Monetary Policy and Uncertainty

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Monetary Policy and Uncertainty

A GVAR Approach

Larry Tunster

Umeå School of Business, Economics and Statistics Department of Economics

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Abstract

This thesis investigates how both changes in monetary policy and monetary policy

uncertainty from the United States Central bank affects 33 countries through various channels - GDP, Inflation, Equity Prices, Exchange rates and long and short interest rates from 1985 to 2016. This study follows a similar approach to Leiand Liu (2015) and Bi and Anwar (2017) who conduct similar research with a focus on the actions of the US Federal Reserve.

The background and Literature review finds overwhelming evidence empirically and theoretically in support of all channels including uncertainty.

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1. Introduction

Nobel prize winner Milton Friedman emphasised the importance of monetary policy. Friedman stressed that regulating the supply of money in the economy will have an impact on macroeconomic variables namely inflation (Friedman 1968). Friedman’s work really emphasised the relationship between inflation and the money supply, and that inflation could be avoided with proper regulation of the monetary base growth rate. This has remained a topic of interest in the field of Macroeconomics. With countries having closer economic ties such as the introduction of the Euro¸ the Transatlantic Trade and Investment Partnership we see more spillovers from one country to another. Spillovers from one country may have an adverse impact on another economy, which can be seen via the great recession, fluctuations in currencies and stock markets etc. These spillovers motivate the question, what effects do the United States Monetary Policy and the uncertainty around the decision making of the Federal Reserve affect other countries?

The aim of this thesis is to provide some empirical evidence on how the actions and uncertainty of the US Federal Reserve affects 33 different countries using the Global Vector Autoregression Model. An important starting point for this line of research is to investigate spillovers from the United States as the US Dollar is one of the most important currencies, not only does it have an important domestic effect, impacting the country with the largest gross domestic product (GDP) there is also an effect globally as it usually is the currency for many international trades, such as commodities and oil. Therefore, the actions of their central bank should have a global impact. The relevance of this holds ever more important as the United States in the last year have gone through a lot of changes in their foreign policy such as the withdrawal from the Trans-Pacific Partnership and newly enforced steel and aluminium tariffs.

There is an abundant amount of literature based on the shocks on domestic US monetary policy such as (see,Kim 2001, Bhuiyan 2015, Qureshi 2015) however only a handful cover the Global impacts like Bi and Anwar (2017). The importance of this study will provide more clarity on the scarce amount of literature by looking at an extensive amount of countries and variables. Macroeconomic theory which often factors in uncertainty, this is not commonly accounted for in existing empirical literature, this paper aims to model and measure the effects of uncertainty on macroeconomic variables.

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• To estimate the response of 33 countries macro-variables1_{when there is an unexpected shock} to the Federal Reserve's two primary monetary policy tools which are, setting the discount rate and Open Market Operations2.

• To estimate the response of 33 countries macro-variables when there is an unexpected shock on uncertainty around the actions of the Federal Reserve.

• To provide a practical application of the Global Vector Autoregression methodology.

Why focus on the U.S and the Dollar? The US dollar is regarded as a global currency. Despite there being a substantial rise of the Euro, the US dollar remains the only currency regarded as a world currency (Cetorelli and Goldberg 2010). The U.S dollar is the most popular currency, making up for 64% of all known central bank foreign exchange reserves. It should also be noted that what makes the US dollar impact the global economy is that roughly $580 billion in U.S bills are used outside the country (approximately 65% of all dollars), approximately 85% of forex trading involves the US dollar and furthermore, 39% of the world's debt is issued in dollars3.

As the focus of this study is on the global effects of the Federal Reserve; the United States central bank, it is imperative to understand the aims and tools of the Federal Reserve. The Federal Reserve has three aims, maximum sustainable employment, which is the maximum level of employment an economy can withstand while maintaining a steady inflation rate, stable prices, and moderate long-term interest rates, this is known as the FED’s Mandate.

The remainder of this study is organized as follows: section 2, the background of the study, Section 3, literature review, Section 4, the methodology, section 5; The data section, section 6; contains the specifications of the model used. Section 7 is the results in form of the general impulse response functions and section 8 is the conclusion.

1_{GDP, Inflation, long and Short-Term Interest Rates, Exchange Rates and Equity Prices} 2_{Money supply will be used as a proxy}

3

https://www.federalreserve.gov/faqs/what-economic-goals-does-federal-reserve-seek-to-achieve-through-monetary-policy.htm

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2. Background – Theoretical Framework

The monetary operations taken by most central banks include the control of the money supply and the control of the interest rate. The application of VAR models lacks a theoretical approach; therefore it is important to highlight some of the transmissions of the channels that are affected by monetary actions which this section aims to cover (Bernanke, 2005). As shown in figure 14_{there are four main channels that monetary policy passes through, which are Credit supply,}

exchange rates, interest rate expectations and interest rates which all consequently impact aggregate demand and inflation. This section illustrates the Quantity Theory of Money section 2.1, Monetary Policy and Equity Markets section 2.2 and the Exchange Rate Channel, section 2.3.

Figure 1 Monetary Policy Transmission Channels https://www.oenb.at/en/Monetary-Policy/How-Monetary-Policy-Works.html

2.1 The Quantity Theory of Money

The Quantity theory of money states that the general price level is proportional to the amount of money circulating in an economy. This theory provides a direct channel between money supply and price level. To provide more clarity an increase in money supply will have an upward impact on the price level and vice versa. The Quantity theory of money can be explained by Fisher’s equation of exchange which can be defined as:

𝑀 ∙ 𝑉𝑇 = ∑(𝑝𝑖 ∙ 𝑞𝑖) = 𝑝𝑡 𝑖

𝑞 2.1

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Where, money in the system over a period of time denoted by M. 𝑉_𝑇 is the velocity of money, this is the frequency at which one unit of currency is used to purchase domestically produced goods and services within a given time period5. 𝑝_𝑖 is defined as the price of the 𝑖𝑡ℎ_transaction and 𝑞𝑖 is the quantity of the 𝑖𝑡ℎ transaction. 𝑝𝑡 is a column vector of 𝑝𝑖 and 𝑞 is a column of 𝑞𝑖, subscript t is the transpose operator. Mishkin (1996) highlights that this model represents the money transmission process, however, this only works when real income, interest level or other factors are disregarded. Another criticism of the model is money velocity is a constant however velocity is principally influenced by consumer behaviour. The quantity theory of money can only reflect a partial explanation as other factors are not accounted for however it does give economic content for the suitability of the GVAR model in this section.

2.2 Monetary Policy and Equity Markets

A second channel explored is monetary policy and Equity markets. As well as a theoretical model with is presented in equation 2.2. There are many empirical studies such as Bernanke, Gertler and Gilchrist (1996) Thorbecke (1997) Cassola and Morana (2004). Ioannidis and Kontonikas (2006) highlight discount flow models show how the monetary change effects stock markets. 𝑆𝑡 = 𝐸𝑡[∑ ( 1 1 + 𝑅) 𝐾 𝑗=1 𝐷𝑡+𝑗 ] + 𝐸𝑡[( 1 1 + 𝑅) 𝑆𝑡+𝐾] 2.2

Where, 𝑆𝑡, is the stock price at the present value of the expected future dividends 𝐷𝑡+𝑗 .One assumes a constant discount rate (R). 𝐸_𝑡 is the conditional expectations operator based on information available to participants of the market at period 𝑡. The rate of return used by market participants to discount future dividends is denoted by R, and K is the stock holding period. The transversality condition here implies that as the horizon K increases the second term in the right-hand side is set to zero (under the assumption of no rational stock price bubbles).

lim 𝐾 → ∞𝐸𝑡[(

1

1 + 𝑅) 𝑆𝑡+𝐾] = 0

2.3

The derivation leaves us with the standard version of the present value model.

