An empirical investigation of the relation between fiscal policy decisions and economic growth using a GVAR model

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MS

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HESIS

An empirical investigation of the relation

between fiscal policy decisions and

economic growth using a GVAR model.

Author: Marie-Anne BEENS Student Number: 11095792 Supervisor: Dr. K.J.VANGARDEREN Second reader: Dr. J.C.M.VANOPHEM

A thesis submitted in fulfillment of the requirements for the Econometrics track of MSc. Econometrics

in the

Faculty of Economics and Business Amsterdam School of Economics

Faculty of Economics and Business

Amsterdam School of Economics

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Statement of Originality

This document is written by Student Marie-Anne BEENSwho declares to take full respon-sibility for the contents of this document. I, Marie-Anne BEENS, declare that the text and

the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Eco-nomics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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UNIVERSITY OF AMSTERDAM Economics and Business Amsterdam School of Economics

MSc. Econometrics

An empirical investigation of the relation between fiscal policy decisions and economic growth using a GVAR model.

by Marie-Anne BEENS

Abstract

The main purpose of this thesis is to empirically analyse the effectiveness of area-wide and domestic fiscal and monetary policies on economic growth. Outcomes of previous literature were varying because they are largely depending on empirical setting, tech-nique and sample. Moreover, the majority of studies considered single-countries or mod-elled the countries in isolation when a multi-country framework was adopted. In order to improve the results of the investigation, there are several important areas where this thesis makes an original contribution. First, this thesis addresses the sources of hetero-geneity in the previous results by providing a Ward’s cluster analysis based on a coun-try’s governmental quality measured in the six World Governance Indicators (WGI). The cluster analysis results in six clusters with small within-variances and relatively large dif-ferences between clusters. Subsequently, a global VAR (GVAR) model is built to account for the interdependencies between countries. The input for the GVAR model is a new dataset consisting of a complete and comprehensive set of countries to obtain a full rep-resentation of the global economy whereas this completeness is missing in previous liter-ature. The dataset ranges from 1994 to 2014 and contains six variables for 148 countries and quarterly observations. Moreover, this thesis fills a gap in the existing literature by imposing several long-run relations suggested by economic theory. Understanding the link between long-run relations and the theory will provide an exciting opportunity to advance our knowledge of the forces that are at the root of the functioning of the (macro) economy. In this thesis, some interesting conclusions regarding the effects of fiscal poli-cies are presented. In general, an area-wide shock in government spending results in a negative real GDP per capita. Moreover, a domestic shock results in a positive stimu-lation of real GDP per capita in the country at the origin of the shock but the spillover effects indicate that increasing the fiscal expenditures in one country will not boost the pace of the economic growth in other countries.

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“He who buys what he does not need, steals from himself.”

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Acknowledgements

I would first like to thank my thesis supervisor Dr. K.J. van Garderen of the Faculty of Economics and Business at the University of Amsterdam for the patience, motivation and immense knowledge. His guidance helped me in all the time of writing this thesis. He consistently allowed this thesis to be my own investigation, but steered me in the right direction whenever he though I needed it.

I would also like to acknowledge Dr. J.C.M. van Ophem of the Faculty of Economics and Business at the University of Amsterdam as the second reader of this thesis and for enlightening me the first glance of econometric research.

My sincere thanks also goes to Dr. L. Vanessa Smith of the Department of Economics at the University of York. Without her passionate participation, input and expertise, the thesis could not have been successfully conducted.

I would also like to thank Mo for all the hours in the library and lunches in the can-teen.

Finally, I must express my very profound gratitude to my parents for providing me with unfailing support and continuous encouragement throughout writing this thesis and my life in general .

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Introduction

In the last two centuries global income has undergone a spectacular increase. While in 1800 global income was around 175 billion USD, it rose to 77,686 billion USD in 2015 (The World Bank, (2015)). With a population growth from 1 billion in 1800 to over 7 billion today, this led to a tremendous increase in income per capita . The discussion on whether or not government spending can boost the pace of economic growth flared up years ago and has not yet extinguished. Many politicians and journalists engage in the discussion and claim to say the truth. However, there is no point in simply stating an opinion without a solid justification. Plausible arguments for both sides of the discussion can easily be found causing theoretical reasoning to be insufficient to determine the net effect of government spending on growth. This thesis tries to clarify the ambiguities by analysing the relation between government spending and economic growth empirically. As a consequence of the strong increase and improvement of data collection in past decades, it is possible to assess the relation between government spending and economic growth in an empirical manner more sufficiently than before. Although there is a large volume of empirical research investigating the effects, robust conclusions have been dif-ficult to establish. A major obstacle in estimating the relation is the fact that government spending is part of the GDP which results in biasing towards finding a positive effect of government spending on growth. Moreover, it is quite likely that an increasing in-come gives rise to an increase in government spending. These events cause government spending to be endogenous with respect to economic growth.

It has conclusively been shown that the outcomes of previous studies are highly de-pendent on the empirical setting, technique and sample. A possible explanation for the latter might be that, when it comes to government spending, differences in structure of the authorities cause countries to be highly diverse and will result in heterogeneity in the fiscal variables. This thesis argues that the quality of government affects the efficiency of the allocation, uncertainty of agents, and risks in the market. Therefore, countries will

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respond differently to certain shocks of government spending and the intercept, slope and variance of shocks will be regime-specific. To circumvent these issues, a number of studies focussed solely on one country. However, modelling a single country ignores the interdependencies and chained effects between countries. There have been several stud-ies that were aware of this fact and, in order to prevent issues concerning the intercept heterogeneity, grouped a set of countries according to various pre-determined criteria: OECD membership, income per capita, growth levels, or geographical characteristics. The main drawback of such criteria is that, although they might result in more signifi-cant and efficient regressors, they do not explain the source of heterogeneity. In order to avoid this issue, this thesis uses cluster analysis based on governmental quality to im-prove the correctness of the results. Cluster analysis results in clusters with homogenous governmental quality and therefore in clusters with similar risks, uncertainties and allo-cations such that problems concerning slope heterogeneity will be avoided. The cluster analysis is based on the Ward’s minimum variance method evaluated on the squared Eu-clidean distance measure. The analysis results in six clusters of different sizes that are proven to have little differences within a cluster and relatively large differences between clusters.

