Bachelor Thesis Economics and Business
Faculty of Economics and Business
Academic year: 2017 – 2018
The influence of the Great Recession on the U.S.
currency ratio
Specialisation: Economics and Finance
Student Name: Nastasiia Sokil
Student Number: 11065087
Statement of Originality
This document is written by Student Nastasiia Sokil who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This paper compares the behaviour of the U.S. currency ratio prior and after the Great Depression in the light of four factors: the real GDP, the nominal interest rate, income tax evasion, and the financial innovations. The time series techniques are employed for the data analysis. The data pre-testing shows the existence of the cointegration. The error-vector correction mechanism is used to estimate the parameters of the cointegration equation. All variables except income tax evasion have significant effects in both periods. Income tax evasion is only significant after the crisis. Based on the comparison of the estimates, it is concluded that the effects of the currency ratio determinants have significantly changed after the crisis. The effects of the real GDP, the nominal interest, and the financial innovations have decreased. Those changes can be explained by the effects of the recession on the economy and the Fed’s policies to fight them.
Table of Contents
1. Introduction ... 4
2. Literature review ... 6
2.1. Money multiplier framework ... 7
2.2. Currency ratio ... 8
2.3. Determinants of the currency ratio ... 8
2.4. Summary of the literature review ... 11
3. Methodology ... 13 3.1. Empirical models ... 13 3.2. Hypotheses ... 14 3.3 Data ... 15 3.3.1 Sources. ... 15 3.3.2 Transformations. ... 16 3.4. Pre-testing ... 17 3.4.1. Stationarity. ... 18
3.4.2. Optimal amount of lags. ... 19
3.4.3. Cointegration. ... 20
3.5. Parameters of the cointegration equation ... 22
4. Results and interpretations ... 25
5. Limitations and discussion ... 28
6. Conclusion ... 29
References ... 32
Appendix A ... 35
Appendix B ... 37
1. Introduction
In 2008 the United States (U.S.) economy faced its most severe crisis since the Great Depression (Havemann, 2009). Bernanke (2002), the Chairman of the Federal Reserve (Fed) from 2006 to 2014, admitted that the Fed made a mistake during the Great Depression by “antispeculative” policy tightening in 1928-29 that has led to the depression. He stated that the Fed can avoid crises by providing the economy with a stable monetary background. Though this been said, the monetary policy was too expansionary in 2007 and did not aim to stabilise the economic boom (Havemann, 2009). Anna Schwartz in her interview pointed out that the Fed is itself the primary cause of the credit bubble in 2007 (Carney, 2008). Though the Fed failed to avoid the crisis, it channelled all its resources to combat the recession (Carpenter & Demiralp, 2012).
The Fed aimed to push the economy on a recovery path by injecting liquidity into the banking sector (Lothian, 2009). These actions resulted in a substantial increase in the reserves balance, going from around $15 billion in July 2007 to over $788 billion in December 2008 (Carpenter & Demiralp, 2012). The monetary base doubled over that period while the M2 money aggregate grew only by 8.5% (Carpenter & Demiralp, 2012). The biggest monthly increase of 23.83% in the monetary base was in December 2018 which resulted in only 2.7% increase of the M2 money aggregate as is shown in Figure 1. The money multiplier effect was no longer observed (Lothian, 2009). Consequently, this evidence renewed interest in researching it (Lothian, 2009).
Figure 1. The monthly changes in the M2 money aggregate (M2) and monetary base (MB). M2(change) and MB(change) are calculated as the first log differences.
Carpenter and Demiralp (2012) named two causes of the money multiplier drop: the increase in the reserves ratio and the decrease in the currency ratio. The Fed has control over the reserves but cannot directly influence the currency ratio (Mishkin, Matthews, & Giuliodori, 2013). Hence, the increase in the reserves ratio can be reversed by the Fed, while the decrease in the currency ratio requires understanding the economic factors influencing it.
This paper is dedicated to examining the currency ratio before and after the Great Recession. To specify, the research aims to construct the currency ratio as a function of its determinants and analyse the effect of the Great Recession on each of them. Consequently, the research question arises: How the effects of the currency ratio determinants have changed after the Great Recession? What are possible explanations for those changes?
The analysis expects to find that the effects of the determinants have changed which will be tested against the null hypothesis of no changes in the effects. To perform this test, firstly, the empirical models are constructed based on the literature review. Subsequently, the constructed models will be empirically analysed using the time series techniques. The hypotheses testing will be based on the empirical estimations. The author's interpretations of the results and their possible explanations will answer the research questions.
The structure of the paper is as follows. Section 2. Literature review gives the overview of the researches performed in the same field, discusses the currency ratio and its important variables of influence. Section 3. Methodology follows. In this section, the empirical models are contracted and the hypotheses are stated. Moreover, the data gathering and transformation processes are described. The pre-testing procedures and the parameters estimations for the models close this section. Section 4. Results and interpretations presents the hypotheses testing and explains the main findings. Section 5. Limitations and discussion describes the pitfalls of this research and makes suggestions for the further research. Section 6. Conclusion summaries the analysis and restates the main findings.
2. Literature review
In the preface to his monography, Cagan (1965) pointed out the debate between the classical group of economists, who consider money as an independent source of an economic disturbance, and the critics, who view money as a factor with a little independent influence that adapts to the business conditions. The first attempt to resolve the debate by explaining the role of the money in the economy was made by Friedman and Schwartz (1963). While Friedman and Schwartz’s (1963) work is primarily a qualitative analysis, Cagan’s (1965) work aims to measure the factors responsible for changes in the money stock. By focusing on empiricists’ point of view, Cagan (1965) changed the way money supply is to be examined.
2.1. Money multiplier framework
Cagan (1965) performed his analysis based on the widely used money multiplier framework. This model is presented by Equation 1, where the money supply 𝑀 is the product of the money multiplier 𝑚 and the monetary base 𝑀𝐵 (Brunner & Meltzer, 1968).