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Equation 2.3 shows changes in monetary policy can impact returns in two manners. Starting with the direct effect on returns, by changing the discount rate used by market participants. Monetary policy tightening will lead to an increase in the rate at which firms’ future cash flows are capitalised resulting in equity prices to decline (Loannidis and Kontonikas 2006). It is based on the underlying assumptions that discount factors used by market participants are normally linked to the market rate, which the central bank can influence. Monetary policy easing is predicted to increase the level of economic activity, resulting in positivity in stock prices, therefore, higher cash flows in the future. This channel assumes a link between both real output and monetary policy. Patelis (1997) defends this assumption by stating that stocks are claims on future economic output, therefore if monetary policy has an impact on stock markets it influences output.

2.3 Exchange Rate Channel

When looking at an open economy, the exchange rate is a significant channel in monetary policy transmissions. This is due to exchange rates fluctuations having a significant effect on the development of aggregate demand and aggregate supply, meaning an impact on output and prices (Goeltom 2008). Assuming a floating exchange rate, for example, the Central bank chooses an easing6 monetary policy which will depreciate the domestic currency. The depreciation in the domestic currency will result in import prices increasing, resulting in an increase in domestic prices when there is no expansion in aggregate demand. However, Boivin, Kiley and Mishkin (2010) go further to explain that the lower value of the domestic currency will make domestic goods cheaper, making them attractive to foreign buyers. The consequence will be a rise in net exports, which directly causes aggregate demand to increase. They go further to explain that exchange rates are sensitive when there has been an increase (or decrease) in interest rates, meaning, the implications can be quite volatile. It is also stated that smaller open economies see a larger effect through this channel. As well as these theoretical assumptions we make empirical studies have also proved this channel (see Bryant, Hooper and Mann (1993), Taylor (1993), and Smets (1995)).

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This section aims to provide some theoretical understanding and previous studies to justify selections of the variables used. As explained and highlighted in Figure 1 that transmissions from exchange rates, Equity markets and how money supply directly affects price level.

3. Literature Review

Since the development of Sims VAR (1980), there has been a vast amount of literature on monetary theory. The literature in GVAR is limited, thus this section will focus on reviewing previous studies in similar subjects.

It is central to highlight Macro-modelling has divided opinion on the best approach, this argument goes back to "Econometric Policy Evaluation: A Critique (Lucas, 1976)". This paper was a big milestone in econometrics and Macro modelling, it led to macroeconomics to establish micro foundations. Its main premise is that it is elementary to try and estimate policy change wholly on relationships of aggregated historical data. An example of this is how Lucas highlights the decision rules of Keynesian models such as consumption functions cannot be ignored with respect to changes in government policy. Lucas mentions that policy advice given from macroeconomic models, would draw invalid conclusions, this is due to the parameters are not structural. The critique concludes stating “structure of an econometric model consists

of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models.”

(Lucas, 1976, p. 41.)

Sims (1980) was critical of the identification strategies7 being proposed (no clear-cut identification of endogenous vs. exogenous variables), which led to the development of the Vector Autoregression models (VAR), they did not distinguish between endogenous and exogenous variables, avoiding identification problems. One of the main reasons behind the popularity is due to Box and Jenkins, Autoregressive moving average models is that models are not built with the purpose of being a structured nor theory-based model, it was more seen as an approximation approach. VAR being the multivariate of this approach.

7_{Additional identifying assumptions which are based on institutional knowledge, conventional economic theory, or other}

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Since the 1970’s, these approaches have been popular for forecasters and researchers. Though variations have now been made, VAR models were simply a set of unrestricted systems of equations, these equations are reduced from equations to model the responses of variables to shocks, specifically Sims put forward the idea to use Cholesky decomposition to identify the system shock. Following the pattern of development of a model, then criticism, Cooley and LeRoy highlighted the choice of causal order. Following this, Sims 1986 developed the structured VAR models, what differentiated this from the original model is it includes a structural element to the identification of the causal orders of the VAR model.

3.1 Monetary Policy and VAR

The beginning of VAR and monetary policy can be traced back to Bernanke and Blinder (1992) and Sims (1992). Since the development of VAR, there has perhaps not been a more popular method for looking at monetary policy shocks, with Evans and Kuttner (1998) mentioning that it is the procedure which makes it attractive. It is questioned in Evans and Kuttner (1998) that like with most econometric procedures, whether VAR really can describe the monetary authority's response to economic conditions. VAR models usually involve only a small number of variables; however, this can be solved with variations of the approach. Also, VAR assumes linearity, meaning VARs rule out plausible asymmetries in the response of policy.

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Bernanke et al. (2004) explains the approach conducted in his study is based on the identification of the effects of monetary policy shocks, that require only a plausible identification of those shocks. This follows the approach of Bernanke and Blinder (1992). The justification for this is due to the results provided empirically and the assessments of the dynamic responses of macro-variables. This type of identification is widely used for assessing the empirical fit of structural models and in policy applications (Boivin & Giannoni, 2003). Simply put, the approach of using a VAR or a variation to measure monetary policy shocks have previously and continuously delivered useful structural information. This approach has naturally come with some criticisms and the main outline being researchers have disagreed about the appropriate strategy for identifying policy shocks (see Christiano et al. 2000). Alternative identification of monetary policy innovations obviously leads to different results, such as the shape of the response and timing of the responses of macro variables. Another issue is that standard VARs only look at the impact of unexpected changes in monetary policy rather than the two systematic portions of monetary policy or the choice of monetary policy rule (Bernanke, Gertler Watson, 1997, Sims and Zha, 1998).

3.2 Monetary policy Using GVAR

Leiand Liu (2015) also use the application of GVAR, and like the current study, it has a focus using money supply. Like this thesis and Bi and Anwar (2017) both treat money as an endogenous variable for the US and a global factor for other economies.

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Given the existence of exchange rate targeting for some countries, international trade and then the global economy will be further influenced (Lei& Liu 2015).

The final channel discussed in this paper is the change in the value of the dollar, it would cause countries’ net exports and current accounts fluctuate with the dollar causing changes in holdings of dollar assets, such as the US government bonds, and foreign exchange reserves. This consequently will have impacts on the US domestic economy and the global economy. They find evidence that the U.S money supply shocks have a global influence. Generally developed countries, namely the Euro Area, the United Kingdom (U.K) and the U.S, neither display real output decline nor inflation pressure, whereas China exhibits a significant decline of real GDP. It is also found that the real output of some developing countries may also face a negative impact, therefore, Leiand Liu (2015) study provides some evidence that spillovers of the liquidity effect exist. Like the approach in this thesis Lei and Liu (2015) use the same countries in the study, however, they do not discuss why they have excluded certain countries from the results leaving gaps which can be easily filled.

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initially positive but it diminishes quickly to zero. The model used in their study uses a vast number of variables and involves several countries however not all results are presented. It is concluded that US money supply growth rate causes an increase in China’s inflation rate, but the effects disappear over a short period. This happens because China reduces its money supply growth rate to cope with input cost inflation risk, leading the short-term interest rate increase.

It is explained that a positive standard error shock from the US increases the US output and asset prices, which lead to an increase in Chinese exports, therefore the net effect is positive. When the Federal reserve increases their short-term interest rate, the People's Bank of China does the same, resulting, in a decrease in inflation and real output growth rate.

3.3 Uncertainty

Prüser and Schlösser (2017) paper does not directly discuss monetary policy however it draws comparisons with the research question. The aim of the paper describes how Economic political uncertainty (EPU) affects investment, the second aim investigates the effect on consumption and the third explains how EPU8 affects the cost of finance or more generally financial variables.