There are several ways to model issues such as the relation between government spending and economic growth in economies. According to Canova and Ciccarelli (2013) there are two main movements. The first is to build sector, market, multi-country dynamic stochastic general equilibrium (DSGE) models, where agents are opti-mizers and where preferences, technologies and constraints are fully specified. Canova and Ciccarelli (2013) state that the main advantages of a tightly parameterized DSGE model are that they offer clear answers to policy questions and provide easy-to-understand welfare prescriptions. However, the major drawback of this approach is that it largely de-pends on the assumptions made in the specification of such a DSGE model. Difficulties arise when an attempt is made to implement the outcomes in real world situations be-cause they are highly relying on the assumptions of the model. Therefore, DSGE models should be considered solely as a benchmark. The second approach is to build a Vector Auto Regressive (VAR) model. There are several extensions on a standard VAR model such as a structural VAR (SVAR), panel VAR, and global VAR (GVAR) model. The com-mon factor in all extensions is that all variables are assumed to be endogenous and in-terdependent. This is ideal when investigating influences on economic growth for two reasons. Firstly, a VAR model deals with the anticipated endogeneity of government

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spending. Secondly, it allows for other factors affecting economic growth additionally to government spending such as the monetary policy and political system. In light of recent decisions in interest rate policies across several central banks, it is getting difficult to ig-nore the influence of monetary policies on economic growth. As monetary policies often target interest rates to contribute to economic growth and stability, it might be useful to study whether such policies achieve their goals. Several previous studies made an at-tempt to address the effect of government spending on economic growth using a (panel) VAR model (for example, Blanchard and Perotti (2002), Castro and Cos (2008), Burriel et al. (2010) Beetsma and Giuliodori (2011), Afonso and Sousa (2012)). The most important publications will be discussed in more detail in Chapter 2 Literature Review. While many of these studies constitute a sound basis for investigating the effect of government spend-ing on economic growth, the majority of these studies are of sspend-ingle countries or consider the countries in isolation when a multi-country framework is adopted. Therefore these studies do not properly take into account an important phenomenon in modelling the economy: although a country’s fiscal policy is a national issue it induces both benefits and negative impact across borders, known as spillover effects. This is due to the fact that economies of individual countries in the global economy are interdependent through a variety of channels. Chudik and Pesaran (2014) state that ’these channels include sharing scarce resources (such as oil and other commodities), political and technological developments, labour and capital movements across countries, cross-border trade in financial assets as well as trade in goods and services’. As these channels of interaction play a crucial role in alloca-tion of government spending and the rate of the economic growth, they should be taken into account when modelling the economy. In order to do this, this thesis builds upon the multi-country Global Vector Auto Regressive (GVAR) model originally developed by Pesaran, Schuermann, and Weiner (2004). The reason for using this model is not just that it is a convenient way to model interdependencies between countries but also because it effectively allows for combining countries in certain groups and, similar to standard VAR models, deals with the endogeneity of government spending. Therefore, the GVAR model has emerged as a powerful tool to address the effect of fiscal policy on economic growth in a global model.

The main purpose of this thesis is to assess to which extend fiscal policies have in-fluence on economic growth. This results in the main research question: ’What are the consequences of both exterior and interior policy shocks on economic growth? To take into ac-count the interaction of channels between economies, a GVAR model is being built.

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Fol-lowing Ricci-Risquete and Ramajo-Hernández (2015a), this thesis considers government receipts and government spending separately as both government expenditure and tax-ation affect the level of growth (Blanchard and Perotti (2002)). As the existing literature fails to explain the source of heterogeneity that is causing a lack of robustness in their obtained results, this thesis tries to improve the estimation of economic growth and takes into account unobserved heterogeneity by grouping the sample of countries using clus-ter analysis based on the quality of government. Thereafclus-ter, the resulting clusclus-ters are estimated and aggregated using the GVAR model. Moreover, this thesis considers the application of several long-run macroeconomic relations suggested by economic theory based on arbitrage conditions in (financial) markets. In this way, a cointegrating GVAR model is being build providing transparency with respect to the theoretical foundations and insights in the forces that are at the root of the functioning of the (macro) economy. Therewith this thesis aims to provide answers on the sub research questions:

• How should countries be grouped based on their alleged governmental quality?

• What are the effects of an instantaneous increase in government spending, especially in the cluster that consists of countries with a ’very satisfying’ level of government quality, on the economic growth in all clusters (including itself)?

• Does the quality of a government have an effect on the pace of economic growth induced by an increase or decrease in government spending?

• What are the effects of a shock in interest rates on economic growth and does this entail that the recently implied monetary policies will or will not achieve their desired targets?

In general, the results of this thesis show that the response of real GDP per capita to a positive domestic or area-wide shock in government spending are heterogenous across economies but mainly have a negative impact on the economic growth. However, the effects of domestic shocks are larger in the county at the origin of the shock. Moreover, it appears that the quality of the government indeed has an effect on the effect of gov-ernment spending on economic growth. With regard to the interest rate policies, this thesis reports on results that better resemble the intended goals. The effects of a negative domestic shock in interest rates are positive in the long-run for the country at the ori-gin of the shock, whereas it induces varying effects on the aggregated predetermined six clusters.

This thesis is organized as follows. In Chapter 2 a review of relevant previous litera-ture is provided. Chapter 3 presents the cluster analysis including the methods, data and

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results. Thereafter, Chapter 4 presents the methodology of modelling the GVAR frame-work. Chapter 5 describes the construction of the data. Subsequently, Chapter 6 displays the main results of the analysis of shocks on the pace of the economic growth. Finally, conclusions of this thesis are presented in Chapter 7.

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Chapter 2

Literature Review

A considerable amount of literature has been published on the effects of fiscal policies on economic growth. These studies vary largely in empirical setting, technique and sample of countries. Generally all literature since the early 2000s acknowledge economic biases such as the endogeneity bias and make efforts to avoid those. Therefore, the heterogene-ity of the results may at best be explained by the differences in the estimation strategy and sample of countries which result in issues with unobserved heterogeneity. This chapter mainly concentrates on literature using VAR, panel VAR, or GVAR methods and avoids a detailed review of literature using other approaches. For a comprehensive literature review of a great part of the literature, one is referred to the paper of Kneller and Misch (2016). In their paper, an overview of the research on effects of tax reforms on output levels and growth over the short- and long-run is provided. Moreover, the publication of Chudik and Pesaran (2014) surveys the latest developments in GVAR modelling and provides a synthesis of existing literature. In the current chapter the key papers on the effects of government spending on economic growth are discussed.

In 2002, the publication of Blanchard and Perotti (2002) reported a convenient struc-tural VAR (SVAR) procedure to capture the dynamic effects of government spending and tax shocks on economic activity and investment spending after the World War II in the U.S.A.. A structural form of the VAR model is preferred to represent underlying relations because in the structural form the error terms are not correlated and the vari-ables can have a contemporaneous impact on other varivari-ables. The paper was the first significant analysis and discussion, using a VAR type model to assess the relationship between government spending and economic growth. The authors used quarterly data and a three-dimensional vector of endogenous variables to find that positive government spending shocks have a positive effect on output and positive tax shocks have a negative effect on output. Moreover, they found that an increase in both types of shocks have a

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strong negative effect on investment spending. Although this study focusses solely on one country - the U.S.A. - its importance is justified as it is the foundation of a large vol-ume of published studies investigating the relation between government spending and economic growth.

