Repo Rates and
Private Consumption
in Sweden from 1995 -2019
BACHELOR
THESIS WITHIN: Economics NUMBER OF CREDITS: 15 ECTS
PROGRAMME OF STUDY: International Economics AUTHOR: Jacob Söderström Hallberg & Zixuan Xu JÖNKÖPING May 2020
An analysis of negative repo rates with regards to private
consumption
Bachelor Thesis Economics
Title: Repo rates and Private Consumption in Sweden from 1995 - 2019 Authors: Jacob Söderström Hallberg & Zixuan Xu
Tutor: Andrea Schneider Date: 2020-05-11
Key terms: Repo rate, Private Consumption, Negative interest rates, IS-LM model.
Abstract
The aim of this thesis is to examine whether repo rates have any impact on private consumption in Sweden. After the financial crisis in 2008, the repo rates in some periods become negative. Whether negative repo rates have impact on private consumption is an additional analysis in the thesis. In the theoretical framework the IS-LM model and some explicit hypothesis are derived. In the empirical part, data for repo rate, income, inflation and saving in Sweden are collected from 1995 to 2019 with a time unit of quarterly data. With the collected data one multiple linear regression is estimated and one additional test where the same model is modified with a dummy variable that isolates the periods with negative repo rates. In line with the theoretical prediction, the first multiple linear regression result exhibits that the repo rate has statistically significant negative impact on private consumption. The second multiple linear regression with the dummy variable shows that the impact of negative repo rates is not different from positive repo rate. Limitations and shortcomings are discussed in the section limitations and weaknesses.
Contents
1.
Introduction ... 1
2.
Theoretical framework ... 2
2.1 IS-LM model ... 3
2.2 Monetary Policy and Liquidity traps ... 4
2.3 Repo Rates Effect on Market Rates ... 5
2.4 Hypothesis ... 6
3.
Data and control variables ... 7
4.
Methodology ... 8
4.1 Correlation-Matrix ... 9
4.2 Stationarity ... 9
4.3 Choosing lag length ... 12
4.4 Estimated model ... 13
4.5 Diagnostic test ... 13
5.
Results and analysis ... 16
5.1 Estimated Results... 17
5.2 Estimated Results NIR ... 18
5.3 Limitations and weaknesses ... 19
5.4 Additional empirical tests using Market Rates ... 21
6.
Conclusions ... 21
Bibliography ... 23
1. Introduction
Interest rates are an integral economic phenomenon that allows the economy to function. The interest rate dictates the price of money and is a backbone for the whole financial industry. The reason why we want to investigate this topic is due to the rising concern in the society regarding the interest rate. The media sometimes narrate the relatively low and sometimes negative interest rates as something that is “just bad”. Dealing in absolutes might not give a fair picture to a topic that is quite complex. The Swedish central bank has in their own investigation concluded that negative interest rates have an expansive effect on the economy, a decrease of interests rates usually leads to increased consumption spending, but with potential negative side effect that are of uncertain nature (Riksbanken, 2019). In this thesis we will investigate this further and see what our result would suggest, thus this is merely a statistical contribution to something that is controlled by central banks around the world.
The purpose of our study is to investigate the connections between private spending and repo rates inspired from the ongoing debate presented from Whites notes (White, 2019). The repo rate is the central banks reference rate that controls all the market rates in the economy, a deeper analysis of the repo rate can be found in the section 2. The thesis will also investigate periods where the repo rates shift from the zero-lower bound to a negative range. In macroeconomics private consumption is a main driver in the economy and are derived from millions of micro decisions. We are interested to see if neo-classical theory still holds in this new age where rates and inflation are relatively low if measured from before 1995.
Our data stretch from 1995-2019 and probably the most significant economic shock that happened during this time interval was the financial crisis. After the financial crisis in 2007-2009 several economies needed stimulation to increase consumption and investments that are key components for growth in the national accounts to avoid a deep depression. The Swedish central bank coined the expression that extra ordinary measures was needed in the wake of a crisis (Riksbank, 2010). Many different monetary policies were implemented to stabilize the economy to ensure that the financial system could stay liquid. Examples of polices that were implemented was to increase the credit supply by lending both USD and SEK to banks, where the issued loans had longer than normal maturity. The reason for this policy was to reduce the market risk and decrease the interest rates on credits. On some occasions the Swedish central bank extended the reach of counterparties that could borrow from the central bank, thus effectively allowing other financial market participants to access the liquidity offered by the central bank. The repo rate was also reduced from the peak of 4.45% to 0.25% (Riksbank, 2010). As briefly mentioned above there are several different types of economic tools central banks can use to increase the effectiveness of monetary policy, however the one that is particularly interesting in this thesis is the drastic repo rate cut.
The problem we have identified is that after a decade from the financial crisis, repo rates has remained low, compared to the repo rates before the financial crisis as seen in (Fig 1). Sweden and many other developed economies have entered a period of ultra-low interest rates and at some periods even negative interest rates (NIR) (Jobst & Lin , 2016). There is a current debate going on about the implication of having ultra-low interest rates in the long term.