Prüser and Schlösser (2017) highlights that political uncertainty can have many effects on the economy. This thesis looks at investment real options, whereas this paper uses equity prices. This variable is included on the premise that both employment and investment are decisions that can be costly to revert. If the decision-maker faces uncertainty about the future it may result in a wait and see attitudes resulting in deferring either investment or hiring. Thus, the option value is high when uncertainty is high and vice versa (Prüser & Schlösser 2017). There is supporting evidence via empirical research that gives evidence for this channel, for example, Bloom et al. (2007), Carrière-Swallow and Céspedes (2013) and Meinen and Röhe (2016). The second channel theorised by Romer (1990) gives an insight why uncertainty affects consumption. If future income is not certain then a similar effect occurs with investments, therefore the consumption of durable goods is postponed until there is no longer uncertainty (assuming consumption is irreversible). This can be referred to as precautionary savings channel, simply put, uncertainty can affect the intertemporal consumption decisions made by households. Again, with theoretical evidence, empirical studies from Benito (2006), Carrière-Swallow and Céspedes (2013) and Caldara et al (2016) support this. Both investment and

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consumption account for approximately 75% of the Euro Areas GDP. Prüser and Schlösser (2017) estimate that a negative effect on GDP will decrease. This indirect effect has been supported by Donadelli (2015) and Baker et al. (2016). Uncertainty and inflation have been researched by Colombo (2013) and Belke and Osowski (2017) both provide evidence in a negative relationship.

Prüser and Schlösser (2017) investigates that uncertainty may affect financial markets, which is known as the risk premium effect. This is relevant as it explains how uncertainty may affect the transmission channels in this thesis. The risk premium effect stipulates that the increase in uncertainty may result in a reduction in expected profits of firms, which increases their perceived riskiness. As uncertainty increases, firms may become more profitable, resulting in the perception of riskiness. Furthermore, as risky investors would like to be rewarded for taking higher risks will result in a higher long-term interest rate. Theoretical evidence can be provided by Gilchrist et al. (2014) using a general equilibrium model and empirical is provided by Nodari (2014) and Waisman et al. (2015). Credit and uncertainty do not have a vast amount of literature, however Bordo et al. (2016) offers both a theoretical justification and empirical evidence on this subject, arguing that following the financial crisis, bankers complained the delay of implication of the Dodd-Frank Act created regulatory policy uncertainty which restricted giving loans, resulting in a slower recovery. Bordo et al. (2016) used a VAR model to provide evidence that EPU has a negative effect on bank loans.

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on many channels, however, most of these studies are domestic rather than global, thus this thesis aims to fill that gap.

4. Methodology

When looking at macro modelling there are variables that we would like to observe using the VAR, however, the Curse of dimensionality is the biggest obstacle. This section outlines how the GVAR model solves this issue.

The GVAR model made prominent by Pesaran, Schuermann and Weiner (2004, PSW), has become a useful tool not just modelling a large number of variables, allow for modelling for regions and countries. The method combines time series, panel data, and factor analysis techniques, it also deals with the curse of dimensionality problems in both a theoretically coherent and statistically consistent manner.

The model is made up of a large number of unit-specific models, these units can be either countries, regions counties, municipalities, industries, or sectors of a given economy. The model is developed on common and core macroeconomics domestic variables, all of which are included in this model (exchange rates, inflation, interest rates, real output, real equity prices) as well as global variables such as energy prices and commodities and foreign specific variables. Foreign variables are constructed as a weighted average of foreign variables that corresponds to the domestic variable in question, this has been done using trade weights. The ‘curse of dimensionality’ is avoided by approximating the country-specific error-correcting models separately, conditional on the foreign variables that are treated under the assumption of weakly exogenous variables which is usually upheld (Mauro & Pesaran 2004).

4.1 Curse of dimensionality GVAR solution

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not enough of a time series for an estimation. This issue is widely known as the as “the curse of dimensionality”.

While this VAR model generally is a common practice and an attractive approach, it is clearly constrained. Though, it is possible (hypothetically) to extend the model to cover the same variables m, in each of, say, 𝑁 + 1 different economies. While this would require the estimation of a co-integrated VAR involving roughly 𝑚𝑝 (𝑁 + 1) (where p represents the order of the VAR). An illustration, in a model, we have 5 variables, 20 countries (Economies), and say a lag order of 2, this will result in at least 210 parameters to be estimated in each equation. Again, this is improbable.

4.2 GVAR Model

To give a clearer understanding of how the GVAR model is structured, this section will cover key components such as the VAR model and the VARX model before going on to the GVAR model itself.

The Vector autoregressive model is a random process model that is used to capture linear interdependencies among multiple time series. All the variables are included in the model identically, where each variable has an equation based on its own lagged value as well as the lagged value of the other model variables, and an error term. This can be represented by formula (4.0) in a bivariate system with variables x and y.

𝑦_𝑡 = 𝛽₁₀+ 𝛽₁₁𝑦_𝑡−1+ 𝛽₁₂𝑥_𝑡−1+ 𝑣_𝑡𝑦

𝑥𝑡= 𝛽20+ 𝛽21𝑦𝑡−1+ 𝛽22𝑥𝑡−1+ 𝑣𝑡𝑥 (4.0)

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are met, the long-run relationships are then derived from the theory associated with the cointegrating relationship between the variables and the existence of these cointegrating relationships imposes restrictions on a VAR model as a VARX Garratt et al. (p.7 2006a).

As mentioned in the section above, the GVAR model works in two stages, this section will present the methodology. The method used is the same approach used by Dées et al. (2007). The first stage, formulating the individual VARX* model for every country. As the model used in this study uses a vast number of variables, the notation in this section is generic linear notation.

STAGE 1: The country-specific VARX* models

It is assumed that there are N + 1 countries in the global economy; denoted by 𝑖 = 0,1,2 … . 𝑁, the objective is to model the number of macroeconomic variables that are country specific for example, exchange rates, inflation, interest rates etc; collected in a vector 𝐱_𝑖𝑡, over a period of time t = 1,2,3 …T and across N+1 countries. As highlighted by Dess et al (2008), living in a more interconnected world, interdependencies may exist in the world economy. It is evidently desirable that country specific variables, denoted by 𝑥𝑖𝑡, 𝑖 = 0,1 … , 𝑁 and the

observed macro variables are treated as endogenous. Continuing from the model given in each individual country model is represented by a VARX* (2,2) Equation (4.1)

𝒙𝑖𝑡 = 𝒂𝑖0+ 𝒂𝑖1𝑡 + 𝚽𝑖1𝒙𝑖,𝑡−1+ 𝚽𝑖2𝒙𝑖,𝑡−2+ 𝚲𝑖0𝒙𝑖𝑡∗ + 𝚲𝑖1𝒙𝑖,𝑡−1∗ + 𝚲𝑖2𝒙𝑖,𝑡−2∗ 𝒖𝑖𝑡

4.1

Where 𝐱_𝑖𝑡 and 𝐱_𝑖𝑡∗ are vectors of dimension of 𝑘_𝑖 × 1 𝑎𝑛𝑑 𝑘_𝑖∗× 1 𝐱_𝑖𝑡 respectively. Where, Vector 𝐱_𝑖𝑡 characterizes the domestic macroeconomic variable and 𝐱_𝑖𝑡∗ characterizes the foreign variable; both indexed by, time 𝑡 and country 𝑖. 𝐮_𝑖𝑡represents a serially uncorrelated and cross-sectionally weakly dependent process (Di Mauro & Pesaran 2013). The remaining parameters are similar to those in a standard VAR model, the parameters are to be estimated to provide some economic interpretation.

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𝐱𝑖𝑡∗ = ∑ 𝑤𝑖𝑗x𝑗𝑡 𝑁

𝑗=0

4.2

, where 𝑤_𝑖𝑗, 𝑗 = 0,1 … , 𝑁 are such weights that 𝑤_𝑖𝑖=0 𝑎𝑛𝑑 ∑𝑁_𝑗=0𝑤_𝑖 = 1. There are different ways to determine the weight for the model, such as trade weights, financial connections, or economic unions. The weights are predetermined, they capture the importance of each domestic country 𝑗 for the 𝑖th economy.

