Essays in macroeconomics

Instituto Superior de Economia e Gestão

Essays in Macroeconomics

Rui Alexandre Rodrigues Veloso Faustino

Orientador: Prof. Doutor Luís Filipe Pereira da Costa

Tese especialmente elaborada para obtenção do grau de Doutor em Economia

Instituto Superior de Economia e Gestão

Essays in Macroeconomics

Rui Alexandre Rodrigues Veloso Faustino

Orientador: Prof. Doutor Luís Filipe Pereira da Costa

Tese especialmente elaborada para obtenção do grau de Doutor em Economia

Júri:

Presidente: Doutor Nuno João de Oliveira Valério, Professor Catedrático e Presidente do Conselho Científico, Instituto Superior de Economia e Gestão da Universidade de Lisboa Vogais:

Doutor António Manuel Pedro Afonso, Professor Catedrático, Instituto Superior de Econo-mia e Gestão da Universidade de Lisboa

Doutor Pedro Batista Maia Gomes, Senior Lecturer, Birbeck College from London Uni-versity

Doutor Luís Filipe Pereira da Costa, Professor Associado, Instituto Superior de Economia e Gestão da Universidade de Lisboa

Doutor Pedro Miguel Soares Brinca, Professor Auxiliar, NOVA School of Business and Economics da Universidade Nova de Lisboa

Doutora Ana Paula Ferreira Ribeiro, Professora Auxiliar, Faculdade de Economia da Universidade do Porto

ATUS American Time Use Survey

BEA Bureau of Economic Analysis

BLS Bureau of Labor and Statistics

CES Constant elasticity of substitution

DH Deep habits

DSGE Dynamic stochastic general equilibrium

GDP Gross Domestic Product

GVA Gross Value Added

IRF Impulse-response function

NK New Keynesian

PCE Personal Consumption Expenditures

PVAR Panel vector autoregression

RBC Real Business-Cycle

TFP Total-factor productivity

VAR Vector autoregression

This thesis has as its object of study the way consumer preferences affect structure and market power, measured through the markups of the firms that compete in it. By modifying the way consumer preferences are defined, it is possible to generate endogenous markups that significantly alter the responses of macroeconomic variables generated by different shocks. The thesis consists of three essays, the first of which analyzes the dynamics of markups in durable and nondurable consumption over the economic cycle and their response to shocks. For this, I take a New Keynesian model with durable goods and modified to include the habit formation at both types of goods. Depending on how the habit formation over durable consumption is defined, the model is able to replicate the responses of consumption variables, markups and prices observed in the data.The second essay deals with the effort made by consumers to compare prices between various sellers over the economic cycle. From microdata for the US, it is shown that increases in individuals’ hourly compensation translate into reductions in time spent comparing prices. From this, a mechanism is presented to generate countercyclical responses of the time spent in price comparison by consumers. When incorporated into general equilibrium models, this mechanism is capable of generating an amplifying effect on the responses of the main macroeconomic variables. Finally, a general equilibrium model is presented where the number of firms, varieties and quality of the consumed products are determined endogenously. Through the model, it is possible to analyze the dynamics of product creation and destruction, as well as the changes in their quality during the economic cycle, and their impact on the dynamics of the main macroeconomic variables.

Keywords: Endogenous markups, prices, consumer preferences, general equilibrium

models, market structure, business cycles.

Esta tese tem como objeto de estudo a forma como as preferências dos consumidores afetam a estrutura e o poder de mercado, medido através de markups, das empre-sas que nele concorrem. Modificando a forma como são definidas as preferências dos consumidores, é possível gerar markups endógenos e alterar significativamente as re-spostas de variáveis macroeconómicas a diferentes choques. A tese é composta por três ensaios, sendo que no primeiro são analisadas as dinâmicas dos markups nos bens de consumo duradouros e não duradouros ao longo do ciclo económico e a sua resposta a choques. Para isso, é apresentado um modelo Novo-Keynesiano com bens duradouros e não duradouros, modificado de forma a incluir a formação de hábitos nos dois tipos de bens. Dependendo da forma como é definida a formação de hábitos de consumo de bens duradouros, o modelo permite replicar as respostas observadas para o consumo, markups e preços. O segundo ensaio aborda o esforço despendido pelos consumidores na comparação de preços ao longo do ciclo económico. Partindo de microdados para os EUA, demonstro que aumentos da remuneração horária dos indivíduos traduzem-se em reduções no tempo despendido na comparação de preços. Em seguida, é apresentado um mecanismo capaz de gerar respostas contracíclicas do tempo despendido pelos consumidores na comparação de preços. Quando incorpo-rado em modelos DSGE, é capaz de gerar um efeito amplificador das repostas das principais variáveis dos modelos. Por fim, é apresentado um modelo DSGE onde o número de empresas e a qualidade dos produtos consumidos são determinados de forma endógena. Através do modelo, é possível analisar as dinâmicas de criação e destruição de variedades, bem como das variações na sua qualidade durante o ciclo económico, e o seu impacto na dinâmica das principais variáveis macroeconómicas.

Palavras-chave: Markups endógenos, preços, preferências dos consumidores,

Acronyms . . . i

Abstract . . . ii

Resumo . . . iii

List of Tables . . . vii

List of Figures . . . ix

Acknowledgements . . . xii

1 Introduction 1 2 Deep habits in New Keynesian model with durable goods 8 2.1 Introduction . . . 8

2.2 Empirical evidence on markups . . . 12

2.2.1 Methodology . . . 13

2.2.2 Cyclical properties of markups . . . 14

2.3 Model . . . 18

2.3.1 Households . . . 18

2.3.2 General Government . . . 22

2.3.3 Firms . . . 23

2.3.4 Market-clearing conditions . . . 25

2.3.5 Calibration and solution method . . . 26

2.3.6 Results and discussion . . . 27

2.5 Conclusion . . . 33

3 Price research and the business cycle 36 3.1 Introduction . . . 36 3.2 Empirical evidence . . . 38 3.2.1 ATUS data . . . 38 3.2.2 Cross-section . . . 40 3.2.3 Panel data . . . 43 3.3 Model . . . 46 3.3.1 Households . . . 46 3.3.2 Firms . . . 49

3.3.3 Calibration and results . . . 51

3.3.4 Comparing the model with data . . . 54

3.4 Firm-entry model . . . 58

3.5 Conclusion . . . 61

4 Endogenous quality and firm entry 63 4.1 Introduction . . . 63

4.2 Model . . . 66

4.2.1 Households . . . 66

4.2.2 Market structure . . . 67

4.2.3 Firms . . . 69

4.2.4 Calibration and results . . . 71

4.2.5 IRF-matching and second moments . . . 76

4.3 Quality as a stock . . . 79

4.4 Conclusion . . . 83

Appendix A Deep Habits in New Keynesian model with durable goods 89

A.1 Data sources and model . . . 89

A.2 Model with capital accumulation . . . 90

A.3 Determinacy . . . 93

Appendix B Price research and the business cycle 95 B.1 Alternative aggregation of consumer goods . . . 95

B.2 Indivisible labor . . . 96

B.3 Non-separable utility function . . . 97

B.4 US data and markup estimation . . . 99

B.5 Firm-entry model . . . 101

Appendix C Endogenous quality and firm entry 105 C.1 Main model . . . 105

C.2 Quality as stock . . . 106

2.1 Unconditional correlation coefficients between markups and real GDP (Y ), real industry GVA (Yi_{) and real PCE (C) in US (1980:I-2016:IV) 16}

