The impact of a change of the monetary
base on income
Thesis BSc Economics and Finance
Abstract
The impact of the monetary base on income has gained importance in central banking as more central banks use the monetary base as an instrument to stimulate the economy in times of crisis. It is therefore important to investigate the relationship between the monetary base and income. From economic theory and previous research, it has been found that there is an overall positive impact of the monetary base on income. However several regression analysis on panel data of 214 countries conclude a negligible impact of the monetary base on GDP which is in contradiction with these findings. The decisive argument is formed by taking the regression analysis into consideration. This yields the conclusion that a change of the monetary base does not impacts GDP.
Student Mick Hendrikx -‐ 10003325
Field: Macroeconomics
Supervisor Mr. R.E.F. van Maurik MSc
Table of Contents
1. INTRODUCTION ... 3
2. LITERATURE REVIEW ... 4
2.1 THE MONETARY BASE AND ITS COMPONENTS ... 4
2.2 INFLUENCES ON THE MONETARY BASE ... 5
2.3 THE EFFECT OF THE MONETARY BASE ON INCOME ... 6
2.4 SOME FORMER AND RELEVANT RESEARCH ... 10
3. EMPIRICAL STUDY ... 14 3.1 DATA ... 14 3.2 METHOD ... 17 4. RESULTS ... 20 5. CONCLUSION ... 25 6. REFERENCES ... 27 7. APPENDIX ... 28
1. Introduction
The global financial crisis that emerged in august 2007 is considered to be the worst financial crisis since the Great Depression. This crisis was characterized by a severe financial turmoil combined with a sharp economic downturn (Mishkin et al, 2012). The main objectives of a central bank are to maintain price stability, to maintain financial stability and to support the state’s financing needs at crisis (Goodhart, 2011). To enhance economic recovery in times of crisis central banks have a variety of tools. This typically indicates the conduct of monetary policy through control of short-‐term nominal interest rates that have the potential to affect the economy to a variety of channels (Fawley & Neely, 2013).
Fawley & Neely (2013) state that inflation expectations do not react linear to changes in the nominal interest rates. Central banks can therefore also control real interest rates over the short and medium term that in turn affects asset prices. The real interest rates affect asset prices that positively impacts the willingness of banks to lend, firms to invest and individuals to consume or invest in housing (Fawley & Neely, 2013). This increase in willingness stimulates economic output.
When short rates approach the zero-‐lower bound (ZLB) the conventional policy turns out to be ineffective. Mishkin et. al. (2012) argue that a central bank can implement unconventional monetary policies such as quantitative easing (QE) to pursue its goals. When a central bank implements QE it purchases outright private and public securities from bank and non-‐bank sectors (Mishkin et al, 2012). In early 2008/ late 2009 interest rates reached the ZLB and the Bank of Japan (BOJ), the Bank of England (BOE), the European Central Bank (ECB) and the Federal Reserve (Fed) used this policy to stimulate economic growth (Fawley & Neely, 2013).
Open market operations, such as QE, have a certain and direct effect on the monetary base (Mishkin et al, 2012). With this effect central banks aim to affect economic output (Mankiw, 2012). It is therefore worthwhile to investigate whether the monetary base has a significant effect on income. In this thesis an answer will be given on the following research question; does a change of the monetary base impacts income?
The thesis proceeds as follows. Section 2 consists of a literature review. In this review a theoretical analysis is done on; the components of the monetary base, the influences on the monetary base, how it impacts income and finally some former and relevant research is discussed. Section 3 lists all variables used and includes the method used in the empirical research. The results of the performed regressions are covered in section 4. Section 5 contains a conclusion.
2. Literature review
In this section the monetary base and its components are first discussed. The influences on the monetary base are analysed secondly. In addition the effect of a change in the monetary base on income is examined building upon different macro-‐economic models and monetary transmission mechanisms. Finally some former and relevant research is discussed.
2.1 The monetary base and its components
The description of Mishkin et.al. (2012, pp. 301-‐307) is followed to explain the monetary base and its components. The monetary base (MB) consists of the sum of currency in circulation(C) and reserves (R). Both currency in circulation and reserves are on the liability side of the central bank’s balance sheet. Equation 2.1 shows the formula of the monetary base.
𝑀𝐵 = 𝐶 + 𝑅 (2.1)
The currency in circulation refers to non-‐bank currency and accounts for the currency held by the public. Banks also hold currency but in contrast to currency in circulation the latter counts for reserves.
The reserves component of the monetary base includes deposits from banks at the central bank plus their vault cash. Vault cash refers to currency that is physically held in vaults by banks. The deposits of banks held at the central bank are counted as a liability for the central bank but as an asset for the banks. At any time, banks can request payments on their deposits and obligate the central bank to fulfil this request by paying these banks with notes.