Following Blanchard and Perotti (2002)’s standard SVAR framework, Burriel et al. (2010) investigated the sample of the aggregated Euro Area over 1981-2007. Their main results were that GDP and inflation increase in response to government spending shocks. They compared their sample to the U.S.A. and found that the outlier responses are simi-lar in both areas and typical below unit. In the same vein as Burriel et al. (2010), Kirchner, Cimadomo, and Hauptmeier (2010) investigated the aggregate Euro Area but they allow the effects of government purchases shocks to be varying by investigating time-varying structural VAR techniques. They found that short-run effectiveness of a shock increased until the end of 1980s, after which it declined again. In another previous major study, Ravn, Schmitt-Grohé, and Uribe (2007)’s study of government purchases covered only four industrialized countries: Australia, Canada, UK and U.S.A.. They again fol-lowed Blanchard and Perotti (2002)’s approach and found that an increase in government purchases raises output and consumption but leads to deterioration of the trade balance. Being aware of homogeneity problems when investigating a variety of countries, Castro and Cos (2008) targeted their research on Spain. They found that government expendi-ture shocks have a positive on output in the short-term at the cost of higher inflation an public deficits and lower output in the medium and long-term. Tax increases are found to drag economic activity in the medium term while entailing an only temporary improve-ment of the public budget balance. To repeat once again, it is important to bear in mind that modelling countries in isolation results in findings that only apply to that particu-lar country and moreover, it does not take into account the interaction channels between countries.

Unlike the previous studies mentioned in this chapter, Christiano, Eichenbaum, and Rebelo (2009) did not use a VAR-based model but carried out a DSGE model. Christiano, Eichenbaum, and Rebelo (2009) argued that the government-spending multiplier can be much larger under certain assumptions. However, as mentioned in Chapter 1 Introduc-tion, the assumptions imposed by a DSGE model are too restrictive and therefore a DSGE model, as such, cannot be considered as a reflection of real-life situations. Nevertheless, Afonso and Sousa (2012) used Christiano, Eichenbaum, and Rebelo (2009)’s insights and modelled a Bayasian SVAR to identify the fiscal policy shocks using Christiano,

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Eichen-baum, and Rebelo (2009)’s recursive partial identification for Germany, Italy, U.S.A. and UK. Their model illustrated that government spending shocks have a small effect on GDP and lead to crowding out effects.

Another study that is evading the use of a VAR model approach, but that is important to be mentioned, is the publication of Romer and Romer (2010). Their approach began by defining a dummy variable capturing the main episodes of military build-ups due to foreign policy crises and then it traced the effects over time of a shock to this dummy variable on several endogenous variables. The research of Monacelli and Perotti (2008) compared a reduced form SVAR model and a variation on the method of Romer and Romer (2010) with government spending on good and services, GDP, private consump-tion, private investment and in turn: mark-up, real consumption wage and real product wage. They found that government spending shocks cause private consumption and real product wage to rise but that mark-up responds negatively. In a follow-up study, Mona-celli and Perotti (2010) employed VAR techniques to a sample of U.S.A., Canada, UK and Australia from 1980 to 2006 to find that a rise in government spending induces a depreci-ation of the CPI real exchange rate and a trade balance deficit. Moreover, they illustrated that private consumption would rise and co-move positively with real exchange rates.

Born, Juessen, and Müller (2013) used a bigger unbalanced panel of OECD countries in the period 1986-2011 using an SVAR model and found that government spending mul-tipliers are larger under fixed exchange rate regimes. Corsetti, Meier, and Müller (2012)’s study covered a somewhat comparable time-period from 1975 to 2008 for 17 OECD coun-tries using a two-stage procedure to estimate impulse response functions for economies that differ in terms of their exchange rate regime. They found that the response of the real exchange rate to a spending shock varied systematically with the exchange rate regime and that there was an increase in fiscal multipliers during the time of a financial crisis. In the previous year, Beetsma and Giuliodori (2011) employed a SVAR model on 14 EU countries over the period 1970-2004. They divided the GDP into 4 categories: exports, private consumption, private investment and imports. The main results of the study were that government purchases raise output, consumption and investment but reduce trade balance.

A more recent study from Papaioannou (2016) estimated public spending multipliers following the original Blanchard and Perotti (2002) structural VAR economic framework using time series for each country in the EU for a period over 2004 and 2014. They found that size varies considerably across countries. After the SVAR model approach, they

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es-timated annual cross country data using an econometric framework and used interest rate as interaction effects. Their main result from the new analysis is that government spending can affect growth positively only when real interest rates become negative. The econometric model was estimated using GMM with level instruments to account for en-dogeneity. However, such level instruments are sensitive to suffer from the problem of weak instruments and the estimation could be improved using a GMM/IV Panel VAR model using the new instruments proposed by Hayakawa (2015).

In recent years, a great deal of literature studying economic growth through a VAR framework did not concern government spending. Major studies that are useful to men-tion because of their method and use of data are concerned with: excess liquidity using a sample of Sub-Saharan Africa (Saxegaard (2006)), public debt using a sample of 31 EU and OECD countries from 1995 to 2013 (Ogawa, Sterken, and Tokutsu (2016)), institu-tional quality using a short panel of 199 countries over 10 years (Góes (2016)). Saxegaard (2006) found that excess liquidity weakens the monetary policy transmission mechanism, whereas Ogawa, Sterken, and Tokutsu (2016) found no causal link from public debt to GDP irrespective of the level of debt, but the reverse effect does have a causal relation. Góes (2016) found that exogenous shocks to a proxy for institutional quality have a pos-itive and statistically significant effect on GDP per capita, but the main concern of this research is the definition of a shock in institutional quality.

As explained in Chapter 1 Introduction, channels of interaction play a crucial role in modelling the world economy. These channels of interaction are not taken into account in the above mentioned literature since those are not incorporated in the standard VAR and SVAR models. To better understand and take into account the mechanisms of in-terdependencies and its effects, Pesaran, Schuermann, and Weiner (2004) have built a GVAR model. The GVAR model was originally build to illustrate the effect of global risk scenarios on a bank’s loan portfolio for 26 countries that are grouped into 11 regions us-ing quarterly data from 1979-1999. With this as a basis, the GVAR model is extended and updated by Dees et al. (2007). In their paper Dees et al. (2007) analysed 26 regions with the Euro Area being treated as a single economy. The analysis in the paper fo-cussed on effects of external shocks on the Euro Area economy, particularly in response to shocks in the U.S.A.. Thereafter, the GVAR approach has been used to assess a great deal of diverse problems. As the input for the GVAR model does not need to be on country-level but might as well be on region-, section-, industry-, or company-level, the applications of the GVAR model are versatile. The model of Dees et al. (2007) is used

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by Hebous and Zimmermann (2013) and Ricci-Risquete and Ramajo-Hernández (2015b) to estimate the relation of macroeconomic variables such as fiscal policy and monetary policy shocks. Hebous and Zimmermann (2013) included 12 Euro countries in their esti-mation to analyse the effect of a shock in one country on the shock in the rest of the area. Ricci-Risquete and Ramajo-Hernández (2015b) modelled not only Euro Area economies but also included countries of former EU15 and the U.S.A. in their model. Moreover, a major contribution of the paper is the inclusion of total government receipts and total government expenditure separately. This contribution is followed in this thesis since it is considered to be an important contribution because expenditures and taxation both affect the level of growth. Surprisingly, all previous literature only take into account a small part of world’s economy. So far, no attention has been paid to modelling a more complete and comprehensive set of countries. While the insertion of the use of a GVAR model is to take account of the interaction channels between countries, only a small and incomplete part of the interaction channels is being covered when a small part of the economy is being modelled. Therefore, a systematic understanding of how government spending contributes to economic growth is still lacking in previous literature. A part of the contribution of the current thesis is therefore to increase the number of countries in the sample to obtain a better representation of the global economy. This is not straight-forward as a large amount of data is required that is not at disposal in certain countries and difficulties may occur with the stability of the GVAR model.