3.1 Coefficients from the working-time regression . . . 41

3.2 Coefficients from regressions on earnings . . . 42

3.3 Panel-data regression coefficients . . . 44

3.4 Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, benchmark model (RBC) and the model with price research (P-R) . . . 55

3.5 Estimated parameters from the matching with VAR . . . 56

3.6 Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, firm-entry-only model (F-E), and firm-entry plus price research (FE+PR) . . . 61

4.1 Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, firm-entry model (F-E) and endogenous-quality model (FE+Q) . . . 79

A.1.1 Auxiliary Indicators . . . 89

B.4.1 Data sources 1960:I-2017:IV . . . 100

C.1.1 Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, model with θ = 1 and model with θ = 1.5 . . . . 106 C.2.2 Second moments of main macroeconomic variables from US data for

1960:I-2017:IV, for firm-entry model (F-E) and firm-entry with quality as stock (FE+Q) . . . 106

2.1 Cross-correlation between real GDP and average markups (constant returns) durables plus construction (blue), nondurable plus services (red) . . . 17 2.2 Impulse-response functions to one percent monetary-policy (yellow),

government-spending (red), and productivity (blue) shocks for the model with and without DH in nondurable and durable purchases . . 28 2.3 Impulse-response functions to one percent shocks for the variables of

employment, wages and inflation . . . 30 2.4 Impulse-response functions to one percent monetary-policy (yellow),

government-spending (red), and productivity (blue) shocks for model with deep habits over durable stocks . . . 33 3.1 Impulse-response functions to a one percent shock for the PVAR with

95% confidence interval . . . 46 3.2 Impulse-response functions to a one percent productivity shock . . . 52 3.3 Impulse-response to a one percent preference shock . . . 53 3.4 Impulse-response functions to a one percent productivity shock for

estimated VAR and calibrated model . . . 57 3.5 Impulse-response functions to a one percent productivity shock for

4.1 Impulse-response functions to a one percent productivity shock in the firm-entry model with θ = 0.75, 1 and 1.5 . . . . 72 4.2 Impulse-response functions to a one percent quality shock in the

firm-entry model with θ = 0.75, 1 and 1.5 . . . . 74 4.3 Impulse-response functions to a one percent TFP shock in firm-entry

model with and without endogenous quality . . . 75 4.4 Impulse-response functions to a one percent productivity shock for

estimated VAR and the calibrated model . . . 77 4.5 Impulse-response functions to a one percent TFP shock for

quality-as-stock model . . . 81 4.6 Impulse-response functions to a productivity shock for estimated VAR

and the calibrated model with quality as a stock . . . 82 A.1.1 Markups (incr. returns) of consumer durables (blue), nondurable plus

services (red) and recession periods (shadows) for 1980:I to 2016:IV . 89 A.1.2 Impulse-response functions to a one percent shock for model with

Deep Habits only on nondurables, and the model with Deep Habits on nondurables and stocks . . . 90 A.2.3 Impulse-response functions for model with capital accumulation . . . 92 A.3.4 Determinacy regions for deep habits models . . . 93 B.2.1 Impulse-response functions to a one percent productivity shock with

indivisible labor . . . 97 B.3.2 Impulse-response functions to a one percent productivity shock . . . 99 B.5.3 Impulse-response functions to a one percent shock for Cournot vs

Bertrand competition . . . 103 C.1.1 Impulse-response functions to three types of shocks for the main model105

C.2.2 Impulse-response functions to a one percent TFP shock for firm-entry model and quality-as-stock model . . . 107

First and foremost, I would like to thank my advisor, Luís Costa, who was essential in the development of this thesis. His guidance was crucial from the beginning, to establish the goals of this work and to maintain the focus.

Secondly, I would like to thank the various participants of Lisbon Macro Club for the comments and suggestions received, which helped shape the essays comprising this thesis since their early stages. In particular, I would like to thank Pedro Brinca and João Duarte for the helpful reviews and remarks during the various presentations. I am also thankful for the inputs of the participants in the different conferences and workshop where I presented the papers that came to be this thesis.

I would also like to acknowledge the contribution of Elsa Fontainha for sharing references that prove to be instrumental throughout this work.

On a further note, I would like to thank the people working in the Masters and Doctorates Office, specially Isabel Moura, for their help with the administrative work. I am also grateful to all my colleagues at INE for their support and patience throughout these years. Moreover, I would also want to thank them for the help in editing and proofreading this thesis.

Finally, I want to thank my family and friends for their permanent support and encouragement during this period.

Introduction

The study of markups has gained traction in the past few years mainly due to the new focus on the rise of market power in advanced economies such as the United States (US), linking it with the fall of labor share and the increasing inequality in income distribution - De Loecker & Eeckhout(2017). However, the study of markups – i.e. the measure of market power of firms – and their effects on the economy started long before, with seminal papers fromBils(1987) andRotemberg & Woodford(1991), which presented empirical evidence on the cyclical properties of markups.

The cyclical properties of markups are an important subject of study due to its role in the transmission of shocks to the economy. If markups increase during upturns, it means that part of the positive effects in the economy from shocks are mitigated and absorbed by firms’ profits. On the other hand, if they are countercyclical, profits are increasing proportionally less than the quantities sold and there is a crowding-in effect. This feature assumes a key importance when analyzing the effectiveness of fiscal and monetary policies.

Empirical evidence for the US, produced by later studies, has shown that the average markup tends to respond procyclically to productivity shocks, e.g. Nekarda & Ramey(2013) andAfonso & Costa(2013), and countercyclically to demand shocks, e.g. Galí et al. (2007) andMonacelli & Perotti (2008).

Due to its importance for the analysis on the impact of fiscal policies, a significant literature was produced, resorting to general equilibrium models with endogenous markups. One of the most notable contributions on the theoretical impact of en-dogenous markups on fiscal and monetary policy is the concept of deep habits (DH) introduced in Ravn et al. (2006). With DH, consumers develop habits at the level of the individual varieties consumed, affecting the demand faced by firms. During expansions, firms decide to lower their prices to capture market share and, later, raise prices to exploit their locked (by habits) consumers. This generates countercyclical markups to demand shocks that lead to a crowding-in effect of fiscal policy on private consumption. Likewise, negative monetary-policy shocks (i.e. interest-rate hikes) in models with DH are more recessive due to the increase in markups.

As for the case of supply shocks, the main contribution to the literature is based on models with endogenous firm creation, whereBilbiie et al.(2012) andJaimovich & Floetotto (2008) are two noteworthy examples. In this type of models, the decrease of marginal cost resulting from productivity shocks diminishes the entry barrier to new firms. With an increase of firms, the profit margin of each firm is reduced leading to a reduction of average markup. As a result, the models are able to generate higher responses to shocks and be more consistent with data.

In this thesis I aim at contributing to the literature on markups and prices by studying how consumer preferences and habits affect market power and structure. Through this work the core theme is the interaction between consumer preferences and the market structure during the business cycle. While in the first essay the theme is the response of markups of durables and nondurables goods to different types of shocks, in the other two essays two new mechanisms that can generate endogenous markups are explored.

In the second chapter, the dynamics of the markups for durable and nondurable goods are studied. Firstly, I estimate the markups for manufacturing and services’

industries in the US and their cyclical properties. I find that markups of individual industries tend to be more negatively correlated with output and consumption when considering increasing returns, comparing with constant returns, but this difference is less pronounced for the average of domestic industries, durable goods and nondurable goods. Moreover, I find that markups of consumer durables and nondurables display similar cyclical properties and tend to be even more countercyclical than the average of domestic industries.