The monetary base can also be divided into non-‐borrowed monetary base (𝑀𝐵!) and borrowed reserves (BR) that are fully controlled and partially
controlled sequentially by the central bank. Equation 2.2 shows a modified equation of the monetary base.
𝑀𝐵 = 𝐵𝑅 + 𝑀𝐵! (2.2)
With this equation the influence that a central bank can exert on the monetary base is examined in the following section.
2.2 Influences on the monetary base
What influences the monetary base is discussed here by following the theory of Mishkin et. al. (2012). Mishkin et. al. specify for simplicity a central bank’s asset side of the balance sheet in two components: government securities and loans to banks. Changes in these assets change the liability side and thus the monetary base. A central bank can change these assets by open market operations and through its extension of loans to banks. The process of changing these assets in order to change the monetary base is explained in this section. Finally
quantitative easing (QE) is discussed in addition as this policy directly expands the monetary base.
The first component of the asset side on the balance sheet consists of government securities held by a central bank. A central bank can change the monetary base by buying or selling government bonds, called an open market operation (OMO). When a central bank performs an open market purchase, a variant of an OMO, it can purchase bonds from both commercial banks and from the non-‐bank public. Both are taken into consideration.
When a central bank performs an open market purchase from commercial banks, it buys bonds from banks in exchange for cheques. These banks in
question can decide whether to deposit the cheque in their accounts at the central bank or exchange the cheque for cash and hold it in their vaults. The effect on the reserves component of the monetary base is certain and the reserves increase. The currency in circulation is not altered in this case so the monetary base increases by the same amount as the reserves do.
A central bank can also perform an open market purchase from the non-‐ bank public, indicating persons or corporations. When persons or corporations receive cheques from the central bank after an open market purchase, they have two options. The first option is that they can deposit the cheque in a bank that in
turn deposits the cheque in their account with the central bank. The effect on reserves is in this case the same as an open market purchase from a commercial bank. This increase in reserves increases the monetary base by the same amount. The second option is that they can cash the cheque for currency at a bank. In this case the currency in circulation increases but the reserves are unchanged.
Nevertheless the monetary base increases with the same amount of the purchase.
A central bank thus has full control over the monetary base when
performing an OMO and can thus directly increase the monetary base through an open market purchase because the effect on the monetary base is always certain.
The second asset Mishkin et. al. (2012) describe consists of loans to banks. Central banks can use these loans to banks to provide the banking system additional reserves. A central bank charges on these borrowed reserves an interest rate, named the lending rate. A change in borrowed reserves changes the monetary base by the same amount. However the central bank has no full control on borrowed reserves as banks decision to borrow play a role too.
When a central bank is at the zero-‐lower bound (ZLB) it is unable to stimulate the economy by lowering the interest rate. Therefore a central bank may implement an unconventional monetary policy tool such as QE. This policy tool is a variant of an open market purchase that consists of an outright purchase of public and private securities from bank and non-‐bank sector. Because at the ZLB a central bank cannot lower the interest rate any further, it aims at
increasing the quantity of non-‐borrowed reserves. Fig. 8.1 presents this mechanism. By increasing the non-‐borrowed reserves a central bank can even with interest rates near the ZLB still expand the monetary base.
Summarized, a central bank can control the monetary base fully by open market operations even in the case at the ZLB by implementing QE. However a central bank can control the monetary base less tightly by providing loans to banks.
2.3 The effect of the monetary base on income
The effect of a monetary base expansion on income is discussed here. First it is explained how a change in the monetary base changes the money supply.
Thereafter it will be discussed how a change in the money supply changes income. Finally, some monetary transmission channels are discussed that capture the effect of the monetary base on aggregate demand.
With the direct effect of an open market purchase on the MB, a central bank may want to influence the money supply within an economy. When a central bank succeeds in expanding the money supply this affects income within an economy explained by both the Quantity Theory of Money and the Aggregate Demand (AD) – Aggregate Supply (AS) model.
The Traditional Money Multiplier model, drawn from Mishkin et. al., explains how a central bank can target the money supply (2012, p. 312) This model states that the money supply (𝑀!) is fully and precisely controlled by the central bank through changes in the monetary base (MB). Equation 2.3
formalizes this relationship.
𝑀! = 𝑚 ∗ 𝑀𝐵 (2.3)
In this research the same assumption as in Poole’s model on optimal instruments is used (Poole, 1970). This assumption entails a stable money multiplier. Given this assumption one can conclude that a central bank changes the money supply within an economy by directly influencing the monetary base.
The Quantity Theory of Money states that an increase in the money supply results in an expansion of nominal income or real income depended on the stickiness of prices (Gärtner, 2009, p. 15). This theory states that the money supply (M) times the velocity (V) of money in circulation equals nominal income (PY), assuming V is constant. Where P is the price level and Y denotes real income. If P does not change as a result of a change in money supply, i.e. prices are sticky, then changes in the money supply affect real income Equation 2.4 formalises this relationship.