𝑀 = 𝑚 ∗ 𝑀𝐵. (1)
The framework defines the money supply as being jointly dependent on the actions of the monetary authority, the general public, and commercial banks (Friedman & Schwartz, 1963). The versions of the money multiplier 𝑚 differ among authors. Mishkin et al. (2013) presented it as Equation 2. The money multiplier is a function of the currency ratio set by depositors 𝑐, the excess reserves 𝑒 set by the commercial banks and the required reserves ratio 𝑟 set by the central bank (Mishkin et al., 2013).
𝑚 = 1 + 𝑐
𝑟 + 𝑒 + 𝑐 (2)
In the study of the U.S. business cycles, Cagan (1965) concluded that high fluctuations in the money multiplier are primarily due to the changes in the currency ratio. His work changed the view on the importance of the money multiplier components, showing that the currency ratio is the primary cause of changes in the money supply.
In the article on the determinants of the currency ratio, Cagan (1958) explained that the currency ratio differs notably from most of the other monetary variables. He stated that any simple trend cannot explain its fluctuations as the ratio is the net result of movement in the currency and deposit functions. Therefore, it is essential to understand influential factors on the deposits and currency. The following section assesses and compares the views of different
authors on the calculation methods of the currency ratio and importance of variables that could have caused a substantial variation in the ratio.
2.2. Currency ratio
There exists a divergence in the methods of the currency ratio calculations among the researchers. The difference arises from the country and time specifications. Nonetheless, the most used measure is the ratio of the currency over the demand deposits (Boughton & Wicker, 1979; Dadkhah & Mookerjee, 1988; Hess, 1971; Hasan, 2001; Khaskheli, Ahmed, & Hyder, 2013; Tchaidze & Tvalodze, 2011; Zaki, 1992). Beenstock (1989) for the research in the United Kingdom (U.K.) used the sight deposits as the currency ratio denominator. Other authors use a sum of several types of deposits for the currency ratio calculations in their analyses. For instance, Cagan (1958) used the total of the demand and time deposits. Khatkhate et al. (1974) used an even broader definition of the deposits, i.e., the total private deposits held at the banks. 2.3. Determinants of the currency ratio
The individuals’ willingness to hold a certain level of currency or deposits depends on the cost and advantages of holding either of the assets (Cagan, 1958). The individuals divide their income into the currency holding and money depositing (Cagan, 1958). Therefore, Cagan (1958) identified the real income as a variable of significant influence. Boughton and Wicker (1979) proved that the demand for deposits has higher income elasticity than the demand for currency. They stated that higher income elasticity of deposits results in a negative effect of the real income on the ratio. The real income is a variable used by Beenstock (1989) for the study of the money multiplier determinants in the U.K.; for the analysis of the currency ratio behaviour in Tanzania (Ndanshau, 2004), Pakistan (Khaskheli et al., 2013), India (Dadkhah & Mookerjee, 1988), Georgia (Tchaidze & Tvalodze, 2011), and mainland China (Hasan, 2001).
The interest rate was one of the core determinants of the currency ratio for studies in the U. K. (Beenstock, 1989), Venezuela (Khaskheli et al., 2013), Georgia (Tchaidze &
Tvalodze, 2011), Pakistan (Khatkhate et al., 1974), and mainland China (Hasan, 2001). All researchers that used the interest rate as an independent variable found its significant effect on the currency ratio. Boughton and Wicker (1979) described the interest rate as the relative cost of holding currency because currency yields no interest. Higher interest rate diminishes the attractiveness of currency holding and prompts individuals to deposit money instead (Hasan, 2001). The not significant influence of the interest rate in Ndanshau’s (2004) and Zaki’s (1992) papers lies in the country-specific factors. Zaki (1992) and Ndanshau (2004) stated that during the sample period of the researches, no interest was paid on the demand deposits. They stated that this signals that the interest rate is an inadequate measure of the opportunity cost of holding. In addition, Zaki (1992) explained that the interest rate is a poor estimator of the holding cost if the developed financial market is absent, or the authorities fix the interest rate. Hence, Ndanshau (2004) suggested using inflation as a measure of the opportunity cost.
From a theoretical standpoint, inflation could also be used as a stand-alone factor of influence on the currency ratio (Dadkhah, & Mookerjee, 1988; Khaskheli et al., 2013; Tchaidze & Tvalodze, 2011; Zaki, 1992). The inflationary upsurge diminishes the benefits of holding deposits and motivates people to invest money in consumer-durable goods or physical assets (Hasan, 2001). However, if the supply of such assets is scarce, consumers tend to hold cash longer which increases the currency ratio (Hasan, 2001). Khaskheli et al. (2013) explained other effect of the rising inflation: an inflationary pressure forces people to hold more cash for everyday transactions, which they finance from deposit withdrawals. Subsequently, the deposit withdrawals increase the currency ratio (Khaskheli et al., 2013). Overall, inflation has a significant and positive effect on the currency ratio (Dadkhah & Mookerjee, 1988; Hasan, 2001; Khaskheli et al., 2013; Zaki, 1992).
Income tax evasion as a determinant of the currency ratio was first suggested by Cagan (1958). He argued that a high tax on income motivates people to avoid paying it by using
currency to conceal taxable transactions. Income tax evasion was measured by Cagan (1958) as the ratio of the personal income collected to total taxable income. The estimate of income tax evasion is positive and significant (Cagan, 1958). Matthews (1982) adopted “black economy” as a variable of comparable influence. He suggested that cash transactions in the black economy are prevailing to avoid bank records and detection by tax authorities. The “black economy” is measured by the ratio of the government total tax revenues to the nominal GDP (Tchaidze & Tvalodze, 2011). Beenstock (1989) failed to find a significant influence of the “black economy” on the currency ratio in the U. K. However, Tchaidze and Tvalodze (2011) found a significant and positive effect of the “black economy” on the currency ratio in Georgia.