Then, I introduce deep habits into a New Keynesian (NK) model with durable and nondurable goods. The NK model with durable goods is especially useful in the analysis of the effects of monetary policy, since durable goods are more reactive to changes in interest rates. Nevertheless, it presents important shortcomings for the analysis of fiscal shocks, namely the negative response of consumption and the procyclical response of the markups. Likewise, the model generates negative responses of markups to supply shocks.

With the introduction of habit formation, I am able to rectify the responses ob-tained from the model. Since the consumption of durable goods is the consumption of the undepreciated stock of past and present purchases, one can define the habit being formed over the stocks - consumption of durables - or the flow - purchases of durable goods. I present the two alternative definitions of habits over durable goods and analyze the results obtained.

Even when formed only over nondurable consumption, the two-sector model with DH generates a positive response of the markup of nondurables to total-factor produc-tivity (TFP) shocks and negative response of both durables and nondurables markups to an increase in government spending. When added to the model, DH over pur-chases of durable goods amplify the responses of markups to shocks and generates a crowding-in effect of government spending on the consumption of both goods.

However, the performance of the model is remarkably different when the existence of habit formation over stocks of durable goods is assumed. As stocks of durable goods are larger than the flows of durable purchases, volatility of marginal utility is substantially lower, leading to a dampening of the effect of DH. Likewise, the determinacy of the model with habits on stocks is only marginally affected by the degree of habits.

In the second essay, I study the behavior of consumers during the business cy-cle, specifically the time spent on price-comparison activities. The time spent on researching the best prices available tends to increase during economic downturns, as households are more cash-constrained (lower wages) and less time-constrained (fewer working hours). This is one of the many ways households adapt during the business cycle. Other examples are the increase in home production activities, Aguiar et al. (2013), trading down the quality of goods and services consumed, Jaimovich et al. (2019), and buying more frequently but less each time, Aguiar & Hurst (2007).

However, other authors such as Petrosky-Nadeau et al. (2016) found that, using data from American Time Use Survey (ATUS), consumer shopping is procyclical and increasing with earnings. To disentangle this apparent puzzle where households spend more time shopping in economic booms but have higher price sensitivity during recessions, I run cross-section and panel-data regressions on microdata from the ATUS database.

In my study, I depart from the previous studies on the subject by considering separately the time spent on the acquisition of goods and services – shopping - and the time spent on researching and comparing prices and products - shopping research. Then I analyze how these variables are influenced by changes in earnings and working time. I conclude that, while shopping time tends to increase with earnings, the time spent on price research decreases. Simultaneously, time spent on shopping and on price research decreases with the increase in the working time.

I introduce a new variable of endogenous price comparison into a monopolistic-competition dynamic stochastic general equilibrium (DSGE) model. The new vari-able, defined as price research, gives disutility to the consumer and is non-separable from labor supply, while increasing price elasticity. Consumers equate together the labor supply and the price research effort, which implies a negative correlation be-tween labor supply and the time spent on price research that, in turn, translates into a countercyclical behavior of this variable. Since I assume that elasticity of substitu-tion between varieties, in the consumers aggregasubstitu-tion funcsubstitu-tion, depends on the time spent on price research, the elasticity of demand becomes countercyclical.

One of the key results of the general equilibrium model is that, with price research, it generates a procyclical response of the price markups to productivity shocks, while amplifying the responses of labor supply, investment and output. This feature holds for different types of specifications of utility function such as indivisible labor or non-separable preferences. When the endogenous firm creation is introduced into the model, it maintains the results and also outperforms the baseline firm-entry model.

In the fourth chapter I present a general equilibrium model where the number of varieties, determined by the number of firms, and product quality are endogenously determined. Hence, I bring together two different areas of study in macroeconomics in recent years. Firm-entry models such as in Jaimovich & Floetotto (2008), Colci-ago & Etro (2010) and Bilbiie et al. (2012) focus on the role of net firm creation in the propagation of productivity shocks to the economy. In these models, each given variety is produced by only one firm and the number of firms is endogenously deter-mined by the number of firms entering the market. This simplification is backed by empirical evidence presented in Broda & Weinstein (2010), which suggests that net product creation is strongly procyclical and mainly determined by firm entry rather than firm exit.

Broda & Weinstein (2010) also find that improvements of product quality are procyclical as during economic booms replacement of outdated goods by new ones is accelerated. Since statistical authorities do not fully account for the impact of quality on prices, the inflation rate is overestimated by the presence of the quality

bias. In light of these findings, some literature in the past years introduced models

focused on product quality. One of the main examples is Schmitt-Grohé & Uribe (2012) that show, through a model with exogenously determined quality, that quality improvements are crucial to the definition of inflation targets. Another example is the paper fromJaimovich et al.(2019) that includes a model where consumers traded down the quality of goods after a negative TFP shock. The authors also find that, during the Great Recession, consumers traded down the quality of goods and services consumed while trying to maintain the quantities.

In this essay, I take a step further and consider that quality is endogenous and defined at variety level and interacts with endogenous product creation as defined in firm-entry models. While maintaining the features of the canonical firm-entry model such as the procyclical behavior of firm entry and countercyclical behavior of markups, the model is able to produce a procyclical response of quality to positive productivity shocks. Also, the model is not only able to replicate the dynamics produced by the model inJaimovich et al.(2019), but has a wider reach since the quality affects market power. As a result, the dynamics of prices and markups, as well as consumption and output, are a product of the interaction between the number of varieties and quality. Depending on the key parameter (θ), that determines the marginal utility obtained from quality, the influence of improvements in quality on the rest of the economy can be either positive, negative or null. When the marginal utility of quality is constant, the transmission of changes in quality to the rest of the economy is shut off. In this case, we obtain results similar to Hamano & Zanetti (2018), but for increasing marginal utility, changes in quality tend to be contractionary.

However, if we consider the case of decreasing marginal utility (θ < 1), a positive exogenous shock on the quality leads to a positive response of the quantities consumed, output, labor, markups, firm entry, and prices. Since a TFP shock has a positive effect on quality, the response is amplified by the positive feedback loop generated within the model. Therefore, the model produces a greater response of consumption and prices than the firm-entry model without endogenous quality. Moreover, when the deflator of consumption is adjusted by the changes in the quality of products, the response of the price level is lower and the response of real consumption is even higher, making the model consistent with the findings in Broda & Weinstein (2010). Since for most of durable goods, the quality of the products depends on the design and technology used as input, which do not deplete during the manufacturing process, we can also assume quality as a stock that can become obsolete and in need of constant improvement. This is translated into an alternative specification of the model where we consider quality as stock, like physical capital. Due to the higher value of quality as a stock and its relatively lower fluctuations, its effect on other variables is mitigated. As a result, the impulse-response functions (IRF) and second moments become closer to the ones for the no-quality firm-entry model, notwithstanding maintaining a higher performance.

This thesis is organized as follows. Chapter 2 presents the study of markups for durable and nondurable consumption. In Chapter 3 I analyze the fluctuations of price research through the business cycle. Chapter 4 presents a general equilibrium model with endogenous product quality and firm creation and Chapter 5 concludes.1

1_{Chapter 2 was presented as a working paper at 5}th_{PhD Student Workshop in Economics (Braga,}

2017). Chapter 3 was presented as a working paper at 12th _{Annual Meeting of the Portuguese}

Economic Journal (Lisbon, 2018), the 4thDoctoral Workshop on Quantitative Economic Dynamics (Konstanz, 2018), and the 50thAnniversary Conference of the Money, Macro & Finance Research Group (London, 2019).