Unintended effects and undesirable incentives could accumulate over time and create unknown systematic risks. Risks, in forms of increasing levels of global debt and low inflation might make future monetary policy ineffective or less effective to combat future economic turmoil when it is most needed. White (2019) claims that investments levels have been weaker than expected and that household savings have increased during this period of ultra-low interest rates. Which contradicts what neo classical monetary theory suggest. One argument raised in the discussion is the possibility that households might be affected by Keynesian animal spirits, meaning that monetary policies that should induce spending might just as well make the households more defensive and save more instead of ramping up the consumption when the opportunity cost of money is low (White, 2019).
(Fig 1: Repo rate in Sweden 1995-2019 (Riksbanken Database, 2020)).
The remaining thesis is structured as follows: In section 2 we introduce the theoretical framework for the thesis. In section 3 we analyze and introduce data and control variables. In section 4 we present our methodology and empirical study. In section 5 we analyze the result and weaknesses of the empirical study. In section 6 we conclude our thesis.
2. Theoretical Framework
In this section we will present the underlying theoretical framework for our thesis. The central bank has the power to control the short-term interest rate by lending money to another financial institute. Since the central bank controls the money supply the central bank can always print enough money meet the target level of the determined repo rate level. Since the central bank have this capability the repo rate can function as a reference rate that controls the spread of the inter banking rates, in Sweden this is known as STIBOR. The point of analysing the IS-LM curve is to have a framework we can derive certain economic mechanics; these mechanics will be further discussed when we analyse the IS-LM model. The framework will help us understand how monetary policy will according to theory
will utilize the theories of the IS-LM model and discuss some shortcomings. The general expectation regarding the link between repo rates and private consumption should according to classical theory have a negative relationship (Gottfries, 2013). Before the central banks implemented negative interest rates neo-classical theory suggested that interest rates had a zero-lower bound meaning that rates would never fall below zero. Due the zero lower bound assumption the potential effect negative rates might have on the economy is quite unexplored (Czech National Bank, 2018).
2.1
IS-LM Model
The IS-LM model is a macro-economic framework developed by Robert Mundell and Marcus Fleming (Gottfries, 2013). The theory has two key components and that is the goods market (IS) and the liquidity market (LM).
Y = C+I (1)
C = C (Y, Ye, i-πe, A) (2)
I = I(i-πe, Ye, K) (3)
M/P = Y/V(i) (4)
The goods market equilibrium (IS) is defined by private consumption denoted C and investments denoted I, when added together private consumption and investments equals the real production denoted Y see Equ. (1). Private consumption is a function of income denoted Y, expected future income denoted Ye, real interest rate denoted i-πe and private asset holdings denoted A see Equ. (2). Investments is a function of the real interest rate, expected income and the current capital stock denoted K. The liquidity market equilibrium is defined by the monetary base denoted M, the price level denoted P, the real production and the velocity of money which is a function of nominal interest rate denoted i. As we can see in the functions, the nominal interest affects both market equilibria. This means that depending on how the interest rates change we can expect changes in both the IS curve and the LM curve (Gottfries, 2013). π = πe +βŶ+z (5)
The inflation π is determined by expected future inflation πe, the output gap denoted βŶ and the cost push shock denoted z. Central banks often have a pre-determined inflation goal but this goal often deviates slightly from the fixed target due to dynamic changes in the output gap and expected inflation for instance. If the inflation deviates to much in a certain range around the fixed inflation target, the central bank can then adjust the repo rate to achieve the predetermined goal. Consequentially if the central bank would decrease the repo rate the IS-LM model would suggest that the goods market which is defined by private consumption and private investments would increase since the opportunity cost of consumption and the cost of lending money for investments would decrease since this is ruled by the interest rate level. This is true in the opposite direction (Gottfries, 2013).
In the case of an economic shock the IS-LM hypothesises that the central bank has the option to adjust the interest rate depending on the shock. There are many different shocks that the IS-LM model can analyse. The shock used in the description is a shock that shifts IS curve either outward when the economy is overheated and inward when the economy is affected negatively. An example of a shock that would shift the IS curve
inward could be a global pandemic, and a shock that would shift the IS curve outward could be that the inflation target set by the central bank is damaged, thus consumers would expect higher inflation in the future hence they are consuming more today than they would normally. If the shock impacts the economy negatively the total aggregated production will decrease. Thus, potentially impacting consumption negatively. Hence the IS-LM framework suggest that the central bank would decrease the interest rate. A decrease in the interest rate would boost consumption and investment, since the opportunity cost of consumption today decreases, and the cost of debt decreases. One could also include the effect the interest rate has on the exchange rate. The decrease of interest rate would depreciate the domestic currency; thus, export would increase. However, this is not included in the thesis scope since we define total production as the sum of aggregated consumption and investments and do not consider net export (NX). If the shock boosts the total production, there is a risk of increased inflation in the economy. To avoid overheating the economy the central bank has the option to increase the interest rate, thus increasing the opportunity cost of consumption and the cost of debt would also increase. This will decrease the consumption and the investments, thus reducing the inflation rate in the economy (Gottfries, 2013).