According to the hypothesis suggested by Cagan (1965), the currency ratio is likely to be influenced by the financial innovations: as richer varieties of liquid financial assets become available, the currency ratio falls. This hypothesis was rejected by Beenstock (1989), as he found the contradictory evidence. The rapid speed of the financial innovations in the U. K. led to increase in the currency ratio (Beenstock, 1989). However, Ndanshau (2004) supported Cagan’s idea by stating that the liberalization of the financial sector reflected as an increase in the financial innovations and number of commercial banks led to decrease in the currency ratio in Tanzania. Tchaidze and Tvalodze (2011) estimated a significant and negative influence of the financial innovations on the currency ratio in Georgia.
The determinants of the currency ratio also depend on the factors that might have been important during the research period or the country in question (Boughton & Wicker, 1979). For example, the Great Depression caused banks’ failure that reduced availability of banking services which resulted in the increased usage of currency (Boughton & Wicker, 1979). To capture this, Boughton and Wicker (1979) incorporated the variable measuring banks’ failure. Ndanshau (2004) and Khaskheli et al. (2013) included some country-specific variables which are omitted from a discussion as they are only adequate for the developing countries.
2.4. Summary of the literature review
The focal point of all studies discussed is to explain the behaviour of the currency ratio by creating the model that fits the country and time specifications. Though there are a lot of the researches discussed, this research will follow the methodology applied by Tchaidze and Tvalodze (2011). This choice can be explained by the fact that their research is based on a recent data as the paper was published in 2001. That implies that models are constructed to represent the reality closely and the variables used are determined to be a reasonable approximation of the factors influencing the currency ratio nowadays.
Boughton and Wicker (1979) highlighted the importance of accounting for the country and time specifications. Therefore, all variables for the models used in this research will be chosen carefully to closely reflect the currency ratio determinants in the U.S. The real income, the nominal interest rate, income tax evasion and the financial innovations are variables considered to be the main determinants of the currency ratio over the period under the research. The relevance and expectation about the effects of those variables are disused bellow.
This research uses two currency ratios for the analysis due to the differences in its calculations among the studies discussed. The first ratio analysed is the ratio of the currency over the demand deposit. The second one is the ratio of the currency over the total deposits.
The amount of the real income received by the individuals determines the proportion of currency and deposits they hold (Cagan, 1958). The demand for deposits has a higher income elasticity (Boughton & Wicker, 1979). Therefore, it is expected that the real income will have a negative effect on the currency ratio (Boughton & Wicker, 1979). The U.S. real GDP aggregates the real income of all individuals in the country (Mankiw, 2000). Therefore, it is used as a proxy for the real income.
The U.S. financial market can be characterized as a competitive, well-developed, and independent from the direct monetary authority intervention (Jansen et al.,1998). This evidence
suggests that the nominal interest rate is determined primarily by the market (Jansen et al.,1998). Hence, it can be a good approximation of the opportunity cost of holding currency. The effect of the nominal interest rate is expected to be negative because the interest rate stimulates people to deposit which decreases the currency ratio.
Despite the contradiction in the literature about the significance of income tax evasion, there are reasons to believe that it had a significant effect during the sample period of this study. The crisis in 2008 resulted in major unemployment (Junankar, 2011) that might have stimulated shadow employment and income payments in cash to avoid tax payments. Therefore, it is expected that income tax evasion has a positive influence on the currency ratio.
The investments in the financial innovations caused a bubble in 2008 which was followed by the big market crash and the Great Recession (Coffee, 2009). Therefore, it is essential to include the variable approximating investments in the financial innovations. This analysis expects to find the negative effect of this variable on the currency ratio.
The inflation in omitted from the model because the nominal interest rate, taken as a proxy for the relative cost of holding currency, already includes the inflation expectation (Mishkin et al., 2013). Assuming rational expectations of individuals and commitment of the Fed to maintain the price stability, the inclusion of inflation will result in a double accounting of the same effect.
To summarize, two dependent variables (the currency over the demand deposits and currency over the total deposits) and four independent variables (the real GDP, the nominal interest rate, income tax evasion and the financial innovations) will be used to construct the empirical models and analyse them.
3. Methodology
The methodology starts with constructing the models used in the research. The hypotheses concerning those models follow. Then the number of the pre-tests are carried out to analyse the specification of the data collected. Based on the results of the pre-testing the appropriate method to estimate the coefficients of the models is applied.
3.1. Empirical models
Based on the variables chosen for the analysis in 2.4. Summary of the literature review two models were constructed. They are presented in Table 1.
Table 1
The empirical models that contain the interest rates on deposits as an independent variable
Model No. Models
1.1 2.1
𝑙𝑛𝐶𝑈𝐷𝑑𝑒𝑚𝑎𝑛𝑑3= 𝛼 + 𝛽 𝑙𝑛 𝐺𝐷𝑃𝑅3+ 𝜑𝐷1𝑀3+ 𝜙𝑙𝑛𝑇3+ 𝜓 𝑙𝑛 𝐹𝐼3+ 𝜀3
𝑙𝑛𝐶𝑈𝐷𝑡𝑜𝑡𝑎𝑙𝑀1𝑀23 = 𝛼 + 𝛽 𝑙𝑛 𝐺𝐷𝑃𝑅3+ 𝜑𝐷3𝑀3+ 𝜙𝑙𝑛𝑇3+ 𝜓 𝑙𝑛 𝐹𝐼3+ 𝜀3 The models present the currency ratio as the function of four independent variables and the error term, where 𝐶𝑈𝐷𝑑𝑒𝑚𝑎𝑛𝑑3 is the currency to the demand deposit ratio, 𝐶𝑈𝐷𝑡𝑜𝑡𝑎𝑙𝑀1𝑀23 is the ratio of the currency to total M1 and M2 deposits, 𝐺𝐷𝑃𝑅3 represents the real GDP, 𝐷1𝑀3 is a one-month deposit interest rate, 𝐷3𝑀3 is a three-month deposit interest
rate, 𝑇3 is income tax evasion, 𝐹𝐼3 is the ratio approximating the financial innovations, and 𝜀3 is the error term.