Deep habits in New Keynesian

model with durable goods

2.1

Introduction

New Keynesian models, with imperfect competition and price stickiness, have become the standard choice for fiscal and monetary policy analysis. More recently, these have been extended to two-sector models to accommodate the evidence from data, where consumption of durable goods responds negatively and more sharply to monetary policy shocks than consumption of nondurable goods.

However, the baseline two-sector model fails to replicate empirical evidence for monetary-policy shocks when the prices of durable goods are perfectly flexible. Fol-lowing a interest rate hike, households reduce their nondurable consumption but increase their durable consumption. Most literature using two-sector NK models, such as Monacelli(2009) and Carlstrom & Fuerst(2010), has focused on solving this problem, known as the comovement problem.

Another shortcoming of the model is its inability to replicate the responses, ob-served in US data, for consumption of durable and nondurable goods, as well as the response of relative price of durable goods, to increases in government spending. In the two-sector NK model, following an increase in government consumption, the re-duction of consumption of both goods is linked to an increase of markups in both

sectors, which goes against the empirical evidence found in Rotemberg & Woodford (1991), Monacelli & Perotti (2008) and Afonso & Costa (2013). Likewise, the model generates countercyclical response of markups to TFP shocks, which goes against with empirical evidence for US that shows a positive response of the average markups to supply shocks.

In this chapter I begin by analyzing the cyclical properties of markups for manu-facturing and services’ industries in the US. I find that the assumption of increasing returns is relevant to the cyclical properties of markups at an individual industry level, but not at a more aggregated level. The markups of individual industries tend to be more negatively correlated with output and consumption when we assume increasing returns, as in Rotemberg & Woodford (1991), comparing with constant returns, as in Nekarda & Ramey (2013).

On the other hand, the markup of overall private industries, as well as the markups of durable goods and nondurable goods display identical correlation coefficients, re-gardless of the assumption made on the returns to scale. Another key finding is that, while inclusion of construction in the consumer durables does not affect significantly the correlation coefficients, if we include services industries in the nondurable indus-tries, the coefficients become more negative for increasing returns and turn positive for constant returns.

Moreover, I find that markups of consumer nondurables are slightly more coun-tercylical than those of durables. Both markups display also similar correlation coef-ficients when comparing to past deviations of GDP, with the markup of nondurables maintaining more negative correlation coefficients. Taking into account this evidence, one can expect a response to shocks of both markups identical to the one observed for the average markup in the US.

To bring the results from the NK model closer to the ones observed in the data, I introduce deep habits - i.e. habits over differentiated goods - into the two sector

NK model. I build on the perfect capital markets model of both Monacelli (2009) and Sterk (2010), extending them to include government spending and TFP shocks. While DH over nondurable goods are formulated in an analogous way to the models with only one type of goods, the specification of DH on durables’ consumption is more challenging.

Since consumer durables are goods that do not wear out quickly, consumption of durable goods comprises not only the goods acquired in the period but also the undepreciated stock of durable goods from past periods. Therefore, unlike in the nondurable goods case, it is different if one defines habit formation over the stock of durables consumed or over the purchases of durable goods. While defining habit formation over stocks is appropriate for when we are dealing with a bigger and long-lasting type of durables, e.g. houses, that can be modified/improved over time, habit formation over purchases is suitable for the case of other consumer durables, e.g. electronics, furniture, etc, where one buys a new one instead of repairing it. Here I present the two alternative definitions of habits over durable goods and analyze the results obtained.

DH were originally introduced into general equilibrium models by Ravn et al. (2006). The firms’ problem in models with DH is analogous to the ones in mod-els of brand-switching costs1_{, where firms decide between lowering prices to capture} market share and raising prices to exploit its current locked consumers. However, in DH models the shift in consumption between differentiated goods is gradual and not discrete, which facilitates their incorporation into a dynamic general equilibrium framework.

These models proved to be useful in the study of effects of government spending shocks. With DH, the consumers’ demand displays a rigid component linked to past consumption. As such, when consumers increase their spending it only affects the

elastic part of demand, leading to a procyclical elasticity. Symmetrically, DH imply countercylical markups by which increases in government spending lead to increases in real wages and private consumption.

Due to the effects of countercyclical markups on inflation, DH were also used in the analysis of effects of monetary policy, where Ravn et al. (2010) and Zubairy (2014) stand as the main examples. Similarly, Gilchrist et al. (2017) introduce DH to help explain the inflation dynamics during the 2008 financial crisis. Other gen-eral equilibrium models produce countercyclical markups in response to TFP shocks. Well known examples are models with endogenous firm entry - Jaimovich(2007) and Jaimovich & Floetotto (2008) - or endogenous product variety - Bilbiie et al. (2012). I find that the two-sector model with DH can generate, even when formed only over nondurable consumption, a positive response of markup of nondurables to TFP shocks and negative response to government spending of both markups. When added to the model, DH over purchases of durable goods amplify the responses of markups to shocks and generates a crowding-in effect of government spending on the con-sumption of both goods. The model with habits on both goods can also generate a procyclical response of the relative price to demand shocks - monetary and fiscal - and countercyclical to supply-side shocks. Even when we consider that prices in the durable sector fully adjust one period earlier than in the nondurable sector, the results from the model hold.

As aforementioned, I also considered the hypothesis of habits being formed over the stock of durable goods. However, I find that they have a small effect on the results generated by the model. Since stocks of durable goods are disproportionately larger than nondurable consumption and durable purchases, the marginal utility and its volatility are substantially lower and, accordingly, the marginal effects of DH are damped.

Additionally, the determinacy of the model with habits on stocks is only marginally affected by the degree of habits. In contrast, the model with habits over purchases of durable goods exhibits multiple equilibria when the degree of habits is relatively high.

The remainder of the chapter is organized as follows. Section 2.2 presents the empirical evidence on cyclical properties of markups for the manufacturing industries in the US. Section 2.3 describes the NK model with two sectors and deep habits and discusses the results. In Section 2.4 I present an alternative specification of the model where habits are formed over the stock of durable goods. Section 2.5 concludes.

2.2

Empirical evidence on markups

To assess the performance of models presented in sections 2.3 and 2.4, one can estimate how the consumption, markups and prices behave in the data. Despite the extensive empirical literature on the behavior of markups and on the behavior of consumption and prices of durables and nondurables, there is a gap in the knowledge of how they interact. So, to fill this gap one must compute the markups for the industries in the two sectors and analyze how they behave during the business cycle. In this section, using quarterly data on industries of US, I calculate the markups and analyze their cyclical properties. As methodology, I follow two different approaches: the one inRotemberg & Woodford(1991) and the other in Nekarda & Ramey(2013) which allow the estimation of markups with data available at industry level.2

2_{By measuring the markups using labor share one is introducing a procyclical bias in it. Since} labor does not immediately adjust to shocks, the labor share tends to be countercyclical, which, in turn, produces more procyclical markups. In Rotemberg & Woodford (1991), the authors correct it by making assumptions about returns to scale, while Nekarda & Ramey(2013) present different measures of hours and wages (e.g. overhead labor). In recent years, with increasing availability of microdata and computational capacity, new approaches to measure markups were introduced using the share of intermediates and data at firm level. One key example is Santos et al. (2018), where the authors assumed, supported by their estimates of microeconomic production functions with quantities, that intermediates work as substitutes for labor (e.g. firms can outsource labor). Due to the restricted data availability and for simplification and comparability purposes, in this study,

2.2.1

Methodology

First, theoretical markup of a given industry i at time t can be defined as

µi_t= P i t M Ci t , (2.1)

where P_ti is average price of output and M C_ti is average nominal marginal cost of industry i. Assuming that all firms in the industry minimize costs and equalize input prices to their marginal products, the marginal cost is given by M Ci

t = Wt

M P Li t

, where

Wt is the nominal wage rate and M P Lit is the marginal product of labor.