2.2 Monetary Policy and Liquidity Traps
Monetary policy is the macroeconomic policy operated by central bank by using different tools to adjust the money supply and interest rates. Monetary policy will finally help to realize government’s specific economical goals such as stabilizing the prices of goods, boosting, and cooling down the economy, meeting full employment level (no cyclical unemployment or deficient demand unemployment). Quantitative easing or expansionary monetary policy: Quantitative easing is typically used when the economy is in the recession (when inflation rate is very low). A central bank increases the money supply by repurchasing the treasury bills and government bonds or other financial assets. By doing so, interest rate will be lowered. Quantitative tightening or Contractionary monetary policy: Quantitative tightening is the opposite of quantitative easing. It is used to fight inflation when the economy is over-heated. In this case, central banks will release treasury bills and government bonds which institutions will buy, this leads to a decrease in money supply in the money market. Interest rates would then rise, domestic currency will appreciate, and aggregate demand will decrease (Hausken & Ncube, 2013). By understanding these mechanics, we can better understand why the central banks have allowed for the interest rate to fall after the financial crisis 2008.
“Liquidity traps” is a hypothesis proposed by John Maynard Keynes (Keynes, 1936). The hypothesis indicates at a specific point where the interest rates are at an ultra-low level and the saving rates are at a high level. In this case, expansionary monetary policy or quantitative easing will no longer be effective. No matter how much more money central bank release in the money market, there will not be any effects on interest rates.
According to Gottfries (2013) the real demand for money function is MV(i) = PY. After transforming the formula, M/P = Y/V(i). Where M stands for nominal supply for money in the circulation, P stands for the price level at that point, Y stands for the production level and V(i) stands for the turnover speed of money. For M/P, nominal supply of money divided by the turnover is the real money supply, it is not affected by the interest rate. However, when we consider the money demand, Y/V(i). The turnover speed of money has a negative relationship with interest rate: If interest rate is high, households will prefer saving money in
the banks, otherwise if the interest rate is low, saving money in the bank will no longer be attractive. In this case households will prefer spending (Gottfries, 2013).
In a liquidity trap, investors anticipate the interest rate to soon increase and the prices of bonds are expected to decrease, since bonds have a negative relationship with interest rates. Investors would then prefer cash rather than holding bonds since cash have a higher turnover speed. Higher interest rates are prone to increase savings in cash in the banks since higher yields can be generated. At this specific point, the elasticity of money demand will be infinite. No matter how much money the central bank would release to the liquidity market the money demand is already met, thus the money will instead be saved by the households to generate interest income. When there is a liquidity trap, expansionary monetary policy cannot help to decrease the interest rate. As a result of a constant interest rate, investments and consumptions will not be stimulated. Which means expansionary monetary policy will eventually be invalid if the economy is in a liquidity trap.
2.3 Repo Rates Effect on Market Rates
In this thesis we analyse the repo rate, however in reality the consumers often face another rate other than the repo rate. To differentiate from the repo rate, we may refer to this rate as the market rate. Hence, we need to realise that the repo rate has direct effect on the market rate, but that the consumers who make up the micro decisions in an economy does not directly interact with the repo rate. This section is included to allow us to distinguish the difference between repo rates and market rates later in the thesis. In Fig A15 in the appendix we can see that there is a general correlation between repo rate and market rates. This is expected and in this sub section we will investigate how theory and the Swedish central bank explain this relationship.
When the repo rate changes the first impact the change will have is on the overnight rate. The overnight rate is the market rate for interbank transactions. The overnight rate exists since banks during the day have a certain amount of unpredictable transactions that vary in size, depending on the circumstances the bank can in the end of the day either have excess liquidity or even run a deficit. According to regulations a bank can run a deficit over the day but not overnight. Other banks with excess liquidity can lend out money to the banks that currently have a deficit after the bank closing, by doing so the bank use the excess liquidity to generate interest income. Why the repo rate has direct impact on the overnight rate is that the central bank also offers to lend money overnight, thus if the overnight lending rate is higher than the offer from the central bank the bank with a deficit choose to lend from the central bank instead (Gottfries, 2013).
Interest rates that have longer maturity is also affected by the quantitative effect caused by a change of the repo rate. However, the impact depends on the expectancy of the change. If the change of repo rate is expected the markets have already adjusted for the increased repo rate long before the actual change happens. Since the repo rate impact the market rates, monetary policy has a real effect on total demand (Riksbanken, 2020).