𝑀 ∗ 𝑉 = 𝑃 ∗ 𝑌 (2.4)
Gärtner shows that besides the Quantity Theory of Money, the AD-‐AS model can explain too what happens with income when the money supply increases (2009, pp. 197-‐200). Gärtner states that central banks cannot influence the money supply when exchange rates are fixed. Therefore the AD-‐AS model is taken into consideration that only allows flexible exchange rates. Changes in the AD-‐AS model build upon changes within the Keynesian cross, Mundell-‐ Fleming model
and the labour market. The theory of Gärtner is further analysed here to explain the mechanism after an increase in the money supply.
When the money supply increases, the LM curve shifts to the right within the Mundell-‐Fleming model. Within this model the downward pressure on the interest rate drives up the exchange rate, indicating a depreciation of the home currency that shifts the IS curve to the right too. These shifts of both the IS and LM curve leads to an increase of equilibrium income to 𝑌!′ as can be seen in fig. 8.2 model (b).
Within the model of the Keynesian cross the depreciation of the home currency leads to an increase in exports. The aggregate expenditure (AE) curve sums up all planned expenditures and therefore shifts up. In the Keynesian cross in model (a) of fig. 8.2, equilibrium income rises with the same amount as it does within the Mundell-‐Fleming model.
Within the AD-‐AS model in model (c) of fig. 8.2, the upward shift of AE moves the AD curve to the right for constant prices. Demand for output then exceeds supply, as the latter has not changed so far. This excess demand drives up prices that influence both the supply as the demand side of the model. From the perspective of the supply side, the increase in prices drives down the real wages in the labour market raising employment and demand for labour shown in model (f) of fig. 8.2. The rise in employment and demand for labour result in an upward move on the AS curve, model (e) of fig. 8.2. From the demand
perspective this rise in prices lowers the real monetary supply and the exchange rate. In model (a) the lower exchange rate shifts the AE curve down in the
Keynesian cross due diminished exports. The IS and the LM curve are also altered by the lower exchange rate in model (b). Both curves move to the left in the IS-‐LM model. Finally, there is an upward move along the AD curve in model (c) where prices rise to make supply increase and demand falls until the excess demand is eliminated and equilibrium income is higher than the initial level.
This theory that builds upon the AD-‐AS model, the Mundell-‐Fleming model, the Keynesian cross and the labour market states that the new equilibrium income is higher than the initial equilibrium income.
There are several channels through which an increase in the monetary base affects aggregate demand. From the AD-‐AS model explanation, an increase
in the money supply increases aggregate demand that within this model increases equilibrium income. Kuttner & Mosser (2002) wrote a paper on the conference of Financial Innovation and Monetary Transmission in which they summarize the major monetary transmission channels that have been
distinguished in the literature. These transmission channels are displayed in fig. 8.3. The channels that capture the influence of the monetary base on aggregate demand are taken into consideration to examine the impact of the monetary base on income. These channels include; the interest rate channel, the exchange rate channel and the monetarist channel. The aggregate demand that is analysed is based on the Mundell-‐ Fleming model of a large open economy. Equation 2.5 presents a formula for aggregate demand that is used to explain the interest rate and the exchange rate channel.
𝐴𝐷 = 𝐶 + 𝐼 + 𝐺 + 𝑋 − 𝑀 2.5
According to Kuttner & Mosser the interest rate is the primary monetary transmission mechanism at work in conventional macro-‐economic models. They explain that given some degree of price stickiness a decrease in nominal interest rates lowers real interest rates. A decrease in the real interest rate decreases the cost of owning capital that in turn leads to an increase in consumption (C) and investments (I) and thus increases aggregate demand (AD) as can be seen from equation 2.5 (Kuttner & Mosser, 2002). This mechanism lies behind the
traditional IS curve of the Keynesian macroeconomic models.
In addition Kuttner & Mosser state that the exchange rate channel is an important channel in conventional open-‐economy macro-‐economic models. They explain that the transmission runs from interest rates to the exchange rate via the uncovered interest rate parity. This parity relates interest differential movements to expected exchange rate movements (Pilbeam, 2013). If the interest differential decreases, indicating a lower interest rate compared to foreign interest rates, the home currency will depreciate. This depreciation improves the country’s international trade position and increases the net exports. From equation 2.5 it can be seen that this rise in net exports increases aggregate demand.