As in Rotemberg & Woodford (1991) I assume a production function represented by

Yt = F (Kt, ztLt) − Φt, (2.2) where Ktis the capital stock, Ltis the labor input, ztis the labor-augmenting technical progress and Φt is the fixed cost, growing at rate of trend output. Then, the markup can be written as

µt =

FH(Kt, ztLt) − φt

wt

, (2.3)

where φt is the measure of increasing returns. Assuming that the elasticity of substi-tution between capital and labor is equal to one (i.e. F (.) is a Cobb-Douglas), the log deviation of the markup from trend is given by

ˆ µi_t= ˆyi_t− ˆwi_t− ˆl_ti− (µ∗i− 1)si Lˆl i t, (2.4) where ˆyi

t is log deviation in output, ˆwit is log deviation in real wages and ˆlit is log deviation in hours. From the previous equation it can be defined two different

speci-markup are measured using labor share. This may introduce differences to the estimates obtained using the share of intermediate goods.

fications for the log deviation in industries’ markups - the constant returns case and increasing returns case.

In presence of constant returns, the fixed costs are ignored and the log deviation in markup is equivalent to the log deviation of the inverse of labor share, −ˆsi

Lt. This is in line with the baseline specification in Nekarda & Ramey (2013) and the price markup in Galí et al. (2007).

The second case is the full equation used inRotemberg & Woodford(1991), which includes the effect of increasing returns on markup fluctuations. Since employment, measured by ˆli

t, is correlated with the output, ˆµitwill be more countercyclical (or less procyclical) than in the constant returns model.

2.2.2

Cyclical properties of markups

To find the cyclical properties of cross-industry markups in US, I use quarterly data from Current Employment Statistics and NIPA tables for the 1980-2016 period.3 Specifically, I use data for total gross value added (GVA) and data on aggregate weekly hours and earnings of production and nonsupervisory employees. Since the quarterly data for GVA by industry only covers the period from 2005 onwards, the missing periods were estimated through the interpolation of annual data using auxiliary time series, shown in the Table A.1.1. Table 2.1 displays the correlation coefficients of the markups with real GDP (Y ), real gross value added of the industry (Yi) and real personal consumption expenditures (C).

As expected, the markups computed assuming constant returns tend to be pro-cyclical, while in the increasing-returns case they tend to be countercyclical. This is explained by the countercyclical behavior of labor share4_{, which is only offset when} we consider the increasing returns part of equation 2.4.

3_{The data that support the findings of this study are available on request from the author.} 4_{As aforementioned, this is the main caveat of labor-share approach to markup estimation. Due} to the adjustment costs in labor, the labor-share tend to be countercyclical, leading to a more procyclical markup.

On aggregate level, the markups of manufacturing, as well as the goods-producing industries, tend to be unconditionally countercyclical. Likewise, both durable and nondurable goods industries displaying a countercyclical behavior, although industries of durables only present significant coefficients for increasing returns.

As for services industries, most of them exhibit markups with countercyclical behavior when we consider increasing returns and procyclical or acyclical behavior when considering constant returns. One key exception is the industry of utilities that exhibit unconditional procyclical markups. One reason for this might be the fact that consumption of these services is acyclical and inelastic with respect to households’ disposable income.

When comparing with the GVA at industry level, one observes that markups dis-play more positively/less negative correlation coefficients than with the GDP. This ef-fect is most notorious in services industries such as finance, education and retail trade services. In contrast, the mining industries display a more countercylical markup when one considers the GVA at industry level.

Since we are interested in understanding how consumption behavior interacts with markups, the correlation coefficients between markups and private consumption (C) were also included in Table 2.1. However, these coefficients do not diverge significantly from the correlation coefficients with GDP.

While manufactured goods are a significant part of durable and nondurable con-sumption, they are not the only component. While nondurable private consumption comprises nondurable goods and services, durable consumption includes manufac-tured durable goods and residential investment.5 _{Therefore, to check the relationship} between consumption and markups, Table 2.1 includes the correlation coefficients for the industries linked to durable and nondurable consumption. While the proxy for

5_{Although, in National Accounts, residential investment is classified as Gross Capital Formation,} I considered it as part of durable consumption. The explanation behind this decision is that resident investment is commonly regarded as durable consumption the NK model and my interest is to compare the results from the model to the ones obtained for the US.

Table 2.1: Unconditional correlation coefficients between markups and real GDP (Y ), real industry GVA (Yi_{) and real PCE (C) in US (1980:I-2016:IV)}

Industry Constant returns Increasing returns

Y Yi _{C Y Y}i _C Private Industries .018 .063 -.009 -.189∗∗ .145∗ -.194∗∗ Mining .218∗∗∗ _-.428∗∗∗ _{.107 .188}∗∗ _-.466∗∗∗ _.111∗ Utilities .018 .328∗∗∗ .016 .034 .229∗∗∗ .014 Construction .018 .169∗∗ .038 -.085 -.098 -.017 Manufacturing -.298∗∗∗ -.100∗∗ -.299∗∗∗ -.469∗∗∗ -.280∗∗∗ -.421∗∗∗ Durables -.117 .042 -.143∗ -.367∗∗∗ -.230∗∗∗ -.337∗∗∗ Nondurables -.191∗∗ .180∗∗ -.183∗∗ -.269∗∗∗ -.145∗∗∗ -.243∗∗∗ Wholesale Trade(1) .311∗∗∗ .365∗∗∗ .181∗ -.269∗∗∗ -.145∗ -.243∗∗∗ Retail Trade(1) _{-.068 .455}∗∗∗ _{-.123 -.408}∗∗∗ _.202∗∗ _-.406∗∗∗ Transportation and Warehousing(2) -.120 .300 ∗∗ -.192 -.642∗∗∗ -.197 -.691∗∗∗ Information(2) _{-.037 .635}∗∗∗ _{-.071 -.286}∗∗ _.255∗ _-.289∗∗ Finance, Insuarance

and Real Estate(2)

.046 .829∗∗∗ .117 -.258∗ .602∗∗∗ -.211 Professional and

Business Services(2)

-.164 .263∗ -.176 -.715∗∗∗ -.417∗∗∗ -.677∗∗∗ Education, Health and

Soc. Assist. -.154∗ .595∗∗∗ -.075 -.186∗∗ .385∗∗∗ -.096 Arts, Enterteinment, and Recreation .092 .447∗∗∗ .118 -.363∗∗∗ -.033 -.320∗∗∗ Goods Producing -.186∗∗ -.200∗∗ -.314∗∗∗ -.407∗∗∗ -.047∗∗∗ -.486∗∗∗ Services Providing .148∗ .230∗∗∗ .155∗ -.453∗∗∗ -.368∗∗∗ -.399∗∗∗ Durables plus Construction -.098 -.033 -.128 -.329∗∗∗ -.272∗∗∗ -.318∗∗∗ Nondurables plus Services .112 .270∗∗∗ .121 -.479∗∗∗ -.325∗∗∗ -.420∗∗∗ Notes: Asterisks indicate the significance levels for correlation coefficients: 1%(***), 5%(**) and 10% (*); (1) Only data from 1992 to 2016 is available; (2) Only data from 2005 to 2016 is available. All variables are in log deviations. The log deviations for Y , Yi _{and C were obtained using HP filter.}

durable consumption is given by the industries of manufactured durable goods and construction, the proxy for nondurable consumption is given by nondurable goods plus the industries in "services providing".