The interest rate channel is in line with theory from the IS-LM model, lower interest rates typically induce consumption. When interest rates are low the willingness to save is low since the payoff is low from interest bearing assets, loans are also cheaper thus boosting spending
further and lower interest rates means that financial assets and real assets increase in value, creating an array of stimulation to boost consumption (Riksbanken, 2020).
The credit channels are affected by monetary policy in such way that the demand from banks and other financial institutes can be affected from increasing asset values, since the bank derive these assets as collateral when issuing loans to households and companies. If these assets where to decrease because of increasing interest rates, the banks become more cautious when issuing new loans since the risk has increased. The increased risk induces the bank to increase the interest margins or tighten the conditions and restrictions when lending to the households and companies. The credit channel can amplify the effect repo rates have on demand (Riksbanken, 2020).
The exchange rate channel is affected by monetary policy in the way that when interest rates are reduced the currency is expected to depreciate due to reduced demand of the domestic currency. Lower interest rate makes domestic assets less attractive thus reducing the exchange rate. A deprecating currency boost export since domestic goods are cheaper but on the other hand reduces import since foreign goods are more expensive (Riksbanken, 2020).
2.4 Hypothesis
The goal is to investigate the potential impact repo rates have on aggregated private consumption. Our hypotheses are based on the IS-LM framework. The IS-LM model suggest that interest rates such as the repo rate should have significant impact on the consumption with a negative relationship. Thus, we have the following hypotheses.
H0: Repo rate has no significant negative relationship with private consumption from 1995-2019 in Sweden.
H1: Repo rate has a significant negative relationship with private consumption from 1995-2019 in Sweden.
In the data set from the first regression negative interest rates appear in certain periods. For further investigation we estimate the same regression but isolate the periods with negative interest rate with a dummy variable. This method allows us to investigate the impact negative repo rates could have on consumption using the same data and the same estimated model from our main regression. The Swedish central bank claims that the negative repo rate has had an expansionary effect in Sweden during the period with negative rates (Riksbanken, 2019). Thus, we generate a second hypothesis.
H0: There is not a significant difference between negative repo rates and positive repo rates on private consumption in Sweden 1995-2019.
H1: There is a significant difference between negative repo rates and positive repo rates on private consumption in Sweden 1995-2019.
3. Data and Control Variables
This section exhibits how data of explanatory variables from 1995 to 2019 is collected to analyze the dependent variable private consumption. In this thesis time series data will be used, descriptive statistics are presented below.
The choice of data is dictated by the variables from the consumption function from the IS-LM model, presented in section 2 Equ. (2). As mentioned above consumption is a function of income, expected income, interest rate, inflation, and wealth. The data stretches from 1995 to 2019, since the data have the time unit of quarterly data the observation set is quite small. The argument for why the observations start in 1995 is mainly based on data availability and it allows the data set to reach 100 quarterly observations. Central limit theorem should apply at 30 observations (Anderson & et al, 2017). The time period 1995 to 2019 also captures a period before the financial crisis where the repo rate was high compared to the time period after 2008, where the repo rate was drastically cut to ultra-low level and at some quarters even negative rates. In order to connect the IS-LM model the general form developed to a specific function form of the consumption function. The specific function from is depicted in Equ. (6) (Gottfries, 2013):
Ct = a0 + a1Yt + a2Yet - a3(i-πe)t + a4At (6)
The merit of using Equ. (6) as a measure stick is that the linear relationship of different regressors towards consumption can be observed, hence see if the independent variables should have positive or negative relationship towards consumption based on the sign of the coefficient. Given the specific function form we can connect the data to each variable.
Dependent Variables
The dependent variable in the data set is private consumption collected from the national accounts that can be found in the official database from statistics Sweden (SCB, 2020). This variable represents the consumption denoted C in Equ. (6). The data is presented in the form of volume change from the corresponding quarter from last year in percent. More descriptive statistics of private consumption can be found in table A4 in the appendix.
Independent Variables
Repo rate is the main explanatory variable in this study and this variable represents the interest rate denoted i in Equ. (6). The repo rate is collected from the Swedish central banks data base. The data can be collected in daily, weekly, monthly, quarterly, and yearly time units. Quarterly data was chosen to keep the time unit homogenous; this decision was dictated by the data availability from the other variables that is derived from the national accounts (Riksbanken Database, 2020). The repo rate is presented in percent. In Equ. (6) the sign is negative; hence we expect repo to have a negative relationship with the dependent variable. This expectation is in line with theory. More descriptive statics of the variable repo can be found in table A4 in the appendix.
Income denoted Y in Equ.(6) is derived from GDP and is collected from the national accounts that can be found in the official data base from statistics Sweden (SCB, 2020). The data is presented in the form of volume change from the corresponding quarter from last year in percent. In Equ. (6) the sign for income denoted Y is positive; hence we expect income to have a positive relationship with the dependent variable private consumption. This expectation is in line with theory. More descriptive statistics can be found in table A4 in the appendix.