Finally there is the monetarist channel. This channel focuses on the direct effects of changes in relative quantities of assets within an economy rather than
interest rates (Kuttner & Mosser, 2002). Kuttner & Mosser state that many relative asset prices are just as important as interest rates in the monetary policy transmission mechanism. Their paper considers various assets as imperfect substitutes in investors’ portfolios. Expansionary monetary policy by a central bank, such as an open market purchase that expands the monetary base, increases the relative quantity of outstanding assets within an economy. This increase in relative quantity decreases the relative price of these assets. If the relative price of assets decreases, this can have a real positive effect on aggregate demand.
Summarizing, the traditional money multiplier model explains under the assumption of a stable money multiplier how an increase in the monetary base increases the money supply. The increase in the money supply has a positive effect on income shown both by the quantity theory of money and the AD-‐AS model. The AD-‐AS model has shown that an increase in aggregate demand
increases income. Finally the interest rate, exchange rate and monetarist channel have shown how the monetary base positively influences aggregate demand and thus income.
2.4 Some former and relevant research
In this section the research applied so far on the influence of monetary base within an economy is discussed. In addition some research on economies in a crisis is discussed. Both the crisis in Japan as well as the Great Depression will pass the discourse.
Meltzer (2001) presents in his research empirical evidence for the
significant effect of real monetary base growth on consumption growth in the US. He uses quarterly data and controls for the short-‐term real interest rate. Meltzer states that open market operations affect both the nominal interest rate and the monetary base. If prices are sticky, this in turn affects both the real interest rate and the real monetary base. Meltzer argues that the short-‐term real interest rate does not fully capture the effect of monetary policy on the economy. In his research he finds empirical evidence that besides the real interest rate the changes in real monetary base affect aggregate demand too.
Nelson (2002) also examines the direct effect of the real monetary base on total output. He shows that real monetary base growth is a significant determinant of total output. In contrast to Meltzer’s research, he captures
besides the US also the UK economy. When the long-‐term nominal interest rate is included in the money demand function, Nelson (2002) shows that the standard IS-‐LM model can prove that real monetary base growth is a determinant of total output. When prices are sticky, changes in the long-‐term nominal interest rate changes the real long-‐term interest rate. The long-‐term real interest rate matters for aggregate demand. Thus once the long-‐term nominal rate is included, the effect of nominal money stock changes on aggregate demand increases.
Kimura et. al. (2002) investigates the effect of QE by the BOJ in 2001. This implemented monetary policy resulted in a monetary base growth of 20 percent per year. Since the Japanese economy was at that time at the ZLB the
effectiveness of the policy was questioned. In their research, a VAR with time-‐ varying coefficients is used to extract the effect of the monetary base on prices. In their research the change in monetary policy and the possible non-‐linear money demand at the ZLB is taken into consideration. They conclude from this VAR analysis that the monetary base previously had a positive effect on prices but that at the ZLB this effect is not present. To investigate why there is no positive effect at the ZLB, they estimate a money demand function in order to test whether a satiation level exists of the demand for monetary base at the ZLB. They conclude from this estimate that there is a satiation level and thus an increase in the monetary base can stimulate the economy at the ZLB. However the results of both the VAR analysis and the estimation of the money demand function are controversial. Kimura et. al. explain these controversial results in a way, namely that the effect of an increase of the monetary base on economic output is highly uncertain and limited.
Girardin & Moussa (2011) examine the effectiveness of monetary policy on the Japanese economy during the “lost” decade that was characterized by symptoms of stagnation and deflation. By an empirical framework they provide analysis on the effect of QE on the Japanese economic activity and price level. When a central bank applies QE the monetary base expands. They show with a combination of a Markov-‐switching VAR methodology and factor analysis that
this policy prevents the economy from a further recession. Moreover they find evidence that this policy stimulates both output and prices through the interest rate factor. In their analysis this same property holds when fiscal policy is taken into account. However they conclude from this first experience of QE by the Bank of Japan that this policy only reduces the symptoms of an economy in recession. In order for the Japanese economy to recover, dramatic restructuring in the financial framework is additionally required.
Schenkelberg & Watzka (2013) also apply research on the QE experience of Japan at the ZLB. They examine the real effect of QE when the short-‐term interest rate is constrained by the ZLB using a Structural VAR analysis. In their research monthly data is used from the Japanese economy since 1995. Moreover, they use restrictions from Eggertsson’s (2010) New Keynesian DSGE model at the ZLB. The QE shock increases reserves, and thus the monetary base, by 7 percent. They find that this shock results in a significant decrease in long-‐term interest rates and that after two years industrial production increases by 0.4 percent. In contrast prices are only temporarily affected by this shock that results in a mixed evidence of the success fullness of this QE policy in Japan. Under the assumption that the shock is a small one, they conclude in their paper that real economic activity increases but that it does not increase prices in such a way that Japan could exit its deflationary period.