Together, these studies show that the outcome of an empirical analysis of economic growth and government spending is largely dependent on the sample and highlight the need for an approach to assess source of heterogeneity. In view of the above discus-sion, there is need for a cluster analysis to form homogenous clusters. Moreover, as was pointed out in the introduction to this thesis, the standard panel VAR and SVAR models do not take into account channels of interaction between economies. In addition, litera-ture on GVAR models does take into account the channels of interaction but only covers a small and incomplete sample of the economy. To rule out the possibility that this has an effect on the results, this thesis will consider a more complete set of economies to in-vestigate the effects of monetary and fiscal policies on economic growth. Additionally, this thesis imposes multiple long-run macroeconomic relations because this will pro-vide better insights in the forces that underlie the functioning of the (macro) economy, whereas the studies of Hebous and Zimmermann (2013) and Ricci-Risquete and Ramajo-Hernández (2015b) did not apply such relations and estimated their model under the

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assumption of exact identification. Although exact identification methods are sophisti-cated statistical models and are mathematically convenient given the statistical structure, the problem is that the relations are rather difficult to interpret with economic reasoning.

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Chapter 3

Cluster Analysis

3.1 Data: World Governance Indicators

To control for heterogeneity between countries caused by differences in structure of the society and viewpoint of the authorities, a cluster analysis is performed on the quality of the government. The quality of the government is used to assess the relation between government spending and economic growth because a poor or a good government is believed to affect the net effect of fiscal policies changes on economic growth. The ratio-nale behind this is that a poor government is associated with unbalanced power, more uncertainty in the market, higher risks, and an inefficient allocation, whereas a good government will induce the contrary. Before proceeding to employ cluster analysis, this section elaborates on the characteristics that underset the quality of the government. To determine those characteristics, it is necessary to construct a clear definition of govern-ment. This thesis follows the authors of the World Governance Indicators (WGI) in the publication of Kaufmann, Kraay, and Mastruzzi (2011). They define governance as "the traditions and institutions by which authority in a country is exercised. This includes (a) the process by which governments are selected, monitored and replaced; (b) the capacity of the gov-ernment to effectively formulate and implement sound policies; and (c) the respect of citizens and the state for the institutions that govern economic and social interactions among them.". Kauf-mann, Kraay, and Mastruzzi (2011) divide each of these three areas of government into two measures that result in the following six indicators defining the World Governance Indicators (WGI):

• The process by which governments are selected, monitored, and replaced

1. Voice and Accountability (VA) - the ability of citizens to participate in select-ing the government, as well as freedom of expression, freedom of association, and a free media.

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2. Political Stability and Absence of Violence/Terrorism (PV) - the probability that the government will be destabilized or overthrown by unconstitutional or violent means, including politically-motivated violence and terrorism.

• The capacity of the government to effectively formulate and implement sound poli-cies

3. Government Effectiveness (GE) - the quality of public services, the quality of the civil service and the degree of its independence from political pressures, the quality of policy formulation and implementation, and the credibility of the government’s commitment to such policies.

4. Regulatory Quality (RQ) - the ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development.

• The respect of citizens and the state for the institutions that govern economic and social interactions.

5. Rule of Law (RL) - the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police and the courts, as well as the likelihood of crime and violence.

6. Control of Corruption (CC) - the amount of public power that is exercised for private gain, including both petty and grand forms of corruption, as well as "capture" of the state by elites and private interests.

To construct the WGI for over 200 countries between 1996 and 2015, 31 different indi-cators of governance drawn from 13 different sources are processed by a statistical tool known as the unobserved components model (UCM). The six indicators are constructed on the basis of weighted averages of rescaled data from the different data sources. The construction of the indicators is done in three steps. In the first step the data from the several sources is assigned to one of the six indicators. Note that since not all of the data sources cover all countries in the WGI dataset, the resulting scores are based on a different set of sources for different countries. Thereafter, the data from the different data sources are rescaled to range from 0 to 1 in ascending order with respect to an improvement in the outcomes. In the last step, the rescaled data are aggregated into the six governance indicators by using the UCM. In the UCM the observed scores are assumed to be a linear

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function of unobserved level of governance and a disturbance term that differs between data source. Thereafter, the UCM assigns a weight to the data sources, this meand that a greater weight is assigned to data sources that have a strong correlation. Because the in-dicators are now weighted averages from each source, the data is believed to be corrected for the differences in the rescaled data that are caused by differences in the data sources. Finally, the resulting six indicators are in units of a standard normal distribution having mean zero, a standard deviation of one and they range approximately from -2,5 to +2,5, where -2,5 corresponds to a "poor" government and +2,5 to a "good" government. The six indicators are averaged over the latest five year in order to perform a cluster analysis because it is believed that markets in the U.S.A. and Europe were been stabilized as they were just out of the heat of the battle against the financial crises in that time span.

It is important to note that the six indicators are not thought of as being indepen-dent. This is considered not to cause implications with respect to cluster analysis since the indicators are exhaustive as they capture all three dimensions of the government. Nevertheless, the WGI have attracted some explicit criticisms. The main critique is that governments cannot be compared over time due to scaling issues or the variety in and quality of data sources to construct the dataset. Critics have also argued that the in-dividual indicators are biased towards the view of business elites and are influenced by recent economic performance. In order to reply to this criticisms, in the publication of Kaufmann (2007) the drawbacks are acknowledged and the reasons for considering them to be of minor effect are explained. The pronounced criticism is a general problem with indicators which refer to the phenomena difficult to measure, but without attempts of measuring, it would be hard to concretize the research issues (Zielenkiewicz (2014)). Originally, the WGI dataset contains information of the six indicators on 208 countries. As will be explained extensively in Chapter 5 Data, the data set used for the cluster anal-ysis consists of 148 countries in total. The next section describes the particular cluster method of analysis to form clusters based on the WGI.