Like the unrestricted VAR model, the VARX* model can be modified with an error correction term, VECMX*. The VECMX* model allows us to differentiate the long and short-run effects.

STAGE 2 – Solution strategy

As mentioned, the GVAR approach works in two stages. The first stage requires the estimation of the VARX* model country by country or (economy by economy). Next, all the VARX* equations are stacked together to be solved as a whole.

This stage focuses on solving the model outlined in Equation (4.1), recall the original VARX* (2,2), model. A new term 𝑧𝑖𝑡 is introduced, defined as (equation 4.3)

𝑧_𝑖𝑡 = (𝑥𝑖𝑡 𝑥_𝑖𝑡∗)

4.3

𝑧_𝑖𝑡 the term that combines both the foreign and domestic variables together, which is written in equation (4.1). “This helps in reducing the derivation of the full GVAR model”. (Di Mauro & Pesaran 2004) The remaining terms in equation (4.4), are respective regression coefficient as well the cointegration term.

𝐀_𝑖0𝐳_𝑖𝑡 = 𝐚_𝑖0+ 𝐚_𝑖1𝑡+ 𝐀_𝑖1𝐳_{𝑖,𝑡−1}+ 𝐀_𝑖2𝐳_{𝑖,𝑡−2}+ 𝐮_𝑖𝑡, 4.4

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As a result, we get

𝐀_i0𝐖_i𝐱_t = 𝐚_i0+ 𝐚_i1t + 𝐀_i1𝐖_i𝐱_t−1+ 𝐀_i2𝐖_i𝐱_t−2+ 𝐮_it 𝑓𝑜𝑟 𝑖 = 0,1,2 … . 𝑁

4.5.

Where 𝐱_𝑡 = (𝐱_𝟎𝐭′ 𝐱_𝟎𝐭′ … 𝐱_𝐍𝐭′ ) is the 𝑘 × 1 vector of the collection of endogenous variables in the system. 𝑊_𝑖 is the 𝑘 × (𝑘_𝑖 + 𝑘_𝑖∗) matrix. The result of all stacking the individual models to produce a result for model 𝐱𝑡 given by;

𝐆₀𝐱_t = 𝐚₀ + 𝐚₁t + 𝐆₁𝐱_𝑡−1+ 𝐆_𝟐𝐱_𝑡−2+ 𝐮_t, 4.6 Where 𝐆₀ = ( 𝐀₀₀𝐖₀ 𝐀₁₀𝐖₁ ⋮ 𝐀_N0𝐖_N ) , 𝐆_𝟏 = ( 𝐀₀₀𝐖₀ 𝐀₁₀𝐖₁ ⋮ 𝐀_N0𝐖_N ) , 𝐆_𝟐= ( 𝐀₀₀𝐖₀ 𝐀₁₀𝐖₁ ⋮ 𝐀_N0𝐖_N ) 𝐚₀ = ( 𝐚₀₀ 𝐚₁₀ ⋮ 𝐚_N0 ) , 𝐚₁ = ( 𝐚₀₁ 𝐚₁₁ ⋮ 𝐚N1 ) , 𝐮_t = ( 𝐮_0𝑡 𝐮_1𝑡 ⋮ 𝐮_𝑁𝑡 ) 4.7

The term 𝐺₀ is a known non-singular matrix or invertible matrix, which depends on the trade weights and parameter estimates. 𝐺₀ we know that there is an n x n matrix 𝐺₀−1, therefore 𝐺₀𝐺₀−1 = ln = 𝐺₀𝐺₀−1. Multiplying the inverse, 𝐺₀−1, cancels out. From this, we obtain GVAR (2) with two lags Equation (4.8).

Where

𝐱𝑡 = 𝐛0+ 𝐛1𝑡 + 𝐅1𝐱𝑡−1+ 𝐅2𝐱𝑡−2+ 𝜀𝑡, 4.8

𝐅₁= 𝐆₀−1𝐆₁, 𝐅₂ = 𝐆₀−1𝐆₂

𝐛₀ = 𝐆₀−1𝐚₀, 𝐛₁ = 𝐆−1₀ 𝐚₁, 𝜀_𝑡= 𝐆₀−1𝐮_𝑡

4.9

To differentiate between the long and short run relationship and interpret the long run relationship as cointegrating, we look at the error correction form, VECMX*.

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20 | P a g e 𝐆 − 𝐇 = ( (𝐀₀− 𝐁₀) 𝐖₀ (𝐀0 − 𝐁0)𝐖1 ⋮ (𝐀_N− 𝐁_N)𝐖_𝑁 ) = ( 𝛼₀𝛽′₀ 𝐖₀ 𝛼1𝛽′1 𝐖1 ⋮ 𝛼_𝑁𝛽′_𝑁𝐖_𝑁 ) 4.119

Which can be written as

G₀− 𝐺₁ = 𝛼̃𝛽̃ , ′ _4.12

We define 𝛼̃ as a 𝑘 × 𝑟 block diagonalization matrix, this characterises the short run global adjustment coefficients. 𝛽̃ represents the 𝑘 × 𝑟 cointegration space matrix, which can be mathematically expressed in equation (4.13)

𝛽 = (𝐖₀′𝛽0, 𝐖1′𝛽1, ⋯ , 𝐖𝑁′𝛽𝑁), 𝑟 = ∑ 𝑟𝑖, 𝑁 𝑖=0 𝑘 = ∑ 𝑘𝑖 𝑁 𝑖=0 _4.13

5. Data

This section covers all the data used in this thesis, introducing variables and countries that will be used in the model. The model in this study has 9 different variables across 33 different countries, ranging from the period year 1985 quarter 2 to the year 2016 quarter 4. The data used in this study is based on those from Dees et al (2007) and Bi and Anwar (2017). To capture information more suitable for monetary policy there is a slight variation to the original database, by including money supply and Monetary Policy Uncertainty. The database was originally developed by Dees et al. (2007) and has most recently been updated by Kamiar Mohaddes (University of Cambridge) and Mehdi Raissi (International Monetary Fund). The origin of the data has been taken from the International Financial Statistics (IFS) database, the Inter-American Development Bank (IADB) and Bloomberg. The description of the data can be found in Appendix 1. A summary of the variables can be found in Table 1.

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Variable Source Description Notes

Real GDP; Output International Financial Statistics/ Haver Analytics 𝑦𝑖𝑡 = ln (𝐺𝐷𝑃𝑖𝑡) Seasonal adjustment Quarterly Consumer Price Index; Inflation International Financial Statistics/ Haver Analytics 𝑑𝑝𝑖𝑡 = 𝑝𝑖𝑡− 𝑝𝑖𝑡−1 Quarterly Equity Price Index; Real Exchange Rate

Haver Analytics/MSCI 𝑒𝑝𝑖𝑡 = ln (𝐸𝑖𝑡/𝐶𝑃𝐼𝐼𝑇) Quarterly

Exchange Rates International Financial Statistics 𝑒𝑞𝑖𝑡 = ln (𝐸𝑄𝑖𝑡/𝐶𝑃𝐼𝐼𝑇) Quarterly Short-Term Interest Rates International Financial Statistics 𝑟𝑖𝑡 = 0.25ln (1 + 𝑅𝑖𝑡𝑆 /100) Quarterly Long-Term Interest Rates International Financial Statistics 𝑙𝑟𝑖𝑡 = 0.25ln (1 + 𝑅𝑖𝑡𝐿 /100) Quarterly

Oil Price Bloomberg 𝑜𝑖𝑙 = ln (𝑜𝑖𝑙𝑡) Quarterly

(averages of daily closing price, Ln), Brent blend Money Supply, M2 Thomson Reuters Datastream 𝑀2 = ln (𝑀2𝑡/𝑀2𝑡−1) Quarterly Constant price, SA Standardized Monetary Policy Uncertainty Monetary Policy Uncertainty Indices 𝑚𝑝𝑢 = ln( 𝑚𝑒𝑝𝑢𝑡 /𝑚𝑒𝑝𝑢𝑡−1) Quarterly averaged

Table 1 Summary of the variables that these macro-variables are commonly globally available and are measured frequently.