McCallum (1990) raises the question whether a monetary base rule could have prevented the Great Depression. The monetary base rule specifies the size of the monetary base and according to this rule the nominal GNP of the US would have been growing smoothly at a rate of 3 percent. In his research the
proposition that the GNP growth rate would have kept the real GNP en employment from their deep declines is taken for granted. Counterfactual historic simulations for 1923-‐1941 are used and implemented by the policy rule and a small model of nominal GNP determination. With his research he shows that nominal GNP would have been kept at a steady 3 percent over the period of time if the rule had been in effect.
Thornton (1993) investigates the relationships between money, output and stock prices within the economy of the UK. He uses Granger’s causality as method to investigate these relationships. One of the findings that relates to the
topic of this thesis is that he finds evidence that the monetary base leads real GDP.
Feldstein & Stock (1994) investigate the ability of monetary aggregates to target nominal GDP. A central bank might be able to reduce inflation and the volatility of real GDP if this feature holds. They examine the strength and the stability of the predictive content of the monetary base on nominal GDP. In their research quarterly time series data is used on money, output, prices, and interest rates from 1959:1 -‐ 1992:2 within the US. From fig. 8.4a-‐c it can be concluded that there is no clear cyclical link between the monetary base and nominal GDP. They apply regression analysis with different specifications and find no strong predictive content; the 𝑅!′𝑠 range only from 0.09-‐0.20. Besides, after including the interest rate in the regression, the monetary base fails to be statistically significant at the 5 percent level. Moreover, the stability of the predictive content is examined by tests for parameter constancy. Almost all regressions that are performed reject a stable link between the monetary base and nominal GDP at the 1 percent level. From their paper it can be concluded that the monetary base does not have a significant strong nor stable link with nominal GDP.
Summarizing, there is some evidence in favour and some against the issue whether or not the monetary base impacts income. Real monetary base growth has a positive effect on consumption (Meltzer, 2001) and total output (Nelson, 2002). The QE policy from the BOJ is also taken into consideration as the monetary base expands when this policy is applied. According to Kimura et. al. (2002) the monetary base had a positive effect on prices before Japan entered the stage of QE. However at the ZLB this effect is not present and they conclude that the effect of a monetary base expansion on economic output is highly uncertain and limited. In contrast Girardin & Moussa (2011) state that besides output the policy stimulates prices at the ZLB and explain this by the interest rate factor. Moreover, because real economic activity increases but prices do not Japan is unable to exit its deflationary period (Schenkelberg & Watzka, 2013). McCallum (1990) investigates the Great Depression and concludes that nominal GDP would have been kept at 3 percent if there had been a monetary base rule at work. Thornton (1993) finds that the monetary base leads real GDP. Feldstein &
Stock (1994) ends this section by proving that the monetary base does not have a significant strong nor stable link with nominal GDP.
3. Empirical study
This section starts with the description of the dataset that is used with its corresponding variables. Thereafter the method of the econometric research is explained together with its corresponding models.
3.1 Data
In order to empirically investigate the relationship between the monetary base and income the data of 214 countries are taken into consideration. The
dependent variable that is used is the difference natural logarithm of GDP (dlnGDP) and the independent variable is the natural logarithm of the monetary base (lnMB). In addition the following control variables are used; a lag of GDP (lagGDP), a lag of MB (lagMB), human capital (HC), total population (Pop), net exports (NX), savings (S) inflation (Inf) exchange rate (ER) and employment (Empl). In this research a three-‐year lag of the monetary base (lllagMB) is used to test for simultaneous causality bias. Table 8.5 presents the descriptive
statistics of the variables used. All currency variables are expressed in US dollars. The control variables are used to make sure that there is no omitted variable bias in the performed regression. First the dependent variable and the control
variables are taken from the World Databank. This data is annually and ranges from the period of 1960 up to 2013. Second the independent variable is taken from Undata. This data is also annually and typically ranges from the period 1948 up to 2009. In order to match the data for all these countries, years and variables only a few complete observation sets are left. Because the complete dataset used ranges from 1960 up to 2009 the panel data that is used in considered as balanced. The number of observations is dependent on which regression is used and ranges between 400 and 500.
The Gross Domestic Product (GDP) is used as an indicator of income. The GDP includes the value added of all goods and services that are produced within a country (Pilbeam, 2013). If the net factor income abroad and the net unilateral transfers are neglected, GDP is a good indicator for income according to Pilbeam
(2013). To measure the percentage change of GDP, the natural logarithm is taken into account. As the natural logarithm of GDP is not a stationary variable, the difference of the natural logarithms is taken into account. This variable is indicated as dlnGDP.