3.2 Methodology

Countries are diverse concerning the role of government spending because of difference in structure and viewpoints of authorities. As mentioned in the previous section, these differences cause the sample of countries to encounter problems with heterogeneity when the sample is not divided into subgroups of homogeneous countries. Several previous

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studies have acknowledged the need for homogeneity in the sample and focussed on specifying groups of countries based on some characteristic, for example: OECD mem-bership, income per capita, growth levels or geographical characteristics. However, this thesis argues that such characteristics should be disregarded when merging countries for several reasons. First of all, it is expected that income-based criteria do not explain the relationship between government spending and growth as they do not account for the fiscal policy of the government. Furthermore, criteria such as OECD membership do not clarify the relation between government spending and economic growth because of the diversity in structure of countries within the OECD. It is precisely this structure that causes differences in the risks in the markets and the allocation of investments and fiscal reforms. With the same reasoning, criteria based on whether countries belong to the Asia or Euro Area or other geographical characteristics are inadequate because of the lack of homogeneity with respect to governances in such areas. Overall, these characteristics are not sufficient to explain the existence of heterogeneity and may at best allow for more efficient regressors. Another common way to address problems with heterogeneity is to use fixed or random effect models. These models assist in controlling for unobserved heterogeneity and result in more significant and efficient regressors. However, they do not explain the source of the heterogeneity and do not exclude problems with slope het-erogeneity caused by differences between countries in response to certain shocks. As explained in the previous section, differences in the net effect of government spending on economic growth are believed to be captured in and explained by the quality of gov-ernment because the quality of the govgov-ernment has an impact on the allocation and the market in a country as a whole.

Cluster analysis is a convenient method for identifying homogenous groups of ob-jects, so-called clusters. After cluster analysis, the resulting clusters are internally ho-mogenous with respect to the countries in the same cluster and differ from countries in other clusters. Whereas cluster analysis is used extensively in the field of social sciences such as medical research, biology and marketing, there are few studies that employ clus-ter analysis in economics. Vázquez and Sumner (2012) used clusclus-ter analysis to identify five types of developing countries on a global scale using a set of indicators covering definitions of development based on four conceptual frames. Moreover, the study of Zielenkiewicz (2014) applied cluster methods to the WGI dataset to analyse the social-economic development process. In their study a sample of 27 EU countries is clustered into 4 groups.

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Generally, cluster analysis consists of 4 steps that need to be specified beforehand: 1. Selecting a measure of similarity (or dissimilarity)

2. Deciding on the cluster algorithm

3. Determining the optimal number of clusters

4. Interpreting the solution by defining and labelling the clusters

These steps will be discussed in more detail in the following sections to justify the results and the choices made for this particular cluster analysis.

3.2.1 Specifying the distance measure

Cluster analysis is based on a distance measure based on a certain distance norm. The distance norm in this thesis is the difference or similarity between countries based on the six indicators of the WGI and is under no circumstances related to the physical distance reflecting the geographical location of the countries. The most common used type to mea-sure the distance based on the norm is the Euclidean distance (or straight-line distance). The Euclidean distance is the square root of the sum of the squared differences in the vari-ables’ values and corresponds to the length of the line segment connecting two points. As will be explained in the next subsection, this thesis uses the squared Euclidean distance between countries. Suppose there are two countries A and B that are constituted by the six different government indicators given by {a1, a2, . . . , a6} and {b1, b2, . . . , b6}

respec-tively. Then the squared Euclidean distance relating to the differences between countries with respect to a rescaled version of the six indicators in the Euclidean space R6is given by the formula: d2(A, B) = d2_AB = 6 X i=1 (ai− bi)2 (3.1)

3.2.2 Deciding on the cluster algorithm

After having specified the distance measure, the cluster algorithm has to be formulated. Hierarchical clustering seeks to build a hierarchy of clusters. This thesis uses an agglom-erative hierarchical approach, where each country starts in its own cluster and pairs of clusters are merged as one moves up the hierarchy. The most popular agglomerative

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clustering procedures are: single-linkage, complete-linkage, average-linkage, centroid-linkage and the Ward’s methods. Since the single-centroid-linkage method bases decisions on the shortest distance between any two members in two clusters, the drawback of this method is that clusters may be forced together due to single elements being close to each other, even though many of the elements in each cluster may be very distant to each other. Complete linkage methods avoids these problems. However, as this method is based on maximum distances being close to each other, it is strongly affected by outliers. Whereas single linkage tends to result in one big cluster and several small other clusters, complete-linkage methods are likely to result in tight and compact clusters. The average complete-linkage and centroid methods result in clusters of similar sizes with low within-cluster variance. However, both procedures are affected by outliers. In order to cluster the countries based on the WGI dataset, the Ward’s method is used for cluster analysis. This method mini-mizes the total within-cluster variance.

Suppose that the method begins with N clusters consisting of one country. To be more specific, N is the total number of countries in the sample and every country is positioned in an individual cluster at the start of the cluster algorithm. At each step, the method finds a pair of clusters that leads to a minimum increase in total within-cluster variance after merging. Therefore at each step in the Ward method, two clusters will be merged that have the smallest between-squared Euclidean distance. Hence in the first step, two clusters will be merged based on the smallest squared Euclidean distance such that the sample will consist of N − 1 clusters: one consisting of two countries and the remaining consisting of one country. Then, the squared Euclidean distances between clusters are recomputed. In the second step, N − 2 clusters are formed. These may include two clusters consisting of two countries or one single cluster consisting of three countries and the remaining clusters of size one. In all subsequent steps, the countries and clusters are again combined on the basis of the smallest squared Euclidean distance between the clusters formed in the previous step such that the increase in the total within-cluster variance is minimal. The algorithm continues until all N countries in the sample are combined into one large cluster consisting of all N countries. However, the optimal number of clusters is determined based on motivations described in the next sub section.

3.2.3 Determining the optimal number of clusters

Unfortunately, hierarchical methods provide limited guidance for deciding on the num-ber of clusters to retain from the data. One tool is to plot the numnum-ber of clusters on the

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x-axis against the distance at which objects or clusters are combined on the y-axis. The optimal number of clusters can then be found by looking where the plot shows a distinct break due to increase in distance when adding another level of clusters. Alternatively, a dendrogram of clusters can be used in a similar fashion. A dendrogram displays the distance at which countries and clusters are joined together. The decision on the opti-mal number of clusters here is again based on the distance in each new level of clusters. However, these two distance based decision rules do not work well in practice because it often is difficult to identify where the clusters break and results are highly relying on the accuracy of judgment.

To prevent incorrectness of results, more robust and objective measures to determine the optimal number of clusters are used. Milligan and Cooper, 1985 compare the perfor-mance of a variety of measures and conclude that the six best measures are the Variance Ratio Criterion (VRC), the two measures from Duda, Hart, et al. (1973); the Duda and the Pseudot2 measure, the Cindex, the Gamma index and the Beale index. Suppose the total sample consists of N countries with I characteristic and C clusters, then:

• The optimal number of clusters according to the VRC index is the solution with the highest VRC ratio, V RCC = _SSSS_WB N −C_C−1, where SSB is the overall between-cluster

variance and SSW is the overall within-cluster variance.

• The optimal number of clusters according to the Duda index is the first value such that J e(m+1)_{J e(m)} ≥ critical valueDudawhere Je(m+1) is the sum of squared errors within

cluster for the next step and Je(m) gives the squared errors in the current step and is applied only to the sub portion of the data involved in the cluster merger.

• The optimal number of clusters according to the Pseudot2 index is the first number of clusters such that Pseudot2 ≤ critical valueP seudot2.

• The optimal number of clusters according to the Cindex is the minimum value of the index, Cindex = SW−Smin

Smax−Smin, where SW is the sum of the within-cluster distances,

Smin is the sum of the smallest distances between all pairs of points in the entire

sample and Smaxare the opposite largest distances.