Model 1.1 takes a one-month interest rate on deposits as an approximation of the opportunity cost of holding. This interest rate is chosen because the average holding period of the demand deposits is relatively small as they are the most liquid form of deposits and can be withdrawn at any time from depository institutions (Mishkin et al., 2013).
The savings and time deposits are interest-bearing deposits that have a pre-specified date of maturity (Mishkin et al., 2013). The savings and time deposits are less liquid assets that
are held for a relatively long time (Mishkin et al., 2013). Consequently, this analysis assumes that the average holding period for the time and savings deposits is six months. As the deposits taken in Model 2.1 are a sum of the M1 and M2 deposits, the average holding period is approximated to a three-month interest rate.
Historically, the retail bank rates tended to move approximately in line with the market rates. However, it is also evident that the retail bank rates tend to have a lagged reaction and not entirely change in correspondence to the interest rates changes on the market (Mishkin et al., 2013). Therefore, concerns about not complete pass-through of the deposit interest rates arise in Model 1.1 and Model 2.1. The issue can be resolved by using the interest rates on the Treasury Bills (T-bills). The T-bills are liquid securities that exhibit complete pass-through of the market rates (Mishkin et al., 2013). The data on a one-month T-bills interest rate is not available until 2001. Hence, the analysis will use a three-month T-bills interest rate for both models. Model 1.1 and Model 2.1 are adjusted for the T-bills interest rates (𝑇𝐵3𝑀3) and presented in Table 2.
Table 2
The empirical models that contain the T-bills interest rates as an independent variable
Model No. Models
1.2 2.2
𝑙𝑛𝐶𝑈𝐷𝑑𝑒𝑚𝑎𝑛𝑑3 = 𝛼 + 𝛽 𝑙𝑛 𝐺𝐷𝑃𝑅3+ 𝜑𝑇𝐵3𝑀3+ 𝜙𝑙𝑛𝑇G+ 𝜓 𝑙𝑛 𝐹𝐼3+ 𝜀3
𝑙𝑛𝐶𝑈𝐷𝑡𝑜𝑡𝑎𝑙𝑀1𝑀23 = 𝛼 + 𝛽 𝑙𝑛 𝐺𝐷𝑃𝑅3+ 𝜑𝑇𝐵3𝑀3+ 𝜙𝑙𝑛𝑇G+ 𝜓𝑙𝑛𝐹𝐼3+ 𝜀3
3.2. Hypotheses
The empirical models of the research estimate the influence and the significance of the determinants of the currency ratio. The aim of the research, however, is to compare whether the influence of the currency ratio determinants have changed after the crisis. To answer the central question, the following hypotheses in the form of expectations are put forward:
null hypothesis: there are no significant changes in the influence of the real GDP, income tax evasion, the nominal interest rate, and the financial innovations on the currency ratio after the crisis (testing each set of the variables individually) alternative hypothesis: there are significant changes in the influence of the real GDP,
income tax evasion, the nominal interest rate, and the financial innovations on the currency ratio after the crisis (testing each set of the variables individually) 3.3 Data
The data collected is the historical, time series data of the U.S. economic variables over the period from 1980 until 2018. The database created has 153 observations that are presented in a quarterly format. The choice of the quarterly frequency is explained by the necessity to have a sufficient amount of the observations. The quarterly data is often subjected to the seasonal trend (Jorgenson, 1964). Therefore, the seasonally adjusted data is used to account for the possible seasonal trends. One exception is the monetary base data (used for the financial innovations calculation) that is collected in a seasonally unadjusted form because the seasonally adjusted data was discontinued from the reports after June 26, 2013.
The beginning of the sample period is 1980 because the tax revenues from household income in the U.S. (used for income tax evasion calculation) was found to be reported in a quarterly frequency only from 1980. The end of the time frame is the first quarter of 2018. This analysis assumes that the period before the crisis is the time from the first quarter of 1980 until the fourth quarter of 2007 (112 observations). By mentioning period after the crisis, it is meant the time from the first quarter of 2008 until the first quarter of 2018 (41 observations).
3.3.1 Sources. The GDP in the constant (2009 chained) prices represents the real GDP in the models. The source of this data is Bureau of Economic Analysis, U.S. Department of Commerce (BEA) (BEA, 2018). The same source is used to collect the data on the GDP in the current prices which is used as the nominal GDP in the analysis (BEA, 2018). The nominal
interest rates on the one-month and three-month deposits are the middle-interest rates gathered from the Thomson Reuters database (Thomson Reuters, 2018). The alternative interest rate is a three-month T-bills interest rate gathered from the Fed database (Fed, 2018c). The Fed reports provide the data on the monetary base, M1 money aggregate, M2 money aggregate, and their components. The data on the total M1 money aggregate and some of its components, namely, demand deposits and other checkable deposits are collected for the analysis (Fed, 2018b). Similarly, the data on the total M2 money aggregate, savings deposits, and small denomination time deposits are gathered (Fed, 2018b). The data on the monetary base is collected from the Fed database (Fed, 2018a). Lastly, figures on the tax revenues from household income in the current prices are gathered from Oxford Economics (Oxford Economics, 2018).
3.3.2 Transformations. Tchaidze and Tvalodze (2011) approximated the financial innovations as the M2 money multiplier. This analysis adopts the same technique because it wants to capture the influence of the investments in the retail money fund and the money market deposits components of the M2 money aggregate. The ratio approximating the financial innovations is presented by Equation 3.