Data on the monetary base are taken from Undata. The variables taken from this online database are; base money, base money M0, M0, monetary base and money base. These terms are used interchangeably in the literature and every country uses its own definition of what is considered to be the monetary base. Therefore these variables are all treated as the monetary base. The natural logarithm is used to capture the percentage change of the monetary base. Two control variables that are used in this research are lags of the
monetary base (lagMB) and GDP (lagGDP). These lags are values of the monetary base and GDP with a one-‐year delay. The reason these lags are taken into
consideration is that both affect the dependent variable dlnGDP. If MB is higher in the previous year within a country it is more likely that GDP increases because there are more resources for banks available to extend loans to investors and to stimulate the economy. The GDP from previous year also impacts the current GDP as the current GDP moves up or down from the previous GDP.
Human Capital (HC) is used as a control variable as it is able to filter the effect on GDP. In this research human capital is measured as secondary
education that includes the total number of pupils enrolled at secondary level in public and private schools. The higher the enrolments number the more likely the overall education level within a country. This higher education level results in a higher income per person and thus positively impacts GDP.
Total population is taken into account and counts all residents regardless of legal status or citizenship for the country in question. These numbers are mid-‐ year estimates and come from the World Databank. The more people live in a country the more value they can add to goods and services and thus the higher the GDP. A country with a very small population has a limit to its production of goods and services and thus its GDP. In this research there is controlled for the impact of the population on GDP.
The net exports include a country’s exports of goods and services in current US dollars minus its imports. If a country’s exports exceed its imports it
contributes to the GDP. In contrast if imports exceed exports GDP decreases. These factors that change GDP are accounted for by including them in the regression. Equation 2.5 shows this algebraically.
Savings include a country’s net national savings in current US dollars. The net national savings consists of gross national savings minus the value of
consumption on fixed capital. The higher the national savings of a country the more money is saved by people on average. If we assume that the consumption pattern by people and the investment pattern by corporations are constant a higher level of savings indicates a higher level of GDP. However for a given income if people save more, their consumption decreases and thus GDP decreases. A higher national savings level however also indicates given a
resources constraint for corporations that the number of investments is reduced. This reduction in investments affects GDP negatively. Summarized, it is obvious that savings can filter the effect on GDP, therefore savings are added as a control variable to the regression.
Inflation is also used as a control variable and is measured by the consumer price index. This index measures the growth rate of the prices for a consumer to obtain is specific basket of goods and services. A higher level of inflation increases the prices of goods and services and thus the willingness of consumers to spend. An increase in spending increases GDP. However if the inflation level decreases it can turn into deflation. When there is an extended period of deflation within an economy, goods and services become cheaper and consumers delay their consumption. This reduction in spending decreases GDP. Inflation is therefore an important variable to control for because it filters the effect on GDP.
The exchange rate (ER) is used as an additional control variable in order to perform Robustness check I, a test for robustness of the model. This check will be discussed in section 3.2. The exchange rate is defined as the price of a US dollar expressed in local currency units and is determined by national
authorities. This annual rate is computed by taking the monthly averages. When a country has a higher exchange rate its terms of trade improve as exports
become relatively cheaper for the foreign country and imports become relatively more expensive for the home country. Exports increase and imports decrease
that positively impacts GDP. The opposite holds when a country has a lower exchange rate, there is a negative effect on GDP. Because of these impacts on GDP it is important to include it as a control variable.
Employment (Empl) is used as an additional control variable to ensure robustness of the model. This variable is relevant because a higher employment rate results in a higher production in goods and services and thus contributes to GDP. Moreover, if more people are employed there is more income within a country that stimulates consumption and investments and thus adds to GDP. The opposite case holds too, when the employment rate is low there is less produced within an economy and less money to spend on goods and services. A lag of three years on the monetary base (lllagMB) is used as an instrument variable because it is likely to fulfil both conditions for a valid instrument. First because of its relevance; the three-‐year lag of the monetary base is likely to be correlated with lnMB, the regressor of interest. Second because of its exogeneity; the instrument is likely to be uncorrelated with the error term. The value of the monetary base three years ago does not seem to affect current GDP. If this second assumption holds one can say that the
instrument does not explain the variations in the value of the dependent variable dlnGDP.
3.2 Method
From the literature review there has been already some research done on the impact of the monetary base on income. Most of the research applied so far contains VAR analysis or a Granger causality test. To investigate the impact of the monetary base on income several econometrical tests will be done on a multiple regression model using significance levels of 1 and 5 percent. First the model will be tested with an OLS regression analysis. Second a Robustness check will be done by replacing control variables. Thereafter, a regression that excludes country fixed and time fixed effects is performed. Finally the model will be tested on simultaneous causality by performing an Instrument Variable (IV) regression.
In the multiple regression model the dependent variable is dlnGDP and the independent variable is lnMB. In addition the control variables; lagGDP,
lagMB, HC, Pop, NX, S and Inf are used. Equation 3.1 shows this regression model. In the following models 𝑖 denotes each state (𝑖 = 1, … , 214) and 𝑡 denotes the year (𝑡 = 1960, … , 2009).