Inflation denoted π in Equ. (6) is derived from CPIF with fixed interest and is collected from the official data base from statistics Sweden (SCB, 2020). The available data on statistics Sweden is presented as monthly data in percent, to keep the time unit homogenous the data have been aggregated up to quarterly data in percent. In Equ.(6) the sign for inflation is positive; hence we expect inflation to have a positive relationship with the dependent variable private consumption. This expectation is in line with theory. More descriptive statistics can be found in table A4 in the appendix. The inflation data proved to be non-stationary hence we have applied the differentiation method to achieve stationarity. Wealth denoted A in Equ.(6) also referred to as savings is derived from household net savings in millions, this data proved to be non-stationary, hence the net savings data have been transformed or manipulated with the differentiation method to make the data stationary. The transformation allows us to present the data as volume change from the corresponding quarter from previous year. After the transformation, the data is considered stationary. Stationarity test is presented in the method section, see ADF table 5 in the appendix. The data is collected from statistics Sweden (SCB, 2020). In Equ. (6) the sign for savings is positive; hence we expect savings to have a positive relationship with the dependent variable private consumption. This expectation can be interpreted further and will be discussed in the analysis section. More descriptive statistics can be found in table A4 in the appendix.
Expected Future Income
Consumption should be affected by expected future income as seen in Equ. (6). The empirical model presented in the method section dose not account for the expected future income variable, thus we are actively committing omitted variable bias. The bias will directly impact the explanatory aspect of our model in a negative way. The reason of this omitted variable bias is based on the complexity of finding a suitable variable that can accurately project expected future income. By including variables that may not reflect the impact of expected future income could be more damaging than just recognizing the limitation of our regression.
4. Methodology
In this section we will present our structure and methodology for our empirical work. First, we will investigate the correlation with the help of a correlation matrix. Following the correlation tests, we will check for stationarity and optimal lag length since we have timeseries data. After the stationarity test and optimal lag length determination we can estimate our model. The estimated model produces a result and a diagnostic test that is collected and analysed. The diagnostic test will determine if our time-series model violates any critical assumptions for classical ordinary least square model.
4.1
Correlation-Matrix
A correlation matrix will be used to summarize data better. Correlation matrix is a table illustrating the correlation of coefficients of all variables in the regression. Every single cell in the Correlation Matrix clearly display the correlation of a pair of variables. Correlation between variables is important to investigate because of the risk of a multicollinearity problem in the estimated model. Multicollinearity and variance inflation factors will be presented in the method section. In table A5 we can view the correlation matrix based on all variables used in this study. The most notable correlation in the table is private consumption and repo with a correlation value of –0.23663 and private consumption and income with a correlation value of 0.2714, both are statistically significant. Due to the relatively high correlation compared to the other variables testing for multicollinearity is relevant (Gujarati, 2003).
4.2 Stationarity
When dealing with time series data it is assumed that the underlying time series data is stationary. In time series analysis autocorrelation is likely to appear since the data “follows a natural ordering over time” by ensuring that the underlying variables are stationary the assumption of time series analysis can be satisfied. Autocorrelation indicates the degree of correlation between the different values in the same variable across different observations across time, however autocorrelation can still appear in the time series analysis, but the cause is unlikely to be from stationarity issues.
The non-stationary time series data set have the following characteristics: the means of random variables in the time series change over time, the variances of random variables in the series change over time and the covariances between any two random variables in the series change over time. To achieve weakly stationarity, let Ct be a stochastic time series, let k be the order of lag, let γ and σ2 each refer to constant number. The data should take the form E(Ct) = µ < ∞ for all t, meaning that the mean of the random variables in the series are all equal for all t. Var(Ct) = σ2 < ∞ for all t, meaning that the variance of the random variable in the time series are equal. Cov(Ct, Ct+k) = γk(γ0 = σ2) for all t and k, meaning that the covariance of any two random variables Ct, Ct+k in the in the time series depend on the distance between two time points according to the chapter about stationary stochastic processes (Gujarati, 2003). If the stationarity of a data set is not satisfied, the data have issues with autocorrelation and heteroscedasticity. This makes the set of data unpredictable and hard to run a regression (Gujarati, 2003).
To test the stationarity of the data set an augmented Dicky-fuller test or a (unit root test) is conducted. The derivation process of augmented Dicky-Fuller test starts with an auto regressive model denoted AR(1): Ct = β1 + ρCt−1 + ut with a null hypothesis ρ = 1(ρ>=1), if the null hypothesis is true the data set is nonstationary, otherwise the alternative hypothesis ρ < 1 is true, which means the data set is stationary. By deducting Ct-1 on both sides of the equation, ∆Ct = β1 + δCt−1 + ut will eventually be obtained where δ = ρ-1, with the null hypothesis: δ = 0 and alternative hypothesis: δ < 0. If the null hypothesis is not rejected, the data set will be non-stationary, otherwise if the null hypothesis is rejected stationarity in the data set can be concluded (Gujarati, 2003).