5.1 Monetary Policy Uncertainty

The MPU10 dataset is created by using newspaper articles that satisfy the E, P, U and M criteria, which requires flagging articles which contain E: economic, economy P: Congress, legislation, white house, regulation, federal reserve, deficit; U: uncertain, uncertainty M; federal reserve, the fed, money supply, open market operations, quantitative easing, monetary policy, fed funds rate, overnight lending rate, Bernanke, Volker, Greenspan, central bank, interest rates, fed chairman, fed chair, lender of last resort, discount window, European Central Bank, ECB, Bank of England, Bank of Japan, BOJ, Bank of China, Bundesbank, Bank of France, Bank of Italy. The MPU criteria is applied to hundreds of newspapers across the world. The index is constructed by a raw data count of the articles that meet the criteria and divide the count of all articles in the same newspapers and month.

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5.2 Countries

The model used for this thesis, contains 33 different countries, 8 of which are grouped as the Euro Area and is treated as one country (when estimating the VARX* model). The countries used can be found in Table 2. The countries involved covers the majority of the world economy, estimated at around 90% and have enough data to provide useful for the model (di Mauro & Pesaran 2013).

Europe Asia and Pacific North and South America

Austria* Australia Canada

Belgium* China Mexico

Finland* India United States

France* Indonesia Argentina

Germany* Japan Brazil

Italy* South Korea Chile

Netherlands* Malaysia Peru

Norway New Zealand The Middle East and Africa

Spain* Philippines Saudi Arabia

Sweden Singapore South Africa

Switzerland Thailand

Turkey

United Kingdom

Table 2 Countries within the model. The countries with an asterisk are groups together as the Euro Area

6. Model specifications

This section includes all the diagnostic tests and results that need to be conducted before the GVAR model is estimated.

Lag Order11 of Individual VARX* Models

As stated the VARX* (P,Q) model has two lag orders, one for domestic lags p (endogenous), and foreign variables (weakly exogenous). The lag order was selected by the Schwarz Bayesian 12_{criterion. Results are displayed in Table 3. The Lagrange Multiplier serial correlation} (F-version) test has also been used to estimate residuals of the individual country models, this was specified to be four which is standard for quarterly data. The lag order defined is used for calculating the residual serial correlation F-statistics, for both the VARX* model residuals.

11_{Model with too few lags will provide less rich information about the statistical outcome of the model.}

Including too many lags may result in coefficients in the model being overestimated (Hill, Griffiths and Lim, 2011)

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P, Q

Asia and Pacific

P, Q

North and South

America P, Q

Euro Area 2,1 Australia 2,1 Canada 1,1

Norway 2,1 China 2,1 Mexico 2,1

Sweden

2,1 India 2,1

United

States 2,1

Switzerland _1,1 Indonesia _2,1 Argentina _2,1

Turkey 2,1 Japan 1,1 Brazil 1,1

United Kingdom 1,1 South Korea 2,1 Chile 1,1

Malaysia 2,1 Peru 2,1 New Zealand 2,1 The Middle East and Africa P, Q Philippines 2,1 Saudi Arabia 2,1 Singapore 2,1 South Africa 2,1 Thailand 2 ,1

Table 3 VARX* Order of Individual Models (p: lag order of domestic variables, q: lag order of foreign variables)

Unit Root13_Testing

The GVAR model is indifferent to stationary and the non-stationarity of the inputted variables. However, like most econometrics papers, testing for unit roots always provides to be useful. With the GVAR model, it allows for the identification of long-run relations (as cointegrating) and short run relations (Smith & Galesi 2017). To test for a unit root, the Augmented Dickey-Fuller (ADF) test and Weighted-Symmetric Dickey-Dickey-Fuller introduced by Park and Dickey-Fuller (1995). The tests have been conducted at 95% significance, if the test statistic for the variable is more negative than the critical value then the hypothesis of no unit root is rejected. The test has been calculated at levels, differenced, second differenced, and both with and without a trend. All variables have been tested including domestic, foreign-specific and global variables entering the individual models. The lag selection has been conducted using the Akaike information criterion with a test has been a maximum lag order of 4. Results can be found in

13_{Unit root tests determines whether a series is stationary or nonstationary, if a series is non-stationary at}

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Appendix 2 however the overall finding show that all variables are non-stationary and become stationary after the first difference.

Testing for a cointegrating relationships

After testing for unit roots and the corresponding cointegrating VARX*14 models are estimated as VECMX* tested, the next stage of the process is to identify the cointegrating relationships within the individual models. Cointegration implies 𝑦_𝑡 𝑎𝑛𝑑 𝑥_𝑡 share a similar stochastic trend, as the difference 𝑒_𝑡is stationary, they never diverge too far from each other. Johansen’s trace and maximal eigenvalue statistics have been carried out, to test the

cointegrating relationships for each model. The results are displayed in Table 4.

Europe

Asia and Pacific

North and South

America

Austria* 1 Australia 4 Canada 3

Belgium* 1 China 2 Mexico 2

Finland*

1 India 2

United

States 2

France* 1 Indonesia 3 Argentina

Germany* 1 Japan Brazil 2

Italy* 1 South Korea 6 Chile 3

Netherlands* 1 Malaysia 2 Peru 3

Norway 3 New Zealand 3 The Middle East and Africa

Spain* 1 Philippines 3 Saudi Arabia 2

Sweden 3 Singapore 2 South Africa 2

Switzerland 4 Thailand 2

Turkey 1

United Kingdom 2

Table 4 Cointegrating Relationships for the Individual VARX

Weak Exogeneity Test

As previously stated, the main assumption when using the GVAR methodology, specifically regarding the VARX* models is weak exogeneity of the foreign variables denoted as 𝐱_𝑖𝑡∗. The assumption of weak exogeneity in the context of cointegration models can be explained as there being no long run feedback from 𝑥_𝑖𝑡 𝑡𝑜 𝑥_𝑖𝑡∗ without necessarily ruling out lagged short run feedback (Smith & Galesi 2017). 𝑥_𝑖𝑡∗ the foreign variable is the “long run forcing” for 𝑥_𝑖𝑡,the domestic variable, which indicates the error correction term of each individual country

14_{The Vector Autoregression model is a time series model that measures linear interdependencies among number of time}

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VECMX* are not included in the marginal model 𝑥_𝑖𝑡∗. To test the assumption of weak exogeneity for the country specific foreign variables and the global variables is conducted along the lines based on similar methodology of Johansen (1992) and Harbo et al. (1998). The test is based on the joint significance on the estimated error correction terms in auxiliary equations for the country-specific foreign variables. For each 𝑖𝑡ℎelement of 𝑥𝑖𝑡 the regression model in equation (4.1) is carried out.