𝐹𝐼 =𝑀2 𝑚𝑜𝑛𝑒𝑦 𝑎𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒
𝑀𝑜𝑛𝑒𝑟𝑎𝑡𝑦 𝑏𝑎𝑠𝑒 (3)
Income tax evasion is calculated as the ratio of the tax revenues from the household income and the nominal GDP. Therefore, in the mathematical form, it is stated as Equation 4.
𝑇 =𝑇𝑎𝑥 𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠 𝑓𝑟𝑜𝑚 ℎ𝑜𝑢𝑠𝑒ℎ𝑜𝑙𝑑 𝑖𝑛𝑐𝑜𝑚𝑒
This research will use two separate definitions of the currency ratio. The currency (component of the M1 money aggregate) over the demand deposit is the first ratio used. It is presented in Equation 5. The second ratio is calculated as the currency over the total M1 and
𝐶𝑈𝐷𝑑𝑒𝑝𝑜𝑠𝑖𝑡 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦
𝐷𝑒𝑚𝑎𝑛𝑑 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑠 (5)
M2 deposits. Taking into account the definition of the U.S. money aggregates, the analysis calculates the total M1 and M2 deposits as Equation 6. Subsequently, the second ratio of
𝑇𝑜𝑡𝑎𝑙 𝑀1 𝑎𝑛𝑑 𝑀2 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑠 = 𝐷𝑒𝑚𝑎𝑛𝑑 + 𝑂𝑡ℎ𝑒𝑟 𝑐ℎ𝑒𝑐𝑘𝑎𝑏𝑙𝑒 + 𝑆𝑎𝑣𝑖𝑛𝑔𝑠 + 𝑆𝑚𝑎𝑙𝑙 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜 𝑡𝑖𝑚𝑒 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑠
(6)
the currency over the total M1 and M2 deposits is defined as Equation 7.
𝐶𝑈𝐷𝑡𝑜𝑡𝑎𝑙𝑀1𝑀2 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦
𝑇𝑜𝑡𝑎𝑙 𝑀1 𝑎𝑛𝑑 𝑀2 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑠 (7)
All variables except the interest rates are transformed to the logarithmic form. There are two motivations for these transformations: the economic time series exhibit approximately exponential growth (Stock & Watson, 2012); the standard deviation of the logarithm series is approximately constant (Stock & Watson, 2012). Both reasons provided suggest that it is convenient to transform the data to the logarithmic form to perform the analysis.
3.4. Pre-testing
The pretesting of the variables is carried out using the whole sample period (153 observation) to assess behaviour of the variables over the time.
3.4.1. Stationarity. The first critical issue to account for is whether the time series is stationary (Verbeek, 2008) meaning that the probability distribution of each variable does not change over the time (Stock & Watson, 2012). Nonstationarity can result from different causes, yet Verbeek (2008) specified that the presence of the unit-root is typical for the economic time series. The test for the unit-root begins from the decision on whether to include the trend into the actual test (Stock & Watson, 2012). The informal test of examining the time series plot can help make the decision (Stock & Watson, 2012). Following this informal test, all variables are plotted and presented in Appendix A. By examining the plots one can conclude that only the real GDP 𝑙𝑛 𝐺𝐷𝑃𝑅3 could have a trend.
The actual test on the presence of the unit-root is the Dickey-Fuller test (Stock & Watson, 2012). Equation 8 presents the model with the deterministic trend 𝛽𝑡 used to perform the Dickey-Fuller test for 𝑙𝑛 𝐺𝐷𝑃𝑅3. All other variables ( 𝐷1𝑀3, 𝐷3𝑀3, 𝑇𝐵3𝑀3,
𝑙𝑛𝐶𝑈𝐷𝑑𝑒𝑚𝑎𝑛𝑑3, 𝑙𝑛𝐶𝑈𝐷𝑡𝑜𝑡𝑎𝑙 𝑀1𝑀23 𝑙𝑛𝑇3, and 𝑙𝑛𝐹𝐼3) that do not appear to have a trend follow Equation 9 for testing. Both models include the constant because Baltagi (2008)
∆𝑙𝑛𝐺𝐷𝑃𝑅3= 𝛼 + 𝛽𝑡 + 𝛿𝑙𝑛𝐺𝐷𝑃𝑅3XY+ 𝑢3 (8)
∆𝑙𝑛𝐹𝐼3= 𝛼 + 𝛿𝑙𝑛𝐹𝐼3XY+ 𝑢3 (9)
suggested including it for the economic variables. The null hypothesis of the unit-root existence is 𝐻[: 𝛿 = 0 versus the alternative hypothesis of stationarity 𝐻[: 𝛿 ≠ 0 (Baltagi, 2008). The actual results of the test are presented in Table 3.
Table 3
The results of the Dickey-Fuller test
Variables Z(t) lnGDPR -0.294 lnCUDdemand -2.448 lnCUDtotalM1M2 -1.823 D1M -2.756 D3M -2.605 TB3M -2.407 lnT -2.518 lnFI -0.054 Note. * p < .05. ** p < .01.
Taking common 5% significance level, none of the results presented in Table 3 are significant, meaning that the null hypothesis of the unit-root fails to be rejected. Hence, the variables are non-stationary and require special econometric techniques to analyse them.