The first ADF tests we ran on our data set proved that the data describing the variables; private consumption, repo rate and income was stationary without any data manipulation as seen in table 3, 4, 1, respectively. Inflation and savings proved to be non-stationary according to the very first ADF tests, hence in order to use inflation and savings in the time series we need to manipulate the data, how each variable have been manipulated is presented in the data and control variables section 3. In table 2 and 5 the data has been manipulated before the ADF test were computed. After the necessary data manipulation, the result from all the ADF tests suggest that all variables are stationary as presented in the next segment. We have run several ADF test to control for stationarity and are presented in the following tables 1, 2, 3 and 4 in the appendix section. In table 1 the result of Augmented Dicky fuller test of income data set is presented. The null hypothesis for this test is Income and has a unit root (Income data set is nonstationary) and the alternative hypothesis for the test is Income does not have a unit root. From table 1, the p-value for income is 0.0369, which is smaller than 5% significance level. Hence, Income does not have a unit root and the data set of income is stationary.
Augmented Dicky-fuller test of income
t-statistic P-value ADF test statistic -2.076376** 0.0369 1% level -2.589531
5% level -1.944248 10% level -1.614510 Notes: *significant at 10%, **significant at 5%, ***significant at 1%
In table 2 the output of Augmented Dicky fuller test of inflation data set is presented. The null hypothesis for this test is Inflation has a unit root (Inflation data set is nonstationary) and the alternative hypothesis for the test is Inflation does not have a unit root (Inflation data set is stationary). From table 2, the p-value for inflation is 0.0000, which is smaller than 5% significance level. Hence, inflation does not have a unit root and the data of inflation is stationary.
Augmented Dicky-fuller test of inflation
t-statistic P-value ADF test statistic -8.865496*** 0.0000 1% level -2.588530
5% level -1.944105 10% level -1.614596 Notes: *significant at 10%, **significant at 5%, ***significant at 1% (Table 2: ADF test of inflation)
In table 3 the output of Augmented Dicky fuller test of private consumption data set is presented. The null hypothesis for this test is private consumption has a unit root (Private consumption data set is nonstationary) and the alternative hypothesis for the test is Private consumption does not have a unit root (private consumption data set is stationary). As table 3 illustrates, the p-value for private consumption is 0.0073, which is smaller than 5% significance level. The null hypothesis will be rejected, hence private consumption data set is stationary.
Augmented Dicky-fuller test of private consumption
t-statistic P-value ADF test statistic -2.701169*** 0.0073 1% level -2.588772
5% level -1.944140 10% level -1.614575 Notes: *significant at 10%, **significant at 5%, ***significant at 1% (Table 3: ADF test of private consumption)
In table 4 the output of Augmented Dicky fuller test of Repo rate data set is presented. The null hypothesis for this test is Repo rate has a unit root (Repo rate data set is nonstationary) and the alternative hypothesis for the test is Repo rate does not have a unit root (Repo rate data set is stationary). In table 4, p-value for Repo rate equals to 0.0014. The number is smaller than 5% significance level. The null hypothesis can be rejected. Therefore, Repo rate data set is stationary.
Augmented Dicky-fuller test of Repo
t-statistic P-value ADF test statistic -3.243899*** 0.0014 1% level -2.588772
5% level -1.944140 10% level -1.614575 Notes: *significant at 10%, **significant at 5%, ***significant at 1% (Table 4: ADF test of Repo rate)
In table 5 the output of Augmented Dicky fuller test of Savings data set is presented. The null hypothesis for this test is Savings has a unit root (Savings data set is nonstationary) and the alternative hypothesis for the test is Savings does not have a unit root (Savings data set is stationary). The p-value observed from table 5 is 0.0000. Which is smaller than 5% significance level. Hence, null hypothesis can be rejected, the result of savings data set is stationary can be concluded.
Augmented Dicky-fuller test of Savings
t-statistic P-value ADF test statistic -5.907794*** 0.0000 1% level -2.588772
5% level -1.944140 10% level -1.614575 Notes: *significant at 10%, **significant at 5%, ***significant at 1% (Table 5: ADF test of Savings)
4.3 Choosing Lag Length
If a time series model has lags in the independent variables the model is known as a distributed lag model. There is also the possibility that the dependent variable can be lagged among the explanatory variables and this type of model is known as autoregressive model. According to Guajarati (2003), there are three main reasons for including lagged values of explanatory variables and regressors in the model: Psychological reasons, Technological reasons, and Institutional reasons. Using lags in a time series model can make economic sense if the explanatory variables tend to show economic impact in a later stage, thus one may include lags if the lag makes sense and are statistically justified (Gujarati, 2003). If the lag length is unclear or unknown the probability of running the most efficient regression is reduced. The first option that was considered for testing the most optimal lag structure was the Akaike Information Criterion (AIC). This method was applied and compared with the ad-hoc approach. The AIC approach suggested that certain lag lengths generated significant results, but the sign of the coefficient shifted randomly. In the process of determining the lag length for our estimated model we chose to drop the AIC approach due to the instability of sign shifts and continued with the ad-hoc approach. To control that the estimated model is estimated with the most optimal lag the sequential OLS regression method will be applied. The intuition of sequential OLS method is that we run reduced models where only one variable is checked towards the dependent variable. The first sequence starts with lag k=0 after which, higher order lags will be added with incremental steps of k=n+1, where n is the previous lag order of k. The sequence will stop when the coefficient changes sign or when the variable becomes insignificant at the chosen significant level.