• The optimal number of clusters according to the Gamma index is the maximum value of the index given by s(+)−s(−)_s(+)+s(−) where s(+) represents the number of consis-tent comparisons involving between and within cluster distances, and s(−) repre-sents the number of inconsistent outcomes.

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• The optimal number of clusters according to the Beale is obtained by comparing an F − ratiowith FI,(nm−2)I distribution

3.3 Results and Interpretation

3.3.1 Optimal number of Clusters

The index and critical values of all six indices are given in table A.1. It can be seen from the table that the VRC and C index have little meaning when selecting the optimal number of clusters as both indices have no maximum value. Additionally, 2 clusters is particularly undesirable since this does not impose a real meaning to the governmental quality in the distinct clusters. The table shows that the first time that the Duda index is larger than the corresponding critical value is at 6 clusters. Therefore, the optimal number of clusters according to the Duda index is 6. This result is emphasized by the Beale index as this index imposes that 6 is the optimal number of clusters as well. Moreover, it is apparent from the table that the first time that the critical value of the Pseudot2 index exceeds the index value is also at 6 clusters confirming that 6 is the optimal number of clusters. Interestingly, the Gamma index does not have a maximum within a set of 20 clusters. A robustness check reports that the index would lead to the situation where every country is in its own cluster1. Therefore, the Gamma index is neglected when making a decision on the optimal number of clusters in this thesis.

3.3.2 Interpretation

Table B.1 to B.4 in the appendix show the partition of countries within the six clusters that will be used when estimating the effect of the monetary and fiscal policies on the remaining economies. Figure B.1 and B.2 in the appendix demonstrate the dendrograms according to the cluster analysis given in the country ID and the country name respec-tively. A dendrogram is a tree diagram used to illustrate the arrangement of the clusters. The distance between merged clusters is monotonically increasing with the level of the merger: the height of each node in the plot is proportional to the value.

The order of relative importance of the variables for the interpretation of the clusters is given by: (1) Rule of Law, RL, (2) Control of Corruption, CC, (3) Government Effective-ness, GE, (4) Regulatory Quality, RQ, (5) Voice and Accountability, VA, and (6) Political

1_{The results of the robustness check are not reported because of considerations with respect to the length}

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Stability and Absence of Violence/Terrorism, PV. In order to identify the clusters, the mean of all six variables in every cluster was taken and depicted in table 3.1. In an at-tempt to interpret the quality of government in the clusters even further, the summary statistics on the within-cluster variance, minimum value, maximum value, first quantile and last quantile are computed and shown in the appendix in table C.1 to C.5 respec-tively. Based on these statistics the clusters are labelled according to the governmental quality as follows:

Cluster 1 Very Poor Cluster 2 Poor

Cluster 3 Somewhat Poor Cluster 4 Somewhat satisfactory Cluster 5 Satisfactory

Cluster 6 Very satisfactory

To assess whether the clusters behave differently when it comes to government spend-ing, annual GDP growth and GDP per Capita, one can inspect the boxplots in figures 3.2, 3.1 and 3.3 respectively. The boxplots are a graphical representation of the variables per cluster based on the minimum, first quartile, median, third quartile, and maximum. The top of a rectangle indicates the third quartile, a horizontal line near the middle of a rect-angle indicates the median, and the bottom of a rectrect-angle indicates the first quartile. A vertical line extends from the top of a rectangle to indicate the maximum value, and an-other vertical line extends from the bottom of a rectangle to indicate the minimum value. As can be seen from the figures the clusters are diverse in terms of government spending and economic growth. Based on these six clusters, the GVAR model is used to analyse the effects of fiscal and monetary policies on economic growth.

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FIGURE 3.1: Boxplot for the distribution of Government Spending as a percentage of the total GDP per cluster

FIGURE 3.2: Boxplot for the distribution of anual percentage growth in GDP

FIGURE3.3: Boxplot for the distribution of GDP per capita per cluster

Mean Value

Cluster VA PV GE RQ RL CC Overall Mean

1 -1.31828 -1.50068 -1.28682 -1.31856 -1.36894 -1.21871 -1.33533 2 -0.74836 -0.67769 -0.71755 -0.65092 -0.8085 -0.7921 -0.73252 3 0.122042 -0.169 -0.09669 0.108044 -0.23788 -0.32008 -0.09893 4 -0.91815 -0.13696 0.220983 0.1182 0.149204 0.08463 -0.08035 5 0.899446 0.609168 0.851695 0.916443 0.835496 0.624981 0.789538 6 1.301148 0.980457 1.716128 1.626807 1.728726 1.862047 1.535886

TABLE3.1: Average of individual World Governance Indicators per clus-ter. The valuation of the clusters is based on the results of the cluster analy-sis. In particular, the valuation of the countries is as follows: Cluster 1 ’Very Poor’, Cluster 2 ’Poor’, Cluster 3 ’Somewhat Poor’, Cluster 4 ’Somewhat

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Chapter 4

Model and Methods

In this section, the methodology of the GVAR model will be discussed. The process of building the GVAR model follows the methodology introduced by Pesaran, Schuer-mann, and Weiner (2004). The model is a powerful tool to analyse the interdependencies between different countries across the world economy and is well-known to combine in-dividual country vector error-correcting models (VECM) in a consistent manner. Essen-tially, GVAR model estimation is a two-step procedure. In the first step a country-specific VAR model, a so-called VARX* model, is built for every individual country. Afterwards, the national models are combined using link matrices from the GVAR model. In order to see how the individual countries are interlinked, suppose that the sample of countries for this thesis consists of N + 1 countries, indexed by i = 0, 1, . . . , N where country 0 serves as a numeraire country, the reference country. This thesis follows the majority of previous studies on GVAR models and selects the U.S.A. to be the reference country. The rationale for choosing the U.S.A. lies in the size and dominant nature of the U.S.A. in the world economy. In terms of nominal GDP at current prices measured in U.S. dollar units the U.S. economy is the largest economy in the world. However, not just the size of the economy matters but the U.S.A. has a well-behaving (financial) market and, despite of the rising debt and the diminishing capacity to lead global order due to the array of domestic and foreign policy failures, the U.S. economy remains to be one of the most advanced in the world.

The vector Xit contains a number of country-specific macroeconomic variables over

time for every country i = 0, 1, . . . , N . In this thesis the variables contain: real GDP per capita (yit), inflation (Dpit), interest rates (irit), exchange rates (reit), total government

revenue (grit), and total government spending (gsit). As stated by Pesaran, Schuermann,

and Weiner (2004) it is desirable that all variables in the vector Xitand observed global

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nature of interdependencies that might exist in the world economy. However, this will result in difficulties with significance of the GVAR model because of the risks of being affected by the ’curse of dimensionality’ due to resulting sparsity and dissimilarity of the data. The GVAR model handles the curse of dimensionality by imposing a weak exogeneity assumption on the foreign country-specific and global variables. The weak exogeneity assumption lies at the heart of the validity of the results obtained through the GVAR model, as it allows country-specific models to be estimated individually and, at a later stage, to be combined together and therefore the assumption needs to be tested for.