3.4.2. Optimal amount of lags. In practice, one does not know the process generating the serial correlation in the residuals 𝒖𝒕 (Baltagi, 2008). The inclusion of the additional lags of variables to the Dickey-Fuller test is done to make the error term in Equation 10 and Equation 11 asymptotically a white noise process (Verbeek, 2008). This leads to the Augmented
∆𝑙𝑛𝐺𝐷𝑃𝑅3 = 𝛼 + 𝛽𝑡 + 𝛿𝑙𝑛𝐺𝐷𝑃𝑅3XY+ 𝜆Y∆𝑙𝑛𝐺𝐷𝑃𝑅3XY+ 𝜆b∆𝑙𝑛𝐺𝐷𝑃𝑅3Xb+ ⋯ + 𝑢3 (10) ∆𝑙𝑛𝐹𝐼3 = 𝛼 + +𝛿𝑙𝑛𝐹𝐼3XY+ 𝜆Y∆𝑙𝑛𝐹𝐼3XY+ 𝜆b∆𝑙𝑛𝐹𝐼3Xb+ 𝜆G∆𝑙𝑛𝐹𝐼3XG+ ⋯ + 𝑢3 (11)
Dickey-Fuller test. The null and the alternative hypotheses applied for this test are the same as for the Dickey-Fuller test (Baltagi, 2008).
The methods to define the optimal number of lags diverge among the authors. Stock and Watson (2012) adopted a more statistical approach and recommended to estimate the number of lags using the Bayes information criterion or Akaike information criterion, while Enders’ (2015) approach is based on the seasonality of the time series. Therefore, Enders (2015) suggested using, for instance, the lag lengths that are multiple of four for a quarterly data. This analysis adopts Enders’ method. The results of the test are summarised in Table 4
Table 4
The results of the Augmented Dickey-Fuller test Z(t)
Variables 4 lags 8 lags
lnGDPR -1.225 -1.657 lnCUDdemand -1.639 -1.560 lnCUDtotalM1M2 -1.350 -1.590 D1M -3.294* -2.504 D3M -2.754 -2.596 TB3M -2.858 -2.310 lnT -3.388* -3.211* lnFI -0.572 -0.378 Note. * p < .05. ** p < .01.
Taking common 1% significance level, the null hypothesis of the unit-root fails to be rejected. There cannot be observed a common pattern of the increase or decrease in the significance of the results as the number of the lags increases. Therefore, four and eight lags will be used in the following test for cointegration.
3.4.3. Cointegration. The model used to explain the behaviour of the currency ratio include variables that might have a common trend (Stock & Watson, 2012). In this case,
variables are considered to be cointegrated, i.e., there exists a linear combination of those nonstationary variables which is stationary (Verbeek, 2008). There exist multiple testing techniques for cointegration. The one discussed below follows the Johansen’s methodology.
Enders (2015) emphasised that the results of the test can be quite sensitive to the lag length. Therefore, the analysis incorporates the test with four lags and eight lags. Equation 12 determines the maximum rank of the 𝜋 matrix (maximum number of cointegration questions).
∆𝑥3 = 𝐴[+ 𝜋𝑥3XY+ 𝜋∆𝑥3XY+ 𝜋∆𝑥3Xb+ ⋯ + 𝑢3 (12)
In Equation 12, 𝑥3 is the vector of variables, 𝐴[ is the matrix of intercept terms, 𝜋 is the cointegration vector, and 𝑢3 is the vector of error terms (Enders, 2015). Johansen’s testing procedure starts with the test for zero cointegration equations (a maximum rank of zero) (Enders, 2015). If this null hypothesis is rejected, the null hypothesis of at most one cointegration equation is tested (Enders, 2015). The test continues and increases the maximum number of the cointegration equations in the null hypothesis until it fails to reject the null hypothesis (Enders, 2015). The results of the test are presented in Table 5 and Table 6. Table 5
The results of the test for cointegration for Model 1.1 and Model 1.2
Model 1.1 Model 1.2
lags max rank trace statistics max rank trace statistics
4 lags 0 80.057* 0 83.811*
1 30.146 1 36.041
8 lags 0 82.183* 0 85.963*
1 39.192 1 42.534
Table 6
The results of the test for cointegration for Model 2.1 and Model 2.2
Model 2.1 Model 2.2
lags max rank trace statistics max rank trace statistics
4 lags 0 73.065* 0 78.237* 1 39.144 1 41.615 8 lags 0 77.875* 0 81.160* 1 47.259* 1 45.830 2 29.680 Note. * p < .05. ** p < .01.
The results show that for Model 1.1, Model 1.2, and Model 2.2 the null hypothesis of at most one cointegration equation was rejected, independent of the lags length used. These results suggest that there exists one cointegration equation of the variables in these models. The testing of Model 2.1 shows that there exists one cointegration equation of the variables if the test is performed with four lags and two cointegration equations if eight lags are used.
The existence of the cointegration equation suggests the long run relationship between the variables (Verbeek, 2008). The long-run relationship implies that the way the variables interact in the short-run drives them to their long-run equilibrium relationship (Verbeek, 2008). This implication can be modelled by the error-correction mechanism (VEC) (Verbeek, 2008). 3.5. Parameters of the cointegration equation
The short-run parameters of the variables estimated by the VEC mechanism do the following: they describe how the variables in the short-run consistent with their long-run cointegration relationship (Verbeek, 2008). The analysis uses the VEC mechanism specifying the existence of one cointegration equation and four lags to estimate the parameters of the
cointegration equation for all model. The estimations using eight lags cannot be presented because this number of the lags in the period after the crisis causes collinearity in the models.
The comparison of the models’ fit is carried out to select the models that best explain the variation in the currency ratio. The likelihood values of models are presented in Table 7.
Table 7
The log likelihood of models in two periods Log Likelihood
Models Before crisisa After crisisb
1.1 1099.068 459.475
1.2 1105.427 483.857
2.1 1251.377 515.957
2.2 1248.641 546.191
Note. an=112. bn=41
The log likelihood values suggest that Model 2.1 and Model 2.2 have better fits compared to other models in the period before the crisis. Similarly, Model 2.1 and Model 2.2 have better fits in the period after the crisis. Hence, the results of the parameters of the cointegration equations of Model 2.1 and Model 2.2 are presented in Table 8 and Table 9, respectively. The results for Model 1.1 and Model 1.2 are left out of the methodology and presented in Appendix B.