The main finding is that, despite the procyclical/acyclical behavior of markups in construction, its inclusion in durable consumption does not affect the behavior of markups in durables. On the other hand, the inclusion of services in nondurable consumption industries turns the markup more procyclical for the case of constant returns and more countercyclical with increasing returns. As a result, the coefficients of durables (plus construction) are slightly less negative than those of nondurables (plus services) for increasing-returns case, but they are significantly more positive in the constant-returns case.

Figure 2.1: Cross-correlation between real GDP and average markups (constant re-turns) durables plus construction (blue), nondurable plus services (red)

−8 −6 −4 −2 0 2 4 6 8 GDP(-t)/GDP(+t) (in quarters) −0.6 −0.4 −0.2 0.0 0.2 0.4 co rr el at io n Durables Nondurables

Even when analyzing the correlation coefficients between the markups and past (lags) and future (lead) deviations in GDP, the markup of nondurable consumption continues to display lower correlation coefficients than the markup of durable con-sumption (Figure 2.1). Nevertheless, both markups present a negative correlation

with past to contemporaneous gaps in GDP and a positive correlation with most of the leading GDP.

The lower cross-correlation with GDP observed for the markup of consumer durables in Figure 2.1 may be partially explained by the more volatile behavior of durable consumption, mainly during recessions (Figure A.1.1), that leads to a more volatile markup. This is in line with the findings in Baxter (1996), which suggests that the behavior of durable consumption over the business cycle is more volatile than the nondurable consumption.

Since there is also a comovement in the response to shocks of the consumption of durables and nondurables, one cannot reject that the response of the two average markups has the same signal, in spite of a more acyclical response of the markup of durable industries.

2.3

Model

2.3.1

Households

Consider a representative household who derives utility from consumption basket

Xt and disutility from supplying labor Lt. The aim of this household it to maximize the expected value of its discounted utility:

Eo (_∞ X t=0 βtU (Xt, Lt) ) , (2.5)

where Xt is the consumption basket that aggregates, through a CES technology, the habit-adjusted nondurable goods Hc

t and the stock of durable goods Dt,

Xt=

h

where η ≥ 1 is the elasticity of substitution between services of nondurable and durable goods. The stock of durable goods evolves according to the law of motion:

Dt= (1 − δ)Dt−1+ Htd, (2.7)

where 0 < δ < 1 is the depreciation rate and Hd

t is the amount of habit-adjusted durable goods acquired in period t given by

H_td= Z 1 0 (I_i,td − θdSi,t−1d ) εd−1 εd _di _εd−1εd , εd> 1, (2.8) where Id

i,t is the durable purchases of varieties indexed by i ∈ [0, 1] in period t, θdis the degree of habit formation over durable goods, S_i,t−1d represents the stock of external habit in durable good i in period t and εd is the elasticity of substitution between differentiated varieties of durable goods. This stock of external habits depends on all durable purchases in the past and evolves according to the following law of motion:

S_i,td = ρhSi,t−1d + (1 − ρh)Ii,td, (2.9) where ρh ∈ [0, 1] is the degree of persistence of external habits. For ρh = 0, the habits will only depend on the previous consumption period and the consumption adjusts more rapidly. On the other hand, if we define a sufficiently high degree of persistence, e.g. ρh = 0.85, household will put a greater weight on past levels of consumption and response to shocks will be more moderate. Id

i,t is defined as the level of consumption of each variety i in the period t.

As for nondurables the composite habit-adjusted good, Hc

t, formally described as H_tc = Z 1 0 (Ci,t− θcSi,t−1c ) εc−1 εc di _εc−1εc , εc> 1, (2.10)

where Sc

i,t−1 represents the stock of external habits in nondurable good i in period t,

θc the degree of habit formation and εc are the elasticities of substitution of varieties of nondurables. This stock of external habit depends on all nondurable consumption in the past and evolves according to the following law of motion:

S_i,tc = ρhSi,t−1c + (1 − ρh)Ci,t, (2.11) where Ci,t is level of consumption of each variety i of nondurable goods in the period

t and, as for equation 2.9, ρh ∈ [0, 1].

For any given level of consumption of Itand Ct, the demand of each differentiated variety of goods i ∈ [0, 1] in period t must solve the dual problem of minimizing total expenditures R1

0 Pi,tdIi,tdi and

R1

0 Pi,tcCi,tdi, subject to the aggregation constraints 2.8 and 2.10, where Pd

i,t and Pi,tc are the nominal prices of a durable and nondurable goods of varieties i, respectively, at time t.

The optimal level of demand I_i,td and Ci,tfor i ∈ [0, 1] are given by

I_i,td = P d i,t Pd t !−εd H_td+ θdSi,t−1d , (2.12) Ci,t = Pc i,t Pc t !−εc H_tc+ θcSi,t−1c , (2.13) with Pd

t and Ptc being the nominal price indices defined as Ptd=

 R1 0  Pd i,t 1−εd di  1 1−εd and Pc t =  R1 0  Pc i,t 1−εc di  1 1−εc .

The consumer has the following budget constraint:

P_tcCt+ PtdI d

t + Rt−1Bt−1 = Bt+ WtLt+ Tt+ Πt, (2.14) where Pc

t is the price of nondurable goods, Ptd is the price of durable goods, Bt is nominal debt, Rt is the nominal interest rate, Wt is the nominal wage rate, Tt the

taxes paid, and Πt are the dividends distributed by firms. In real terms, the budget constraint can be expressed as

Ct+ qtItd+ Rt−1 bt−1 πc t = bt+ wtLt+ Tt Pc t + Πt Pc t , (2.15) where wt ≡ W_Pct t is real wage, qt ≡ Pd t Pc

t is the relative price of durable goods, bt ≡

Bt

Pc t

is the real debt, and πc t ≡

Pc t

Pc

t−1 measures the evolution of price index of nondurable

goods.

The first-order conditions or the representative household’s optimization problem are give by −Ul,t Uhc_,t = wt, (2.16) Uhc_,t = λ_t, (2.17) qtUhc_,t= U_d,t+ β(1 − δ)E_t{U_hc_,t+1q_t+1}, (2.18) 1 = βEt ( Uhc_,t+1 Uhc_,t Rt πc t+1 ) . (2.19)

Equation 2.16 is the standard condition linking the real wage to the marginal rate of substitution between consumption and leisure, i.e. the Frisch labor supply elasticity. In equation 2.18 households equate the marginal utility of nondurable consumption to the shadow value of utility obtained from durables goods that includes not only utility from an additional unit of durable goods today, but also the discounted expected value of undepreciated part of stock of durables in the next period. Equation 2.19 is the standard Euler consumption equation.