4.1 **Step 1 - Country-specific VARX* models**

As explained in the previous section, every individual country in the GVAR model con-sists of two types of country-specific variables: (1) domestic variables Xit, and (2) foreign

variables X_it∗. The various countries are interdependent through the foreign variables, global (weakly) exogenous variables and deterministic variables such as time trends. Foreign variables are weighted averages of the corresponding country specific domes-tic variables and denoted as X∗_it. Accordingly, the following set of endogenous variables are used:

Xit = (yit, Dpit, irit, reit, grit, gsit) (4.1)

and

X0t= (yit, Dpit, irit, grit, gsit, poilt) (4.2)

with the following corresponding country specific foreign variables:

X∗_it= (y∗_it, Dp∗_it, ir_it∗, gr∗_it, gs∗_it, poilt) (4.3)

and

X∗_0t= (y_it∗, Dp∗_it, re∗_it) (4.4)

The application and construction of the variables of interest will be explained in Chapter 5 Data. The weights in order to compute the weighted averages wij for i, j = 0, 1, . . . , N

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respect to the average annual trade shares over a fixed period among all countries in the sample with the necessary condition thatPN

j=0wij = 1. Hence the foreign variables can

be expressed as: X_it∗ = N X j=0 wijXjt (4.5)

The global (weakly) endogenous variables are quarterly oil prices. Then, each country i is modelled with the VARX*(p, q) structure:

Xit = ai0+ait+ Φi1Xi,t−1 + · · · + ΦipXi,t−p

+ Λi0X_it∗ + ΛitX_i,t−1∗ + · · · + ΛiqX_i,t−q∗ + uit (4.6)

where ai0is a vector of fixed intercepts; ai1is a vector of coefficients of the deterministic

time trend; Φi is a matrix of coefficients corresponding to the lagged country-specific

variables; Λi0and Λi1are matrices of coefficients associated with contemporaneous and

lagged foreign variables, respectively; and uitis a vector of country-specific shocks. The

shocks uit are serially uncorrelated and a cross-sectional weakly dependent process. It

is assumed that uit ∼ i.i.d. (0, Σii), where Σii = (σii,ls) is a non-singular matrix with

σii,ls= Cov(uilt, uist). In the country-specific VARX*(p, q) models, p indicates the number

of lags of the country-specific domestic variables and q denotes the number of the foreign variables.

4.2 Step 2 - global VAR model

The purpose of the GVAR method is to model the economy as a whole adherence to the interdependencies of the individual countries. Therefore a global vector must be created after the country-specific VARX* models. Firstly, the country-specific models of equation 4.6 are rewritten in the form:

Ai0zit = ai0+ ai1t + Ai1Zi,t−1+ . . . , +AirZi,t−r+ uit (4.7)

where Zit = (X_it0 , X_it∗) is the collection of both the country-specific domestic and the

foreign variables; Ai0 = (Iki, −Λi0); Aid = (Φid, Λid)for d = 1, . . . , r; and r =max(p, q).

Secondly, the global vector having a kx1 dimension with k =PN

i=0kineeds to be created.

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domestic variables of all individual countries are collected in the global vector Xt =

(X_0t0 , X_1t0 , . . . , X_{N t}0 )0. Moreover, country-specific link matrices Wiare created to obtain

the identity:

Zit = WiXt (4.8)

Using this information, the country-specific models in 4.7 can be rewritten as:

Ai0WiXt = ai0 + ai1t + Ai1WiXt−1+ · · · + AirWiXt−r+ uit (4.9)

In order to obtain the GVAR model, these country-specific models are then stacked to yield:

G0Xt = a0+ a1t + G1Xt−1+ · · · + GrXt−r+ ut (4.10)

where G0 = (A00W0, A10W1, . . . , AN 0WN)0 is a known non-singular matrix that

de-pends on the trade weights and parameters; Gb = (A0bW0, A1bW1, . . . , AN bWN)0 for

b = 1, . . . , r; and ac = (a0c, a1c, . . . , aN 0)for c = 0, 1. If G0 truly is non-singular,

equa-tion 4.10 can be pre-multiplied by its inverse, and the soluequa-tion of the GVAR model in the reduced form is obtained as:

Xt = b0+ b1t + F1Xt−1+ · · · + FrXt−r+ t (4.11)

where b0 = G−10 a0; b1 = G−10 a1; Fm = G−10 Gm for m = 1, . . . , r; and t = G−10 ut.

There are no prerequisites on the covariance matrix Σ= IE(t, 0t). Equation 4.11 can be

solved recursively and used to perform impulse response analysis. By construction, the model allows for interaction through three channels:

1. Country-specific domestic variables depend on foreign variables and their lagged values contemporaneously;

2. Country-specific domestic variables depend on global exogenous variables; and 3. Shocks in a country i depend contemporaneously on shocks in country j and are

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4.3 Impulse Response Analysis

In order to analyse the dynamics of the variables triggered by a shock in the monetary and fiscal variables, an impulse response function (IRF) analysis has to be performed. IRFs capture the time effects of a shock on the future states of a dynamic system. This means that IRFs output the effect of a shock in one variable on all variables in the model. Consider equation 4.11 with the k =PN

i=1kicountry-specific errors collected in the

vec-tor ut= (u01t, u02t, . . . , u0N t). Then suppose that there are k structural shocks to the system

defined by vt= P−1ut. Identification of such structural shocks requires the a k x k matrix

P such that

Σ = E utu0t = P P0 (4.12)

Hence the vector of IRFs depends on the specification of the variance-covariance matrix Σ.

In 1980, Sims (1980) constructed an Orthogonalized Impulse Response Function (OIRF) analysis. In this method, P is set to be equal to the Choleski factor of Σ. Although, OIRFs are useful when investigating causal relationships among the variables, the fact that the variance-covariance matrix is based on the Choleski factor immediately leads to the ma-jor drawback of this approach. As the Choleski factor is not unique and not invariant to the ordering of the variables and countries, the resulting OIRFs also depend on the ordering of the variables and countries. Chudik and Pesaran (2014) state that such an or-dering is clearly difficult to entertain in the global setting. In order to overcome these issues, this thesis uses the Generalized Impulse Response Function (GIRF) analysis adopted by Pesaran and Shin (1998). Whereas the OIRFs rely on the orthogonalization of the residu-als based on a pre-specified ordering and economic-based restrictions, this is not needed for the GIRFs as the correlations are assumed to be given by the historical correlations of the variables that are included in an estimated variance-covariance matrix. Therefore the GIRFs are independent of the ordering of the variables and countries.