Table 8
The estimated parameters of the cointegration equation for Model 2.1 Variables
Periods D3M lnGDPR lnT lnFI constant
Before crisisa -0.320** -2.533** 0.771 3.360** 21.838 (0.046) (0.663) (0.862) (0.770) After crisisb -0.040** -0.691** 0.650** 0.272** 10.855 (0.015) (0.132) (0.084) (0.055) Note. an=112. bn=41 * p < .05. ** p < .01. Table 9
The estimated parameters of the cointegration equation for Model 2.2 Variables
Periods TB3M lnGDPR lnT lnFI constant
Before crisisa -0.185** -1.339** 0.291 2.475** 10.391 (0.023) (0.263) (0.368) (0.343) After crisisb -0.093** -0.947** 0.835** 0.325** 13.862 (0.024) (0.179) (0.106) (0.054) Note. an=112. bn=41 * p < .05. ** p < .01.
The variables 𝑙𝑛 𝐺𝐷𝑃𝑅3, 𝐷3𝑀3, and 𝑇𝐵3𝑀3 have a negative effect on the depended
variables for Model 2.1 and Model 2.2 in both periods, as was expected. Income tax evasion 𝑙𝑛𝑇3 is not significant during the period before the crisis but is highly significant after the
innovations is not aligned with the expectation of the analysis. The possible reasons for this result will be discussed in section 5. Limitations and discussion.
4. Results and interpretations
The following section presents and interprets the results of the study. To answer the central question, the comparison of the effects of the currency ratio determinants before and after the crisis will be performed. The test will be carried out by visual comparison of plotted coefficients of the variables.
The estimated coefficients follow the normal distribution. Therefore, 95% confidence intervals for each coefficient are estimated using the Equation 13. Equation 13 uses coefficient of the real GDP 𝛽 as an example.
95% 𝑐𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 = 𝛽 ± 1.96 ∗ 𝜎l (13)
The confidence intervals of the estimates before the crisis are wider due to their higher standard deviations. Higher number of the observations in the period before the crisis probably causes higher variability of the determinants that result in higher standard deviations. Using the same argument, the narrower confidence intervals for the coefficients after the crisis are justified by smaller variations of the determinants due to smaller number of the observations.
For the hypotheses testing, two coefficients of the same independent variable in two periods are plotted. Four plots present the estimates of Model 2.1 and Model 2.2 in Figure 2 and Figure 3, respectively. The plots for Model 1.2 and Model 1.2 are left out from this section and are presented in Appendix C.
The comparison of the coefficients’ positions shows if the effect of the variable in question has changed over the time, while the comparison of the confidence intervals of those
coefficients shows the significance of the change. Therefore, if the confidence intervals of the coefficients overlap, one can conclude that the change in the effect cannot be considered significant. If the confidence intervals do not overlap, the influence has changed significantly.
Figure 2. 95% confidence intervals of Model 2.1 estimates. The variable Crisis presents time, where the zero presents the period before the crisis, and the one is the period after the crisis.
By comparing the estimates of Model 2.1, the significant changes in the effects of all variables can be observed. The variable 𝐷3𝑀3 is significantly small after the crisis which can be explained by decreased interest rates on the deposits at that period. The decrease in the interest rate is due to the policy targeting a zero overnight lending rate and quantitative easing implemented by the Fed to fight the recession.
There can be observed a significant change in 𝑙𝑛 𝐺𝐷𝑃𝑅3 effect. The smaller effect of
the real GDP might be due to the reduced real income of the individuals as the result of the crisis and slow recovery of the economy.
Though plotted for presentation, the comparison of income tax evasion 𝑙𝑛𝑇3 cannot be
performed because the variable is not significant before the crisis. Nevertheless, the variable is significant and positive during the period after the crisis. The evasion of the tax was probably stimulated by the rapid increase in the unemployment that stimulated shadow employment and transactions in cash.
The evidence shows that the financial innovations 𝑙𝑛𝐹𝐼3 affected the dependent variable significantly less after the crisis. Unfortunately, the analysis cannot provide the interpretation of this result. The possible solution to the problem will be presented in section 5. Limitations and discussion.
Figure 3. 95% confidence intervals of Model 2.2 estimates. The variable Crisis presents time, where the zero presents the period before the crisis, and the one is the period after the crisis.
The comparison of the variables coefficients presented in Figure 3 suggests that the influence of the variables has changed, but not all changes are significant. The effects of the
nominal interest rate 𝑇𝐵3𝑀3 and the real GDP 𝑙𝑛 𝐺𝐷𝑃𝑅3 are smaller, but fail to be significantly
smaller. The reasons for the decrease in the influences follow the same reasoning as discussed for Model 2.1. Moreover, the effect of income tax evasion 𝑙𝑛𝑇3 appears to be significant only after the crisis. The same tendency was observed in Model 2.1. Lastly, the influence of the financial innovations 𝑙𝑛𝐹𝐼3 is significantly smaller after the crisis. As was stated above, this result is conflicting with the expectation of the research and the will be discussed in the following section.
To summarise, both models show that the influence of each variable has changed after the crisis. The changes are considered to be influenced by the effect of the recession and the monetary policy tools used to recover from it.
5. Limitations and discussion
The following section presents some limitation of the research, introduces possible solutions to those limitations, and makes suggestions for the further research.
The estimated parameters for the models show that the financial innovations have a positive effect on the currency ratio. This result does not coincide with the expectation of the study. There are two possible explanations for that result. Firstly, it might be the case that the influence of the financial innovations on the currency ratio is positive as was also concluded by Beenstock (1989). He found that rapid speed of financial innovation in the U. K. led to the increase in the currency ratio. If this observation is correct, then one would expect that the influence of the financial innovations should increase in the period after the crisis. The analysis shows the opposite result – the effect of the financial innovations, although significant, approaches zero in the period after the crisis. Therefore, the second reason is that the ratio used for the financial innovations is not a reasonable approximation of the real investment in the
financial innovations in the U.S. Consequently, the further research can investigate the variables that might be a better approximation of the financial innovations in the U.S.