2.3.2

General Government

Each period, general government balances its budget6 _{by collecting T}

tfrom house-holds and spending GtPtc in the acquisition of goods. As in Erceg & Levin (2006) and Cantelmo & Melina(2018), I assume that government only acquires nondurable goods. The real government spending Gt follows the exogenous stochastic process:

ln(Gt/ ¯G) = ρgln(Gt−1/ ¯G) + gt, (2.20)

where g_t ∼ N (0, σg) represents the exogenous innovation to fiscal policy. As inRavn et al.(2006), I also consider that government allocates spending to the several varieties of nondurable goods through the equation:

Htg = Z 1 0 (Gi,t− θcSi,t−1g ) εc−1 εc _di _εc−1εc , (2.21)

where S_i,t−1g also represents the stock of external habits formed on government spend-ing over good i in period t. As for households, the stock of habits is given by

S_i,tg = ρhSi,t−1g + (1 − ρh)Gi,t. (2.22) The rationale behind this that, as stated inRavn et al.(2006), government spend-ing is not wasteful, as households value it, though separately from private consump-tion and labor decisions. Moreover, they also form habits over them. This means that is difficult for the general government to cut significantly its expenditure as house-holds are accustomed to certain level of public services. For any given level of Gt, the demand of each variety of goods i ∈ [0, 1] in period t must solve the dual problem of minimizing total expenditure R1

0 Pi,tcGi,tdi, subject to the aggregation constraint 2.21.

6_{With infinitely-living households Ricardian equivalence holds, so not much is lost from using} this form.

The demand for Gi,t, with i ∈ [0, 1] are given by Gi,t = Pc i,t Pc t !−εc H_tg+ θcSi,t−1g . (2.23)

2.3.3

Firms

Each variety of good i in sector j is produced using labor via the following linear production function:

Y_i,tj = AtLji,t, (2.24)

where Y_i,tj denotes the output of good i in sector j = c, d, Lj_i,t denotes the labor input, and At is the aggregate TFP, which follows a first-order autoregressive process:

ln(At) = ρaln(At) + at, (2.25) where a

t ∼ N (0, σa) is the exogenous innovation in technology. The profits of each producer i in nondurable and durable sectors are given by

Πc_i,t = C_i,tcP_i,tc + Gi,tPi,tc − WtLci,t−

ϑc 2 P_i,tc Pc i,t−1 − 1 !2 Y_tcP_tc, (2.26)

Πd_i,t = I_i,tdP_i,td − WtLdi,t −

ϑd 2 Pd i,t Pd i,t−1 − 1 !2 Y_tdP_td, (2.27) where ϑj 2  P_i,tj P_i,t−1j − 1 2

Y_tjP_tj is the quadratic cost of price adjustment proportional to nominal output of each sector.

The firm’s problem is to maximize the expected discounted value of profits:

E0 ∞ X t=0 βtUhc,t Uhc_,0 Pc o Pc t Πj_i,t, (2.28)

subject the equilibrium conditions in the markets of nondurable and durable sectors: Y_tc= Ct+ Gt+ ϑc 2 (π c t − 1) 2_Yc t , (2.29) Y_td= I_td+ϑd 2 (π d t − 1) 2_Yd t , (2.30)

and to the demand equations 2.13 and 2.23, in the nondurable sector, and 2.12 in durable sector, plus the production function of 2.24 and the equations for the habit accumulation 2.9, 2.11 and 2.22. The first-order conditions for optimization problem of firms in nondurable sector are give by

Ct+ Gt Yc t −εcνtc H_tc+ H_tg Yc t = ϑc(πtc−1)π c t−βϑcEt ( Uhc_,t+1 Uhc_,t Y_t+1c Yc t (π_t+1c − 1)πc t+1 ) , (2.31) ν_tc= 1 − wt At + (1 − ρh)λct, (2.32) λc_t = βEt ( Uhc_,t+1 Uhc_,t  θcνt+1c + ρhλct+1  ) , (2.33) where νc

t and λct are the Lagrange multipliers for the demand equations, 2.13 and 2.23, and habit accumulation equations, 2.9, 2.11 and 2.22, respectively.

From the first-order conditions, we observe that the special case where ρh = 0 and θc = 0, i.e. households do not form habits, is the baseline NK model with two goods. When θc > 0, firms know that selling more goods today implies selling more goods tomorrow, as households and government increase their subsistence point over varieties. This means that each firm has an incentive to lower price charged today,

in order to capture customers and charge them more in future periods.7 _{For the} special case where ρh = 0 and θc > 0, one obtains the first order conditions of firms maximization problem in Zubairy (2014).

As in the nondurable sector, the first-order conditions for the maximization prob-lem of durable producers are:

Id t Yd t − εdνtd Hd t Yd t = ϑd(πtd− 1)π d t − βϑdEt ( Uhc_,t+1 Uhc_,t qt+1 qt Yd t+1 Yd t (π_t+1d − 1)πd t+1 ) , (2.34) ν_td= 1 − wt qtAt + (1 − ρh)λdt, (2.35) λd_t = βEt ( Uhc_,t+1 Uhc_,t qt+1 qt  θdνt+1d + ρhλdt+1  ) , (2.36) where νd

t and λdt are the Lagrange multipliers for the demand equations and habit accumulation equations, respectively.

2.3.4

Market-clearing conditions

Equilibrium in labor market requires:

X

i

Lc_i,t+X i

Ld_i,t = Lt. (2.37)

The monetary policy rule is given by

Rt ¯ R = _π˜ t π φπ exp(εt), (2.38)

7_{This feature is also found in the customer-market pricing models as the one described in Bils} (1989). In the customer-market models, monopolists also reduce their markup to attract new cus-tomers, that have no prior information on the quality of the product being sold.

where ˜πt = πτc,tπ

1−τ

d,t is the composite inflation index and the policy shock evolves according to:

exp(εt) = exp(εt−1)ρπut, (2.39) with ut ∼ N (0, σa) and ρπ ranging from zero to one.

2.3.5

Calibration and solution method

The baseline NK model is calibrated followingMonacelli(2009) andSterk (2010). The discount factor β is set to 0.99, which implies a steady-state annual real rate of return of 4 percent. The quarterly depreciation rate for durable goods (δ) is 2.5 percent. As in Tsai (2016), γ, the utility weight of durable goods, is set to 0.25 and the elasticity of substitution between nondurable and durable services (η) is equal to 1. The steady-state level of government spending is set to 20% of aggregate output, which is in line with the weight of general government expenditure in GDP for the US.

Furthermore, I assume that the utility function of household takes the following form:

U (Xt, Lt) = ln(Xt) − ν

L1+χ_t

1 + χ,

where the parameter ν is positive and calibrated so that, in steady-state, the labor supply is equal to 1/3.

The elasticities of substitution between varieties for nondurable and durable goods (εcand εd) are equal to 6, which implies a steady-state price markup of 1.2. Similarly toMonacelli(2009), the nondurable price adjustment cost parameter (ϑc) is calibrated so that firms can adjust their prices every four quarters. It is assumed that the degree

of habits on durable purchases is lower than that of nondurable consumption and set

θc and θd equal to 0.6 and 0.3, respectively.

The weight of durable goods in composite inflation is equal to the weight of expen-diture on durable goods in total consumption expenexpen-diture (τ = 0.2). The coefficient of inflation in the Taylor rule, φπ, is set to 1.5. As inRavn et al.(2006), the persistence parameters for habits is set to 0.85 and the persistence parameters for productivity shocks and government shocks are set to 0.9. The persistence parameter for monetary policy shocks is set to 0.5. The model is solved by a first-order perturbation method. All IRFs are presented as log deviations from steady-state values.8

2.3.6

Results and discussion

The IRFs from the model with the same degree of price adjustment costs in both sectors are shown in Figure 2.2. When there are no habits, i.e. θc= θd= 0, the IRFs of consumption are fairly in line with the ones from a canonical NK model with only one type of goods. Both durable investment (Id

t) and nondurable consumption (Ct) respond negatively to a policy-rate shock and positively to a technology shock. One caveat of the plain-vanilla NK model is the crowding-out of private consumption in response to increases in government spending.