One of the major contributions of using the GVAR model with respect to this thesis is that the model allows for the option to specify certain ’regions’ of countries. This means that several countries can be aggregated into groups at the outset of the analysis and the effects of shocks within and to these groups can be analysed. In the setting of this thesis, these groups of countries will be the six clusters constructed in the previous chapter by means of the cluster analysis. To be more precise, the countries are modelled at a more

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disaggregate level according to step 1 and step 2. At this stage, the large economies are estimated at a disaggregated level and some small economies are grouped based on their geographical location and size of the economy within the clusters. The reason for grouping countries in this manner are the concerns with the stability of the GVAR model when the model is estimated at a completely disaggregated level. Afterwards, an ex-post aggregation of impulse response is done by specifying the six groups equivalent to the six clusters in order to focus on cluster specific results. This overcomes problems with aggregation bias that will be present when the estimation is performed at the level of the six clusters. The specification of global or regional shocks is given by ugm,t = m0ut. For

those shocks the vector of GIRFs is given by:

g_m(h) = EXt+h|ugm,t = p m0Σm, It−1 − E (Xt+h|It+h) = R_√hG−10 Σm m0Σm (4.13) where m is a vector of aggregation weights and relates to a particular pre-specified region, It−1 is the information set of all available information at time t hence It−1 =

(Xt, Xt−1, . . . )and the k x k matrices Rhare recursively obtained from Rh =Pp_l=1FlRh−l

with R0 = Ik. This thesis uses the data described in the following section, aiming to

sys-tematically provide answers to the sub research questions specified in Chapter 1. There-fore, the specific aim is to analyse GIRFs triggered by a regional monetary or fiscal policy shock.

4.4 Long-run relations

The country-specific VARX* models as given by equation 4.6 are estimated allowing for unit roots and cointegration among both the country-specific domestic variables Xitand

between the country-specific domestic variables and country-specific cross-section aver-ages of the foreign variables X∗it. The unit roots of all country-specific and global

vari-ables included are tested following the standard Augmented Dickey-Fuller (ADF) and Weighted-Symmetric Dickey Fuller (WSDF) tests. Suppose that the assumption of unit roots is satisfied, hence the series are integrated of order one denoted by ∼ I (1), then the long-run relations are tied with a cointegrating relation between these variables. That is, a linear combination of the variables is integrated of order zero, given by ∼ I (0). The rank of the cointegrating space of the country-specific VARX* models is initially computed us-ing the Johansen’s trace and maximal eigenvalue statistics, where the former is preferred

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for this GVAR model, as it is known to have better power properties than the latter. Be-cause the number of cointegrating relations and the imposed restrictions are the basis for the development of the model with econometrically meaningful long-run properties, the choices made with respect to these decisions are crucial for the GVAR model. As stated in Garratt et al. (2012), the Johansen’s trace statistic is a sophisticated method to test the rank of the cointegrating space using statistically motivated exact identification restric-tions but it has one major drawback. The problem with this procedure is that, while the identification of the rank is mathematically convenient given the statistical structure of the problem, the restrictions on the cointegrating relations by the Johansen’s statistic have no economic meaning. This thesis fills a gap in the literature on government spending and economic growth by imposing overidentifying restrictions (OIR) on the model that are justified by economic theory. Economic theory can be imposed on the long-run and short-run relations. Short-run theory relates to outcomes of specific decisions or events at a particular moment in time. The main critique is that economic theory is insufficiently well-defined to impose restrictions on the short-run dynamics. In contrast, the long-run theory refers to relations between variables that are not motivated by particular events or decisions or by a specified moment in time. Since the restrictions will be imposed on the cointegrating relations, the relevant theory for the estimation is that of the long-run, and the criticism accompanying the short-run theory is avoided.

In this thesis, in total four possible OIR are considered, including the Fisher Inflation Parity (FIP), Uncovered Interest Parity (UIP), Output Convergence Parity (OCP), and the Purchasing Power Parity (PPP). The FIP refers to the real interest rate and assumes that the real interest rate is stationary. The rationale behind this is that the real interest rate can be constructed by subtracting the expected inflation rate from the nominal interest rate and therefore, in absence of arbitrage, there must be some equilibrium outcome between holding a bond and investing in an asset. Hence, this results in a decrease of the real interest rates as inflation increases, unless nominal rates increase at the same rate as in-flation. It is important to note that if real interest rate is less than zero, the rate levied on a loan or paid on savings does not outweigh inflation. Secondly, the UIP is concerned with interest rates. This parity is motivated by the absence of arbitrage and law of one price between holding a domestic bond and a foreign bond. The rationale behind it is that the differences between the interest rates of the domestic bond and the foreign bond is offset by the exchange rate in case there is no arbitrage. Thirdly, the OCP is supported by the idea of the Solow-Swann neoclassical growth model in which it is assumed that the rate

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of growth of the income per capita converges in the long-run. Lastly, the PPP relates the (log) effective exchange rate, to the (log) price ratio. The PPP is based on the idea that the price of goods will be equal in different countries when measured in the same relative currency. The mathematical representation of these restrictions on the long-run relations based on the FIP, UIP, OCP, and PPP are respectively given by:

irit− ∆pit∼ I (0) (4.14)

irit− irit∗ ∼ I (0) (4.15)

yit− yit∗ ∼ I (0) (4.16)

epit− ep∗it∼ I (0) (4.17)

Where epitis the real (log) exchange rate in terms of US dollars. Because the GVAR model

does not allow for this specification of the PPP as the exchange rate is not included in the foreign variables of small open economies, 4.17 has to be rewritten. This thesis follows the publication of Dees et al. (2007) in rewriting the exchange rate variable to obtain the variable reitaccording to the following procedure. Suppose that originally the (log)

exchange rates in terms of US dollars, given by eit, are collected. Then the corresponding

real exchange rates are given by epit= eit−pitfor domestic variables and by ep∗it = e ∗ it−p

∗ it

for foreign variables. Moreover, it is important to note that there exists a real effective exchange rate with eeit=PN_j=0wijeijtwhere eijt = eit− ejtsuch that eijtis the exchange

rate from country i to country j. Then the following will hold:

reit= N X j=0 wij ejt− e∗jt + p∗it− pit = N X j=0 wijejt− N X j=0 wije∗jt+ p ∗ it− pit= eit− pit− e∗it+ p ∗ it = epit− ep∗it (4.18)

Therefore, the mathematical representation of the restrictions imposed by the PPP is now given by:

reit∼ I (0) (4.19)

An additional advantage of using the real effective exchange rate instead of the real ex-change rate in terms of US dollars is that the choice of the US dollar to be the reference

An empirical investigation of the relation between fiscal policy decisions and economic growth using a GVAR model

MS

. T

An empirical investigation of the relation

between fiscal policy decisions and

economic growth using a GVAR model.

Faculty of Economics and Business

Amsterdam School of Economics

Requirements thesis MSc in Econometrics.

Statement of Originality

Abstract

Acknowledgements

Contents

Chapter 1

Introduction

Chapter 2

Literature Review

Chapter 3

Cluster Analysis

3.1

Data: World Governance Indicators

3.2

Methodology

3.3

Results and Interpretation

Chapter 4

Model and Methods

4.1

Step 1 - Country-specific VARX* models

4.2

Step 2 - global VAR model

4.3

Impulse Response Analysis

4.4

Long-run relations

**Step 1 - Country-specific VARX* models**