𝑑𝑙𝑛𝐺𝐷𝑃!,! = 𝛽!+ 𝛽!∗ 𝑙𝑛𝑀𝐵!,! + 𝛽!∗ 𝐺𝐷𝑃!,!!!+ 𝛽!∗ 𝑀𝐵!,!!!+ 𝛽! ∗
𝐻𝐶!,!+ 𝛽!∗ 𝑃𝑜𝑝!,!+ 𝛽!∗ 𝑁𝑋!,! + 𝛽!∗ 𝑆!,! + 𝛽!∗ 𝐼𝑛𝑓!,!+ 𝑢!,! (3.1) An OLS regression analysis will be done on equation 3.1. Control variables are
used to eliminate the possibility of omitted variable bias. However by including these variables the variance of the estimates of the coefficient of interest can increase. In the OLS regression robustness is assumed. This assumption is made because the variance of the error term is not allowed to be homoscedastic. To test whether the OLS regression is robust a Robustness check will be done. How the core regression estimates will behave when variables are replaced will result from this check. First the control variable inflation will be replaced by the
exchange rate; Robustness check I. Equation 3.2 shows this regression. 𝑑𝑙𝑛𝐺𝐷𝑃!,! = 𝛽!+ 𝛽!∗ 𝑙𝑛𝑀𝐵!,! + 𝛽!∗ 𝐺𝐷𝑃!,!!!+ 𝛽!∗ 𝑀𝐵!,!!!+ 𝛽! ∗
𝐻𝐶!,!+ 𝛽!∗ 𝑃𝑜𝑝!,!+ 𝛽!∗ 𝑁𝑋!,! + 𝛽!∗ 𝑆!,! + 𝛽!∗ 𝐸𝑅!,!+ 𝑢!,! (3.2) Second the control variable inflation will be replaced by employment;
Robustness check II. Equation 3.3 shows the regression used.
𝑑𝑙𝑛𝐺𝐷𝑃!,! = 𝛽!+ 𝛽!∗ 𝑙𝑛𝑀𝐵!,! + 𝛽!∗ 𝐺𝐷𝑃!,!!!+ 𝛽!∗ 𝑀𝐵!,!!!+ 𝛽! ∗
𝐻𝐶!,!+ 𝛽!∗ 𝑃𝑜𝑝!,!+ 𝛽!∗ 𝑁𝑋!,! + 𝛽!∗ 𝑆!,! + 𝛽!∗ 𝐸𝑚𝑝𝑙!,!+ 𝑢!,! (3.3) One should hold into account that OLS estimates are not the most reliable.
OLS coefficients are known to be inefficient when errors are correlated. In this research errors are likely to be correlated. This is in the first place because time series data are used that often have errors that are serially correlated. In the second place because the dataset has errors that can be correlated within the country. Therefore one might consider the method of OLS regression not as the most appropriate.
Due to the shortcomings of an OLS regression, fixed effects are taken into consideration. First country fixed effects are excluded from the model. In a Country Fixed Effect regression there is controlled for omitted variables that vary across countries but do not change over time. In this regression the
coefficients of the regresssors are estimated by holding constant the unobserved country characteristics 𝐶.
Let 𝛼! = 𝛽!+ 𝛽!∗ 𝐶! then the regression model becomes the one indicated by equation 3.4.
𝑑𝑙𝑛𝐺𝐷𝑃!,! = 𝛼! + 𝛽! ∗ 𝑙𝑛𝑀𝐵!,!+ 𝛽!∗ 𝐺𝐷𝑃!,!!!+ 𝛽!∗ 𝑀𝐵!,!!!+ 𝛽!∗ 𝐻𝐶!,!+ 𝛽! ∗ 𝑃𝑜𝑝!,! + 𝛽!∗ 𝑁𝑋!,!+ 𝛽!∗ 𝑆!,!+ 𝛽!∗ 𝐼𝑛𝑓!,!+ 𝑢!,! (3.4) Second the time fixed effects are hold into account. In a Time Fixed Effect regression there is controlled for omitted variables that are constant across countries but evolve over time. In this regression the coefficients of the regresssors are estimated by holding constant the unobserved time
characteristics 𝑆. Let 𝛾! = 𝛽!+ 𝛽!∗ 𝑆! then the regression model becomes the one indicated by equation 3.5.