∆𝑥𝑖𝑡,𝑙∗ = 𝑎𝑖𝑙+ ∑ 𝛿𝑖𝑗,𝑙𝐸𝐶̂𝑀𝑖𝑗,𝑡−1 𝑟𝑖 𝑗=𝑖 + ∑ 𝜙𝑖𝑠,𝑙′ 𝑝_𝑖∗ 𝑠=1 ∆𝑥𝑖,𝑡−𝑠+ ∑ 𝜓𝑖𝑠,𝑙′ 𝑞_𝑖∗ 𝑠=1 Δ𝑥̃𝑖,𝑡−𝑠∗ + 𝜂𝑖𝑡,𝑙 4.14

Where, 𝐸𝐶̂𝑀_{𝑖𝑗,𝑡−1} 𝑗 = 1,2, … , 𝑟_𝑖 are the ECM terms corresponding to the ri cointegrating relations found for the 𝑖𝑡ℎ country model and p and q are the orders of the lagged changes for both the domestic and foreign variables. The weak exogeneity test is an F-test of the

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Country F test Fcrit_0.05 GDP Inflation EQS RS LRS POIL MPU M2

ARGENTINA F(2,94) 3.093266 0.324498 0.831308 0.147498 2.795323 1.318987 0.283896 0.922489 0.37427 AUSTRALIA F(4,90) 2.472927 0.186686 1.979709 2.136642 1.655513 1.127812 0.163029 0.199327 1.230543 BRAZIL F(2,100) 3.087296 0.047274 4.956229* 0.125363 1.052483 0.564458 2.840856 0.685951 0.015709 CANADA F(3,106) 2.690303 2.287338 1.911613 0.329485 0.500516 0.211988 1.685249 0.320114 2.49048 CHINA F(2,100) 3.087296 1.831705 1.43102 0.270806 4.130857* 3.238386* 2.803795 0.56599 0.156275 CHILE F(3,98) 2.697423 3.170648* 2.078532 1.394416 2.231056 1.592902 0.98337 0.917507 0.753985 EURO F(1,108) 3.929012 1.525272 7.513153* 1.85197 1.473539 1.806548 1.928811 1.01909 4.751437* INDIA F(2,107) 3.081193 0.637713 0.130511 1.696014 0.589392 0.977247 0.437597 1.031117 1.313241 INDONESIA F(3,99) 2.696469 0.2073 0.469021 1.758812 1.057237 1.86216 2.008175 2.359471 0.767046 JAPAN F(2,107) 3.081193 3.91652* 3.762553* 0.710299 3.14324 1.570577 0.095822 0.3242 0.408901 KOREA F(6,103) 2.187868 0.766337 1.010576 2.8717* 0.868611 2.267219* 0.316596 1.153305 1.716305 MALAYSIA F(2,99) 3.08824 2.260672 4.393933* 1.510352 2.650211 0.490874 1.356084 1.448146 0.939481 MEXICO F(2,109) 3.079596 0.221717 1.744254 2.340847 1.400253 0.327437 0.167704 2.894416 0.575749 NORWAY F(3,106) 2.690303 1.735196 0.381916 1.268223 0.235759 0.389748 0.737733 1.359296 0.511951 NEW ZEALAND F(3,97) 2.698398 1.100804 0.366397 0.286941 0.405079 0.81335 0.647397 0.252256 0.923906 PERU F(3,108) 2.688691 0.746964 1.787994 0.184853 2.34921 1.574484 0.912162 1.833859 0.774214 PHILIPPINES F(3,107) 2.68949 0.723033 0.726064 0.326832 2.185454 3.522008* 3.221678* 1.697168 3.633589* SOUTH AFRICA F(2,107) 3.081193 0.106353 0.654199 0.078129 1.323325 0.431548 0.040506 0.022051 0.06722 SAUDI ARABIA F(2,110) 3.078819 0.04389 3.711447 2.910865 1.470583 0.730601 0.899053 2.636421 1.148873 SINGAPORE F(2,108) 3.080387 1.247603 0.078362 2.67121 4.452098* 0.249116 1.673846 2.542146 3.411319* SWEDEN F(3,106) 2.690303 3.60414* 1.160399 1.083816 0.76912 1.087778 2.761908 1.294859 3.187937* SWITZERLAND F(4,105) 2.45821 1.432418 1.352024 1.069689 0.420124 0.994941 1.83523 0.994707 0.667059 THAILAND F(2,94) 3.093266 0.256859 0.208877 0.950193 0.077582 0.329977 0.076689 0.35183 0.338794 TURKEY F(1,110) 3.927394 0.986206 6.120634* 0.008725 2.104814 3.003545 0.0494 0.089854 2.266583 UNITED KINGDOM F(2,98) 3.089203 0.127929 0.31972 1.331854 0.084437 0.51205 0.639955 1.425025 1.00353 USA F(2,110) 3.078819 1.99093 2.568463 - - - 2.496534 0.421787 1.626061

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Structural stability test

Like most time series models, GVAR is also susceptible to structural breaks. Structural breaks are simply the unanticipated abrupt shift of the time-series. The issue of structural breaks has been investigated since the later 1950’s (Quandt 1958, 1960). Quandt proposed the PK Sup F test, which calculates the likelihood ratio for a change in model parameters and estimates the date of the break.

Structural stability tests have been carried out, similar to those considered by Stock and Watson (1996). These tests have been estimated to detect the possibility of the presence of breaks. The tests included Ploberger and Krämer’s (1992) maximal OLS cumulative sum (CUSUM) statistic, which is similar to the CUSUM test (Brown et al. 1975), however, it differs as the latter is based on recursive residuals. A mean square variant of the maximal OLS cumulative sum (CUSUM) statistic has also been calculated. Further tests include parameter constancy against the non-stationary alternative (Nyblom 1989) and sequential Wald-type tests of a one-time structural change at an unknown change point (Smith & Galesi 2014). Results of the breaks can be found in Table 6.

Variables GDP Inflation EQ EP R LR Argentina 1994Q3 1990Q2 1990Q1 1990Q1 1990Q2 Australia 1990Q2 1991Q1 1990Q4 1990Q1 1990Q2 1990Q2 Brazil 1990Q1 1994Q4 1997Q4 1994Q3 Canada 1990Q2 1994Q3 1998Q2 1991Q4 1990Q2 1998Q1 China 1994Q4 1994Q1 1994Q2 1990Q1 Chile 1993Q2 1991Q2 1997Q2 2003Q3 1991Q2 Euro 1990Q3 1992Q4 2011Q4 2003Q3 1994Q3 2011Q2 India 1993Q1 1992Q2 1992Q2 1991Q4 2008Q2 2003Q4 Indonesia 1999Q1 1998Q3 1998Q1 1998Q3 Japan 1990Q1 1990Q2 2011Q4 1995Q2 1993Q4 1993Q4 Korea 1990Q4 1998Q1 1994Q4 1997Q3 1998Q1 1990Q4 Malaysia 1998Q1 2008Q2 1998Q3 1997Q4 1998Q2 Mexico 1995Q2 1990Q1 1995Q1 1995Q1 Norway 2009Q1 2002Q3 1990Q4 2008Q1 1993Q2 1990Q2 New Zealand 1990Q1 1990Q2 1991Q2 1999Q1 1990Q1 1990Q4 Peru 1990Q4 1990Q4 1991Q2 1991Q2 Philippines 1990Q1 1991Q4 1990Q2 1997Q4 1992Q4 South Africa 1993Q1 1993Q1 2000Q2 1990Q1 1997Q4 1990Q3 Saudi Arabia 1990Q1 1999Q3 1999Q3 Singapore 2009Q4 2012Q2 1990Q4 1991Q3 1998Q3 Sweden 1994Q3 1993Q1 2001Q2 1993Q2 1992Q4 1990Q1 Switzerland 1997Q4 1990Q4 1990Q2 2000Q3 1992Q4 1992Q4 Thailand 2011Q2 1995Q2 1997Q3 1997Q4 1994Q4 Turkey 1992Q4 1994Q2 2000Q2 1994Q2 United Kingdom 1994Q4 1990Q3 1990Q3 2003Q3 1990Q2 1990Q2 USA 2005Q3 2007Q3 1990Q1 2005Q2 1998Q4

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Dynamic analysis

Perhaps the main application of VAR analysis is the Generalized impulse response functions (GIRF) and the variance decompositions. The impulse response functions can show what happens to a variable when there is a positive or negative shock in the error term. Again, the focus is to investigate what will happen to our variables when we have a positive shock to the money supply, The US discount rate and Uncertainty.

Generalised Impulse Response Function15

The GIRF differs from the standard orthogonalized impulse responses as the approach considers shocks to individual errors and integrates out the effects of the other shocks using the observed distribution of all the shocks without any orthogonalization (Smith & Galesi 2017).