The methodology of this study is based on the methodology of Tchaidze and Tvalodze’s (2011) research. Their research aims at determining the variable influencing the currency ratio and their significance. Though it was essential to construct the correct model to analyse the currency ratio, the main aim of this analysis was to compare the influence of those variables on the currency ratio in periods before and after the crisis. The non-stationary of the variables in the empirical models constructed poses difficulties on performing the formal test to answer the research question. Therefore, the informal test of visual comparison of the coefficients and their confidence intervals was carried out. The formal test could have been performed if, e.g., Model 1.1 would have been contacted as Equation 14. Equation 14 includes interaction terms
𝑙𝑛𝐶𝑈𝐷𝑑𝑒𝑚𝑎𝑛𝑑3 = 𝛼 + 𝛽Y𝑙𝑛 𝐺𝐷𝑃𝑅3+ 𝛽b𝑙𝑛𝐺𝐷𝑃𝑅3∗ 𝐷 + 𝛽G𝐷1𝑀3+ 𝛽m𝐷1𝑀3∗ D + + 𝛽o𝑙𝑛𝑇3 + 𝛽p𝑙𝑛𝑇3∗ 𝐷 + 𝛽q𝑙𝑛 𝐹𝐼3+ 𝛽r𝑙𝑛𝐹𝐼3∗ 𝐷 + 𝜀3
(14)
of the independent variables and the dummy variable of the time 𝐷. The formal test could have been performed by testing coefficients of the interaction terms on significance. This model specification is useful to consider for the further research.
6. Conclusion
This study aims to estimate how the effects of the currency ratio determinants have changed after the Great Recession and give the possible explanations for those changes. The research constructs the currency ratio as a function of the real GDP, the nominal interest rate, income tax evasion, and the financial innovations. The analysis estimates the effects of the currency ratio determinants during the periods before and after the Great Recession. The
technique applied to estimate the effects is the VEC mechanism. Subsequently, the estimates of variables in two periods are compared on the significance of the change.
The comparison of the effects concludes that for Model 2.1 all variables’ influences have changed significantly after the crisis. The effects of the variables in Model 2.2, although, have changed after the crisis, but some of those changes fail to be significant. Though the significance of the changes differs in the models, the general tendencies in the effects’ changes are the same.
The effects of the nominal interest rates and the real GDP decreased after the crisis. The real income of individuals dropped during the crisis that caused the decrease in the currency holding and money depositing. This explains the decrease in the effect of the real GDP. The Fed’s policy targeting a zero overnight federal funds rate and unconventional monetary tools used to restore the liquidity lowed the interest rates and, consequently, the opportunity cost of holding currency. This decreases the effect of the nominal interest rate on the currency ratio after the crisis. The influence of income tax evasion in both models fails to be significant before the crisis but has highly significant and positive effect after the crisis. As was expected, the income tax evasion is significant during the period of the recession when the unemployment rises. Higher unemployment pushes individuals to find a job in the shadow sector where they probably receive income payments in cash to avoid taxable transactions. Lastly, the ratio approximating the financial innovations was estimated to be significant and positive for both models in two periods. The effect of this variable after the crisis appears to be significantly smaller. This result deviates from the expectation of the analysis.
The limitation of the research addresses the problem of the ratio approximating the financial innovations. The positive and significant effect of the financial innovations is found, while the analysis expected to find its negative influence on the currency ratio. The author suspects that the M2 money multiplier might not be a good approximation of the financial
innovations in the U.S. and suggests finding a more appropriate measure for the further research.
The adjusted model with the dummy variable of the time in the interaction terms is suggested for the further research. Based on the model proposed a more formal test for the changes in variables effects could be performed.
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Appendix A
Figure 1A. Times series plots for the real GDP 𝑙𝑛 𝐺𝐷𝑃𝑅3, income tax evasion 𝑙𝑛𝑇3, the financial innovations 𝑙𝑛𝐹𝐼3, and a three-month T-bills interest rate 𝑇𝐵3𝑀3.
Figure 2A. Times series plots for a one-month deposit interest rate 𝐷1𝑀3, a three-month deposit interest rate 𝐷3𝑀3, the currency to the demand deposit ratio 𝑙𝑛𝐶𝑈𝐷𝑑𝑒𝑚𝑎𝑛𝑑3, the ratio of the currency to total M1 and M2 deposits 𝑙𝑛𝐶𝑈𝐷𝑡𝑜𝑡𝑎𝑙𝑀1𝑀23.
Appendix B
Table 1B
The estimated parameters of the cointegration equation for Model 1.1 Variables
Period D1M lnGDPR lnT lnFI constant
Before crisisa -1.007** -12.515** 5.516* 2.160 134.555 (0.127) (2.417) (2.417) (2.054) After crisisb 0.449** -14.182** 10.072** 1.214** 172.373 (0.115) (1.788) (1.097) (0.435) Note. an=112. bn=41 * p < .05. ** p < .01. Table 2B
The estimated parameters of the cointegration equation for Model 1.2 Variables
Period TB3M lnGDPR lnT lnFI constant
Before crisisa 5.859** 49.250** -19.271 -11.977 -519.077 (0.807) (8.834) (13.625) (11.661) After crisisb 0.061 -7.785** 7.917** 1.407** 102.740 (0.157) (1.637) (0.811) (0.325) Note. an=112. bn=41 * p < .05. ** p < .01.
Appendix C
Figure 1C. 95% confidence intervals of Model 1.1 estimates. The variable Crisis presents time, where the zero presents the period before the crisis, and the one is the period after the crisis.
Figure 2C. 95% confidence intervals of Model 1.2 estimates. The variable Crisis presents time, where the zero presents the period before the crisis, and the one is the period after the crisis.