𝑑𝑙𝑛𝐺𝐷𝑃!,! = 𝛾!+ 𝛽!∗ 𝑙𝑛𝑀𝐵!,!+ 𝛽!∗ 𝐺𝐷𝑃!,!!!+ 𝛽! ∗ 𝑀𝐵!,!!!+ 𝛽!∗ 𝐻𝐶!,!+ 𝛽! ∗ 𝑃𝑜𝑝!,!+ 𝛽!∗ 𝑁𝑋!,!+ 𝛽! ∗ 𝑆!,!+ 𝛽! ∗ 𝐼𝑛𝑓!,! + 𝑢!,! (3.5) Finally the multiple regression model will be tested on unobserved omitted variables that are correlated with lnMB, errors in variables and
simultaneous causality bias that makes the error term correlated with lnMB. In this model it is assumed that causality runs from the independent regressor (lnMB) to the dependent regressor (dlnGDP). However the causality can also run from the dependent to the independent regressor. In this case there is
simultaneous causality in which omitted variable bias cannot be excluded by adding variables to the model. If this treat occurs, the estimates of the
coefficients are biased and inconsistent. By performing an IV regression an instrument variable is added to the model that can mitigate simultaneous causality. The instrument is a variable that needs to fulfill two conditions. First the variable should be relevant. If an instrument 𝑍!,! is relevant, then variation in the instrument is related to variation in the regressor 𝑋!,!. Equation 3.6 presents this property.
Corr(𝑍!,!, 𝑋!,!) ≠ 0 (3.6)
The second property of a valid instrument is exogeneity. If an instrument fulfils this condition then part of the variation in 𝑋!,!,captured by the instrumental variable, is exogenous. Equation 3.7 presents this property.
In order to test the exogeneity of the instrument a variable is generated that represents the error term 𝑢!,!. This error term is measured by taking the difference between the actual observed values of dlnGDP and the predicted values of dlnGDP by the IV regression model.
With IV regression the coefficient 𝛽!can be estimated using an IV estimator called two stage least squares (TSLS). Equation 3.8 shows the first-‐ stage regression model.
𝑙𝑛𝑀𝐵!,! = 𝜋!+ 𝜋!∗ 𝑀𝐵!,!!!+ 𝜋!∗ 𝐺𝐷𝑃!,!!!+ 𝜋!∗ 𝑀𝐵!,!!!+ 𝜋!∗ 𝐻𝐶!,! + 𝜋!
∗ 𝑃𝑜𝑝!,!+ 𝜋! ∗ 𝑁𝑋!,!+ 𝜋!∗ 𝑆!,!+ 𝜋! ∗ 𝐼𝑛𝑓!,! + 𝑣!,! (3.8) In the second stage of TSLS the coefficients from equation 3.1 are estimated by OLS, except that 𝑙𝑛𝑀𝐵 is replaced by its predicted value 𝑙𝑛𝑀𝐵!,! drawn from the first-‐stage regression model. Equation 3.9 shows the second-‐stage regression model.
𝑑𝑙𝑛𝐺𝐷𝑃!,! = 𝛽!+ 𝛽!∗ 𝑙𝑛𝑀𝐵!,!+ 𝛽!∗ 𝐺𝐷𝑃!,!!!+ 𝛽!∗ 𝑀𝐵!,!!!+ 𝛽!∗ 𝐻𝐶!,!+ 𝛽! ∗ 𝑃𝑜𝑝!,!+ 𝛽!∗ 𝑁𝑋!,!+ 𝛽!∗ 𝑆!,!+ 𝛽!∗ 𝐼𝑛𝑓!,! + 𝑢!,! (3.9) The resulting estimators are the TSLS estimators. Stata 12, the software used in this econometric research, performs these two stages automatically within TSLS estimation commands. The OLS estimate of 𝛽! from equation 3.9 is the
coefficient that is excluded from simultaneous causality bias.
Summarized, there will be an OLS regression performed where the
robustness of the model is tested by a Robustness check. Since the OLS method is not the most appropriate, main emphasize is put on the results from the Country Fixed Effect, Time Fixed Effect and IV regression. The next section illustrates the results found.
4. Results
In this section the results will be discussed on the performed regressions. First the OLS regression together with two Robustness checks are analysed.
Thereafter regressions that hold time and country fixed effects into account are discussed together with IV regression. This research emphasizes on the latter comparison of results, as the OLS estimates are not found to be the most appropriate for this dataset.
In table 4.1 the results from the regression performed on equation 3.1, 3.2 & 3.3 are shown. The 𝑅! is the fraction of the sample variance of lnGDP explained or predicted by the regressors. The 𝑅! is the measure of fit with a maximum value of 1. As can be seen from table 4.1 the 𝑅! is equal to 0.0272 in the original model which means that 2.72 percent of the variance in dlnGDP is explained by the regressors. In addition the coefficient of lnMB is 0.0058. Given that GDP is defined in difference natural logarithms and the monetary in natural logarithms this means that given a 1 percent increase in the monetary base the marginal
percentage change of GDP increases by 0.0058 percent. This value is incredibly small, the effect of the monetary base on GDP can therefore be neglected in this