The General impulse response functions are designed and used for simulation analysis oppose to identification. The GIRF presented no longer rely on the ordering of variables, meaning though the information is useful in terms of changes in the underlying variables, however, it cannot provide information on the dynamics of the transmission shocks.

The GIRF for a single country shock can be represented as:

𝒈𝜀𝑗(ℎ) = 𝐸(𝐱𝑡+ℎ|𝜀𝑗𝑡 = √𝜎𝑗𝑗, 𝑰𝑡−1) − 𝐸(𝐱𝑡+ℎ|𝑰𝑡−1), = 𝑹ℎ𝑮0 −1_{∑ 𝒆} 𝑗 √𝒆𝑗′∑ 𝒆𝑗 _4.15

Where, 𝒈_𝜀𝑗 (the general impulse response function) is a 𝑘 × 1 vector, at period ℎ, 𝑗 represents the country index of the country of interest. The E outside the parenthesis is the expectation with respect to the VAR model. Within the parenthesis vector of 𝐱𝑡 at period ℎ, upon a shock on 𝜀_𝑗𝑡 to country 𝑗 at period 𝑡. The expectation is equal to the square of the shock at size 𝜎_𝑗𝑗. 𝐼_𝑡−1 is full information at 𝑡 − 1 which has been defined as the collection of vectors 𝐱_𝑡 at period

15_{Impulse responses refer to the time profile of the effects of variable-specific shocks or identified shocks on}

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𝑡 − 1. 𝐑ℎ is a vector 𝑘 × 𝑘 𝐆𝟎−𝟏 for linking the variables together as the summation as the Cholesky factor. 𝐞_𝐣 is a vector that selects the element of the shocks.

Global shocks impulse response functions slightly vary, for a single country to a global shock, this can be mathematically expressed in equation 4.3. With the difference being that the equation longer have 𝜀𝑗𝑡, rather 𝜀𝑚,𝑡′

𝑔

which can be re written as 𝒎’𝜀𝑡 with 𝒎 being the vector of weights linked to the global economy or region.

𝒈𝜀𝑗(ℎ) = 𝐸(𝐱𝑡+ℎ|𝜀𝑚,𝑡 𝑔 = √𝑚′_{, ∑} 𝑚𝐼𝑡−1, ) − 𝐸(𝐱𝑡+ℎ|𝑰𝑡−1), = 𝑹ℎ𝑮0 −1_{∑ 𝑚} √𝑚′_{∑ 𝑚} 4.16

Within the methodology, the use of impulse response functions have been the main part of the study. For robustness the GIRF are calculated with both some upper and lower bounds defined by the confidence interval, 90% in this case, this has been done by bootstrapping. Bootstrapping is the method which approximates the model, repeating continuously until the solution is stable. Smith and Galasi (2014, p.149), defines stability as, when the eigenvalues are less than or equal to one which is the case in this model.

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7. Results

This section provides the results in the form of generalised impulse response functions16. Impulse response functions show the effects of shocks on the adjustment path of the variables. Due to the vast amount of countries and variables in the model, we will present only significant results or results of interest. Here we look at one positive shock on The US short-term interest rate, one positive shock on Money supply and one positive standard error shock on Monetary Policy Uncertainty.

A positive interest rate shock on GDP can be seen in Figure 2. Firstly, it is important to highlight that the South American17 countries do not provide any significant results. Both Canada and Mexico provide positive and significant results, this is no surprise seeing as they are economically close. As displayed we see a positive increase in Canada’s GDP. This impact is persistent throughout 38 periods peaking at 0.06%. Mexico displays a bigger impact than Canada with the shock peaking at 1.2% at period 16, however, remaining stable through the remaining periods. It can be theorised that an increase of interest rates may lead to an increase in savings/investing, meaning there is less money in the system making the value of the dollar increase, as the United States imports from Mexico18_{this may boost the GDP of the Mexican} economy. These results are in line with the work of Swiston and Tamim Bayoumi (2008), who use a VAR model to investigates global spillovers to Canada and Mexico. They find that a one percent shock to U.S. GDP shifts Canadian growth by 0.75% in the same direction, emphasising that the Canadian business cycle is firmly connected with that of the United States. The authors also explain that since the introduction of the Canada-United States Free Trade Agreement, financial shocks have become the prominent transmission mechanism. Mexico is affected by the actions of the US a lot heavier than Canada, which also supports the research of Swiston and Bayoumi 2008. It is found from Swiston and Bayoumi that one percentage point shock to U.S. growth leads to a change of 1.5% percentage points in Mexican GDP.

16_{Vertical axis measuring the percentage change, whereas the horizontal measures time (one period}

corresponds to one quarter).

17_{Argentina, Chile, Brazil and Peru}

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Within the European Area, we do not find significant results for a long period of time, usually, sufficiency can only be found between periods 4 and 10. Sweden provides a significant positive impact of 0.005% that does not diminish through the 40 periods, this result is similar to that of Poirson and Sebastian Weber (2011), which show an increase of 0.06% over 8 periods. The linkage with the United States and Sweden can be rooted to the number of exports from Sweden to the United States. Between 1998 to 2008 the US has been one of the leading importers with the latest figures being $5,084.1 million.19 As expected the US is affected by its own monetary policy, we see again from period 4 a positive impact on GDP until around period 38, where the results become insignificant. India displays similar results.

A positive interest rate shock on inflation only provides significant results for Singapore (Figure 2). It Displays an initial increase then becomes stable around period 16. This result is of interest because there is no effect on any other economy which is significant or displays any deviation from zero.

Figure 2 US Interest Rate Shock on GDP – Displaying results for Sweden, Mexico, India, Canada, and the USA US Interest Rate Shock on Inflation - Displaying Results for Singapore

A positive interest rate shock on the real exchange rate provides insignificant results for all countries except for Mexico and the Philippines both of which display a negative impact from around period 2 to period 40 with a decrease from 0.4 and 0.2 respectively displayed in Figure 3. Though not significant there is a clear trend with the exception of China, being that there are negative or little movements, while China display a positive effecs.

19_{https://www.census.gov/foreign-trade/balance/c4010.html}

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Figure 3 US Interest Rate Shock on the Real Exchange Rate- Displaying the Philippines and Mexico

The results for equity prices display a positive impact on every country though not all are significant. These results are displayed in Figure 4. Starting with the United States, we see a significant and positive increase which held throughout the whole period. The Euro-Area and Canada response display a similar pattern. The results from Europe are similar. Again, there is a positive shock, however, there is a trend in Norway, The United Kingdom, Switzerland and the Euro Area where the impact becomes insignificant in the later periods.

Figure 4 US Interest Rate Shock on Equity Prices – Displaying Results for Australia, USA, Canada, Norway, Switzerland, New Zealand, Sweden, Euro and The United Kingdom

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most countries, though not significant at 5%. Short-term interest rates display generally positive results, however, only the United Kingdom and the United States are significant whereas Norway and the Euro Area start off significant, then become insignificant. Results are displayed in Figure 5.

Figure 5 US Interest Rate Shock on Short-Term Interest Rates – Displaying results for USA, The United Kingdom, The Euro Area and Norway.

The results show that a positive standard error shock in the short-term interest rates display a positive reaction in most economies GDP, however, only the United States, Sweden, Mexico, India and Canada provide significant results. Like Bi and Anwar (2017) the Euro Area and China are found to be insignificant. However, despite the results being insignificant they display a negative effect. A contradiction to Bi and Anwar (2017) is the results for the United States being significant and positive in the current study rather than negative. This thesis finds that equity prices display the most significant results whereas Bi and Anwar (2017) does not. In terms of short-term interest rates, the findings from the current research correspond with the results of Bi and Anwar regarding the United States, however, Bi and Anwar’s results display a bigger impact but still positive. The results show that some of the largest economies like the United Kingdom, the Euro Area and Norway display increasing interest rates.

