt are
logged and demeaned.3 The observables corresponding to rates S
Y,t and ¯SY,t are simply
demeaned. Finally, we subtract the log-linear trend from the observable p∗X,t.
Since we have 17 observable variables, we must have at least 17 shocks in the estimated model. Hence, in addition to the 16 structural shocks present in the model, we add a measurement error to the world imports, which does not include only manufactured goods imports.
3.2
Calibration
Table1summarizes the calibration procedure. The time length of each period is one quarter. Starting from the normalizations adopted, the steady-state value of the stationary shocks to preferences in consumption ζC and leisure ζH, the efficiency of investment ζI,
risk-premium ζΘ and sectoral productivities Aj, j = X, T, N are normalized to one. The
same procedure is adopted with the steady-state values of real international commodity price p∗X and foreign real output Y∗. Given these normalizations, the calibration of the relative sizes of the productive sectors is performed through the imposition of moment restrictions to sectoral shares in the final good. That is, ωN is set to .797 so that the
steady-state of the model matches the average participation of 80.1% of the non-tradable
3 FollowingCastro et al.(2015), we subtract 4.5% from the original series of CPI inflation and its target,
sector in Brazilian GDP between 2001-2019, the period covered by our sample. Analogously,
ωT is set to .112 to match the average participation of 12.3% of the tradable sector in
Brazilian GDP throughout the same period. The share of home tradable goods in foreign imports ωex is set to .088 to match the average coefficient of exports in the Brazilian
tradable sector (15.46%).4
The remaining steady-state fixed parameters are simply given by long-run values of observable variables. The primary result-to-GDP target ratio ¯SY is set to 2%. The tax
rate τ is set to the average ratio of 35% of government revenues to GDP. Net foreign assets to GDP ratio B∗
Y are set to -.68, i.e. minus the average of net foreign debt over quarterly
GDP. The gross international inflation rate Π∗ is set to the average quarterly US CPI inflation rate, 1.006. The gross international nominal interest rate R∗ is set to the average
nominal gross Fed Funds quarterly rate, 1.007. The gross inflation target ¯Π is set to 1.011, which is equivalent, in quarterly frequency, to the 4.5% yearly target adopted between 2005-2017. Finally, the gross domestic nominal interest rate R is set to 1.031, the average quarterly Selic rate set by the Brazilian Central Bank. The values fixed for R and ¯Π imply an intertemporal discount factor β = .98.
Concerning the remaining fixed parameters, we set standard values adopted by the literature whenever possible. That is the case of the utility curvature parameter σ, the capital depreciation rate δ, the inverse Frisch elasticity of substitution of labor supply
χ, set to 2, .025 and 1.45, respectively. Similarly, the elasticity of substitution between
differentiated goods θ is set to 11 to imply a 10% price markup in goods markets. The share of commodities in the production function of the tradable sector 1 − αT − γT is set
to .15. The capital share coefficients αj, j = X, T, N , are set to match a share of 30% of
income to capital. The elasticity of substitution of labor across sectors η is set to unity as inBouakez, Cardia e Ruge-Murcia(2009). The elasticity of substitution between composite goods ν is set to .8 as in Dib (2008). Following Castro et al. (2015), the elasticity of substitution between labor types ϑ is set to 3 implying a 50% wage markup, and the share of non-Ricardian households λN R is fixed as .4.
4 More specifically, 15.46% corresponds to the average share of manufactured goods produced in Brazil
that were exported between 2001 and 2019, according to the National Confederation of Industries (CNI).
Capítulo 3. Estimation 36
Tabela 1 – Calibrated Parameters
Parameter Description Value
σ Utility curvature parameter of consumption 2
β Intertemporal discount factor 0.98
δ Capital depreciation rate 0.025
χ Inverse of Frisch labor elasticity of supply 1.45
η Labor elasticity of substitution across sectors 1
αT Share of capital in sector T 0.3
αN Share of capital in sector N 0.3
αX Share of capital in sector X 0.3
γT Share of labor in sector T 0.55
ν Elasticity of substitution between composite goods 0.8
ωex Share of home tradable production in foreign imports 0.088
ωT Share of tradables in the final good 0.112
ωN Share of non-tradables in the final good 0.797
θ Elasticity of substitution between differentiated goods 11
ϑ Elasticity of substitution between differentiated labor types 3
λN R Share of non-Ricardian households 0.4
Steady-state values
¯
SY Primary result-to-GDP target 0.02
τ Tax rate 0.35
BY∗ Net foreign assets to GDP ratio -0.68
Π∗ Gross international inflation rate 1.006
R∗ Gross international nominal interest rate 1.007
¯
Π Gross domestic inflation rate target 1.011
R Gross domestic nominal interest rate 1.031
AT Stationary technological shock to sector T 1
AN Stationary technological shock to sector N 1
AX Stationary technological shock to sector X 1
p∗X Real international commodity prices 1
Y∗ Foreign output 1
ζC Stationary preference shock to consumption 1
ζH Stationary preference shock to leisure 1
ζI Stationary efficiency shock to investment 1
ζΘ Stationary risk-premium shock 1
3.3
Priors
The choices of prior distributions for each parameter depend on the sharpness of information we have and on the theoretical constraints the model imposes on them. That is, priors for parameters that we have good guesses from available data are tighter; parameters constrained to lie in the [0, 1] interval have beta prior distributions, and strictly