If the coefficient shift sign during the sequential test the problem of justifying economically a relationship change could prove to be hard or illogical. If these lags always remain significant and the sign of the coefficient never shift there might never be a natural break in the sequence, thus the risk of data mining problem is increased. Data mining can cause problems, since for every sequence the regression loses degrees of freedom, thus the effective sample size will be reduced. Other drawbacks of sequential OLS regression
method can cause multicollinearity due to lags in the model and multiple testing problems (nominal vs true level of significance) (Gujarati, 2003).
We have run several sequential OLS tests and the test result is presented in table A11, A12, A13 and A14 in the appendix. In table A11, it can be observed that when the first lag enters, the coefficient of Income t-1 changes sign. Thus, adding lag to the income variable in the model will be inefficient. The change in sign could be due to severe multicollinearity leading to unstable estimates. Hence, the lag order of 0 would be preferred. In table A12, it can be observed that when the first lag enters, the coefficient of the variable inflation t-1 is insignificant at a 5% significance level. Thus, adding lag to the inflation variable in the model will not be optimal. The insignificance of the coefficient of the variable t-1 could be caused by severe multicollinearity leading to unstable estimates. Hence, the lag order of 0 would be preferred. In table A13, it can be observed that when the first lag enters, the coefficient of Repo rate t-1 changes sign. Thus, adding lag to the Repo rate variable in the model will be inefficient. The change in sign could be due to severe multicollinearity leading to unstable estimates. Hence, the lag order of 0 would be preferred. In table A14, it can be observed that when the first lag enters, the coefficient of Savings t-1 changes sign. Thus, adding lag to the savings variable in the model will be inefficient. The change in sign could be due to severe multicollinearity leading to unstable estimates. Hence, the lag order of 0 would be preferred. The test suggests that our estimated model should have no lags at all.
4.4 Estimated Model
The estimated model aims to replicate the consumption function from the IS-LM model where the theory states that the consumption is a function of income, expected income, interest rate, inflation, and wealth. The consumption function general form is presented in Equ. (2) in section 2. In the previous tests the conclusion stated that no lags should be added and that all variables are stationary according to the augmented Dicky-Fuller test. Based on these principles we have estimated the following least square model:
Private Consumptiont = 𝛽0 + 𝛽1Repot + 𝛽2Incomet + 𝛽3Inflationt + 𝛽4Savingst + 𝜀𝑡 (7)
In the data set of Repo there are periods with negative repo rates. By adding a dummy variable for these negative periods that is categorised as 1 will allow us to isolate the periods for when the repo rate is negative. Thus, generating a slight modification on the original regression:
Private Consumptiont = 𝛽0 + 𝛽1Repot + 𝛽2Incomet + 𝛽3Inflationt + 𝛽4Savingst + 𝛽5Dummyt + 𝜀𝑡 (8)
4.5 Diagnostic Test
In this section we will present our diagnostic tests on the estimated main model that ranges from 1995-2019. This section can only be investigating after the estimated model have been run and the residuals have been computed. The diagnostic test will determine the strength and weaknesses of our model and how well the model satisfy or violates the assumptions of classical linear time series model.
Normality
One of the assumptions in classical linear time series models is that the error terms are normally distributed. To be able to draw conclusions on the coefficients in the explanatory control variables normality must be accounted for. The test we run is a Jarque-Bera test, the test measures skewness and kurtosis. The residuals should have skewness and kurtosis of zero and three, respectively. In Fig 3 we can see that the skewness has the value -0.2227 and the kurtosis have the value 4.005, this is not equal to zero or three. However, the null hypotheses of this test states that the data is normally distributed and the alternative hypotheses states that the data is not normally distributed. Since the p-value is 0.0806 we do not reject the null hypotheses. The skewness and kurtosis do not indicate perfect normality but at the 5% significance level we assume that it is a minor violation (Gujarati, 2003).
(Fig 3: histogram normality test)
Variance Inflation Factors
Multicollinearity occurs when two explanatory variables in a multiple linear regression have a non-zero correlation, in other words, if two explanatory variables are correlated with each other, there will be a multicollinearity problem. Multicollinearity violates the assumption of classical OLS regression model, and it is biased to estimate the model.