The responses of markups and the relative price of durable goods to fiscal and technology shocks are also at odds with empirical evidence. Following a positive shock in government spending, firms do not fully adjust their prices in response to an increase in demand for their goods and, therefore, they partially reflect it through the reduction of the real wage paid, which implies a reduction of marginal costs and increase of markups in the two sectors. When there is a temporary TFP shock, the increase in labor productivity is more than offset by the increase in employment and wages, leading to a increase in marginal costs and decrease in markups.

8_{The data and codes that generated the figures in this chapter are available on request from the} author.

Figure 2.2: Impulse-response functions to one percent monetary-policy (yellow), government-spending (red), and productivity (blue) shocks for the model with and without DH in nondurable and durable purchases

0 2 4 6 8 10 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 No nd ur ab le Co s.

Mo etary Policy

0 2 4 6 8 10 −0.05 −0.04 −0.03 −0.02 −0.010.000.01 0.02

Gover me t Spe di g

0 2 4 6 8 10 −0.10.0 0.1 0.2 0.3 0.4 0.5

Productivity

0 2 4 6 8 10 −200 −150 −100−50 0 50 Du rab le Co s. 0 2 4 6 8 10 −1.0 −0.50.0 0.5 1.0 1.5 0 2 4 6 8 10 01 23 45 67 89 0 2 4 6 8 10 −50 5 10 15 20 Ma rku p No d ura ble s 0 2 4 6 8 10 −0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.050.000.05 0 2 4 6 8 10 −0.6 −0.4 −0.20.0 0.2 0.4 0.6 0.8 0 2 4 6 8 10 −50 5 10 15 20 Ma rku p Du rab les 0 2 4 6 8 10 −0.30 −0.25 −0.20 −0.15 −0.10 −0.050.000.05 0.10 0 2 4 6 8 10 −0.4 −0.20.0 0.2 0.4 0.6 0.8 0 2 4 6 8 10 −5 −4 −3 −2 −10 1 Re lat ive Pr ice 0 2 4 6 8 10 0.00 0.02 0.04 0.06 0.08 0 2 4 6 8 10 −0.3 −0.2 −0.10.0 0.1 0.2 0.3

Baseli e

Deep Habits

The presence of DH, even when only formed over nondurable goods, enhances the responses of consumption and prices to monetary-policy and TFP shocks (see Figure A.1.2). For a moderate degree of habit formation, the response to a government-spending shock of private durable and nondurable consumption would be less negative than in the baseline model.

With sticky prices in durable goods, the habits on nondurable consumption alone allow for a decrease in the markup of both sectors. Since the wage rates are the equal

for both sectors, the increase of real wages in nondurable sector translate into an increase of real wages in the durable sector.

The introduction of DH on durable purchases leads to considerable improvements in the model. The response of consumption of nondurable goods to increases in government spending becomes positive, while the durable consumption is positive at the beginning, but it then turns, negative.

The response of durable markups and relative price of durables to a TFP shock is now positive and in line with empirical evidence. The IRFs of relative price to demand shocks are also in line with the IRFs we obtained from the data.

It is also worth noting that the model with DH generates an initial positive re-sponse of real wages to a government spending shock that translates into an increase in inflation (˜πt) as the markups do not absorb all the impact in marginal cost.

Likewise, the nonlinear response of inflation to a productivity shock is explained by the different dynamics of markups and real wages. Following the shock, the increase in real wages is lower than the increase in marginal productivity, leading to a decline of marginal cost that more than offset the positive response of the markups. However, as real wages continue to increase and the marginal productivity returns to the steady-state level, the inflation picks up, driven by higher marginal cost. As the wage rate decelerates, the marginal costs stabilizes and the decreasing markup contributes to a decrease in inflation rate.

Although empirical evidence from the literature suggests that prices of goods in the durable sector may be more flexible than in the nondurable sector9, I only present the results from the model where prices have the same degree of stickiness for both sectors, as the results are qualitatively similar for lower periods of adjustment in prices of durable goods. With different degrees of price rigidity, the signal of responses

9_{SeeKlenow & Malin (2010) and Nakamura & Steinsson(2008) for microeconometric evidence} on the frequency of price adjustment. Cantelmo & Melina(2018) estimate an Bayesian DSGE and also find a lower degree of price stickiness in durable goods sectors.

remains the same, however the profile of IRFs changes significantly with increasing flexibility in prices of durable goods. The initial responses to fiscal spending and TFP shocks are amplified but, because price adjust faster in durable sector, the responses are less persistent.

Figure 2.3: Impulse-response functions to one percent shocks for the variables of employment, wages and inflation

0.0 2.5 5.0 7.5 10.0 −15 −10 −5 0 Em plo ym en t Monetary Policy 0.0 2.5 5.0 7.5 10.0 0.0 0.1 0.2 0.3 Gover me t Spe di g 0.0 2.5 5.0 7.5 10.0 −0.2 0.0 0.2 0.4 0.6 Productivity 0.0 2.5 5.0 7.5 10.0 −15 −10 −5 0 Re al Wa ge 0.0 2.5 5.0 7.5 10.0 0.0 0.1 0.2 0.3 0.0 2.5 5.0 7.5 10.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.5 5.0 7.5 10.0 −1.5 −1.0 −0.5 0.0 0.5 I f lat io 0.0 2.5 5.0 7.5 10.0 −0.02 −0.01 0.00 0.01 0.0 2.5 5.0 7.5 10.0 −0.02 0.00 0.02 0.04 0.06

Baseli e Deep Habits

In the same way, the results of the model do not change significantly when I introduce capital accumulation in the model, even though it reduces the effectiveness of habit formation (see appendix A.2). The differences are an increase in the crowding-out effect in private consumption, in response to a government-spending shock and the change of signal in the response of markups to productivity shocks.

2.4

Deep habits over stock of durable goods

Unlike the habit formation over nondurable goods, the modeling of habits over durable goods poses the challenge of whether consumers develop habits over the purchases of durable goods or over utilization of stocks of durable goods. In this section I study the effects of DH over stocks of durables and compare it to the results obtained for flows. Consider that the representative household develops habits over stocks of differentiated durable goods. The habit adjusted stock, Hs

t, is given by H_ts = Z 1 0 (Di,t− θkDi,t−1) εd−1 εd _di _εd−1εd , (2.40)

where Di,t is stock of each variety i of durable goods at time t and θk is the degree of habits on each stock of varieties of durable goods. The accumulation of each variety of goods follows the same law of motion of aggregate durable goods:

Di,t = (1 − δ)Di,t−1+ Ii,t. (2.41) For simplification, the depreciation rate, δ, is the same across all varieties and continues to be equal to 0.025, which implies a lifespan of 10 years of each variety. As in the baseline model, the consumer must solve the dual problem of minimizing total expenditures R1

0 Pi,tdIi,tdi, subject to the aggregation constraint 2.40 and the stock accumulation equation 2.41. The demand for each variety of good It is defined by

I_i,td = P d i,t Pd t !−εd H_ts− (1 − δ − θk)Di,t−1. (2.42) From demand equation 2.42, we can see that the household defines the optimal quantity of habit-adjusted aggregate stock of durable goods, Hs

t, and then chooses the quantity of each variety it needs, taking into account the undepreciated habit-linked quantity of stocks of differentiated goods.