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The Euro area and Canada display a negative impact on GDP, however, no results hold to be significant, like Lei and Liu (2015) results. The United States and Sweden both display a significant negative impact until about period eight, then the effect is no longer significant. Results displayed in Figure 6.

Figure 6 Money Supply Shock on GDP – Displaying results for Sweden, Mexico, India, Canada, and the USA

Inflation displays only one significant effect on all countries except the United States where it is only significant to period 16. We see a negative effect displayed which goes against conventional economic theories. However, this pattern is consistent through all countries in the model, with the exception of the United Kingdom. Results Displayed in Figure 7.

Figure 7 Money Supply Shock on inflation – Displaying results for the USA and the United Kingdom

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Similar to the work of Prüser and Schlösser 2017, we would predict that uncertainty would cause a negative effect on most variables. This case of uncertainty, there is a clear display of a negative effect on GDP except in the case of Saudi Arabia, which would require further research to provide economic interpretation. The significant and partially significant results are displayed in Figure 8. Mostly the results are consistent with previous results, theories and studies (see literature review) though most are found to be significant at 10%. Prüser and Schlösser (2017) focused only on European countries all of which are in the European Union, they found all to be significant negative results, which estimating one standard deviation shock on GDP growth.

Figure 8 Uncertainty shock on GDP displaying Canada, India, Euro Area, Mexico, Saudi Arabia and the USA

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Figure 9 Uncertainty shock on Equity Prices – Displaying results for Australia, Canada, Chile, The Euro Area, Japan, New Zealand, Sweden, Switzerland, Thailand, The United Kingdom and the USA

Exchange rates display interesting results exhibiting evidence of both positive and negative results which are significant. Displayed in Figure 10. The majority of developing20 countries show an increase in the exchange rate, whereas most European countries display the opposite. The United Kingdom is an exception to this.

It is found that monetary policy uncertainty provides useful evidence that it has a negative impact on most channels. This research found a lot of significant results in developing countries.

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The one channel that causes a positive impact is exchange rates, except in the case of Switzerland. Apart from exchange rates uncertainty seems to match the conventional economic theory of uncertainty having a negative impact. The biggest impacts are displayed exchange rates and equity prices which are more sensitive to news as they are fast moving time series.

Figure 10 Uncertainty shock on Exchange Rates – Displaying Results for India, Chile, Mexico, South Africa, Singapore, Switzerland, the United Kingdom and the Euro Area

8. Concluding Remarks

How do the actions of the federal reserve affect the Global economy? This question has been answered using the Global Vector Autoregression model. We have investigated how one standard positive error shock from Money supply, Discount Rate and Monetary policy has impacted GDP, Inflation, Short and long interest rates, Exchange rates and Equity prices for 33 different countries, for a description see section 5.

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different data set. Overall, we find that there is evidence across most channels of transmission, though not all results are found to be significant. It is found that countries are particularly sensitive to shocks when it comes to exchange rates and Equity prices and less so when it comes to GDP and inflation. We also see a clear trend like the research of Prüser and Schlösser (2017) that uncertainty from America has a negative to across most nations.

Like all studies, there are limitations that need to be taken into consideration. Firstly, like Jinghua Lei and Kai Liu (2015), the GVAR model can only serve as a reference for global macro effects, nonlinear effects and asymmetries have not been accounted for. Secondly, the GVAR model can account for time-varying co-movement across domestic variables and their foreign counterparts, which would provide richer information, however, this study does not incorporate account time-varying co-movements in the model. Data restrictions was another limitation for other developing countries that have some importance in the world economy, such as Russia, Iran and Nigeria.

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9. Bibliography

• Baker, S. R. Bloom, N. and Davis S. J. (2016). Measuring Economic Policy Uncertainty. Quarterly Journal of Economics, 131(4):1593–1636.

• Belke, A. and Osowski, T. (2017). International Effects of Euro Area versus US Policy Uncertainty: A FAVAR Approach. GLO Discussion Paper, No. 35.

• Bernanke B & M. Gertler (1995). Inside the black box: the credit channel of monetary policy transmission. Journal of Economic Perspectives 9 p27-48.

• Bernanke B S & Blinder A S (1992). The Federal Funds Rate and the Channels of Monetary Transmission American Economic Review, American Economic Association; 82(4), pages 901-921.

• Bernanke B, M Gertler and S Gilchrist (1996). The financial accelerator and the flight to quality. Review of Economics and Statistics 78 p1- 15

• Bernanke BS., Boivin J. & Eliasz P. (2004) Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach. NBER Working Paper No. 10220. National Bureau of Economic Research, Cambridge MA. • Bi Y. & Anwar S. (2017) US monetary policy shocks and the Chinese economy: a

GVAR approach. Applied Economics Letters 24(8), 553-558.

• Bloom D. E. D. Canning, G. Fink & J. E. Finlay. 2007. Realizing the demographic dividend: Is Africa any different? PGDA working paper no. 23. Boston: Program on the Global Demography of Aging

• Boivin J & M P Giannoni 2006 Has Monetary Policy Become More Effective?" Review of Economics and Statistics, 88 45-462

• Boivin J. M. T. Kiley & F. S. Mishkin (2010) How Has the Monetary Transmission Mechanism Evolved Over Time? eds. Ben Friedman and Mike Woodford, Handbook of Monetary Economics, Elsevier, forthcoming.

• Bordo, M. D. Duca, J. V. and Koch, C. (2016). Economic Policy Uncertainty and the Credit Channel: Aggregate and Bank Level U.S. Evidence over Several Decades. Journal of Financial Stability, 26:90–106

(40)

40 | P a g e

• Bussiére M., Chudik A. & Sestieri G. (2009) Modelling Global Trade Flows: Results from a gvar model. Working Paper Series no 1087. European Central Bank, Frankfurt am Main.

• Carrière-Swallow Y. and Céspedes L. F. (2013). The Impact of Uncertainty Shocks in Emerging Economies. Journal of International Economics, 90 (2):316–325.

• Cassola N and Morana C. (2004) Monetary policy and the stock market in the euro area, Journal of Policy Modeling, 26 (3) p387-399

• Cetorelli, N & Goldberg L. (2010). Global Banks and International Shock

Transmission. Evidence from The Crisis. National Bureau of Economic Research. Working Paper 15974 (1), p1-44.

• Christopher A. Sims, 1992. "Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy," Cowles Foundation Discussion Papers 1011, Cowles Foundation for Research in Economics, Yale University

• Chudik A. & Fratzscher M. (2011) Identifying the global transmission of the 2007– 2009 financial crisis in a GVAR model. European Economic Review 55, 325-339. • Chudik A. & Pesaran HM. (2014) Theory and Practice of GVAR Modelling. Federal

Reserve Bank of Dallas Globalization and Monetary Policy Institute: Working Paper No. 180. Retrieved from

https://www.dallasfed.org/~/media/documents/institute/wpapers/2014/0180.pdf on 29 May 2018.

• De Waal A. & van Eyden R. (2016) The Impact of Economic Shocks in the Rest of the World on South Africa: Evidence from a Global VAR. Emerging Markets Finance and Trade 52(3), 557-573.

• De Waal A., van Eyden R. & Gupta R. (2015) Do we need a global VAR model to forecast inflation and output in South Africa? Applied Economics 47(25), 2649-2670. • Dees S., di Mauro F., Pesaran HM. Smith VL. (2007) Exploring the International

Linkages of the Euro Area: A Global VAR Analysis. Journal of Applied Econometrics 22, 1-38.

• di Mauro F. & Pesaran H. (eds.) (2013) The GVAR Handbook: Structure and Applications of a Macro Model of the Global Economy for Policy Analysis. Oxford University Press, Oxford.

Monetary Policy and Uncertainty