Variance inflation factor (VIF) is a method that estimates to what extent the variance of a coefficient estimate is inflated due to linear dependence with other independent variables. VIF is one of the methods to detect the multicollinearity problem in one regression. According to Gujarati (2003), the VIF has a lower bound of 1 while there is no upper bound for VIF. If VIF is exactly equal to 1, there will be no multicollinearity problem. Based on Gujarati, a severe multicollinearity problem will be detected if VIF is greater than 10. The square root of the variance inflation factor exhibits how much larger the standard error is compared with the standard error in the situation where the variable is uncorrelated with other explanatory variables in the model (Gujarati, 2003).
In table 6, the VIF statistics for Repo, Income, Inflation and Savings are 1.0321, 1.0374, 1.0109 and 1.0151, respectively. Since all VIF statistics are close to 1.0 we can conclude that there is no severe multicollinearity problem in the estimated model.
Variance Inflation Factors Sample:1 100
Included observations: 100
Variable Coefficient Uncentered Centered Variable VIF VIF C 0.069599 3.047296 NA REPO 0.004636 2.144733 1.032062 INCOME 0.004465 2.344790 1.037490 INFLATION 0.003154 1.033520 1.010890 SAVINGS 0.005683 1.015547 1.015133 (Table 6: Variance inflation factors table, multicollinearity test)
Breusch-Pagan-Godfrey
Extreme outliers, misspecification in the estimated model and skewness in the distribution of the explanatory variables in the data set can cause heteroscedasticity. If the variance of the residuals is equal in the variance spread, one may conclude that the empirical test satisfies the homoscedasticity assumption. If the variance of the residuals is equal to a non-constant spread the empirical test is considered to suffer from heteroscedasticity problem. Homoscedasticity is one vital assumption of classical linear regression model (CLRM) if heteroscedasticity violates one of the assumptions of CLRM the probability that the ordinary least square will no longer be best linear unbiased estimator. To control that the estimated model has equal spread in the variance to satisfy the homoscedasticity assumption a Breusch-Pagan-Godfrey test is conducted.
The Breusch-Pagan-Godfrey test is one option to test the data for heteroscedasticity. The null hypothesis of the test states that the variance of the residuals should be equal to a constant variance number and the alternative hypothesis states that the variance of the residual should equal to a non-constant variance number. From table 7, the p-value equal to 0.2904 is obtain. 0.2904 is greater than a 5% significance level, hence null hypothesis cannot be rejected. The residuals equal to a constant variance hence we have homoscedasticity.
Heteroskedasticity Test: Breusch-Pagan-Godfrey Null hypothesis: Homoskedasticity
F-statistic 1.262144 Prob. F(4,95) 0.2904 Obs*R-squared 5.046126 Prob. Chi-Square(4) 0.2826 Scaled explained SS 6.842755 Prob. Chi-Square(4) 0.1444
Autocorrelation
In time series data, an autocorrelation problem occurs if the residual term of explanatory variable is dependent on the residual term of any other regressors. The Durbin Watson test can control for autocorrelation in empirical work. The null hypothesis states that the residuals time series data are not correlated (No autocorrelation) against an alternative hypothesis that the residuals of time series data are correlated (Autocorrelation exists). There are there possible outcomes in the Watson test statistic. When the Durbin-Watson statistic equals to 2 there is no autocorrelation in the time series data and the null hypothesis cannot be rejected. When the Durbin-Watson statistic ranges from 0 to 2 we have positive autocorrelation, the severity of auto correlation increases when the value approaches 0. If the order is reversed, that the test statistic ranges from 2 to 4 the time series data suffers from negative autocorrelation, the severity increases if we are closer to the value 4.
As table 8 from the analysis part illustrates,the Durbin Watson statistic is 1.2433. The value 1.2433 falls into the range between 0 and 2. Hence the null hypothesis of Durbin Watson test is rejected, and one can conclude that the data suffers from positive autocorrelation in the residuals of the time series. Implications of auto correlation is discussed further in limitations and weaknesses in section 5.1 and 5.3.
(Table 8: Durbin-Watson Test Range (Gujarati, 2003))
5. Results and Analysis
In this section we will present the result from our empirical models stated in Equ.(7) and Equ.(8). First, we will present and discuss the estimated result from the test that covers the periods 1995-2019. Secondly, we will investigate the estimated result when we have included a dummy variable in the model that isolate the periods when the repo rate is negative (below the zero-lower bound). We will also analyse limitations and weaknesses in our study. And finally, we present additional results from tests that are relevant but lacks a degree of unbiasedness. This test is like the main model but instead of using the repo rate as interest rate this model uses markets rates from large banks and other large financial institutions. Note that the additional empirical tests have not been as strictly tested as compared to our main results, hence this result is inappropriate to draw any conclusions from but rather serves as an additional reference.
5.1
Estimated Results
Estimated result 1995-2019
Dependent Variable: PRIVATE_CONSUMPTION Method: Least Squares
Sample: 1 100
Included Observations: 100
Variable Coefficient std. Error t-statistic C 1.454692*** 0.263816 5.514048 REPO -0.318324*** 0.068092 -4.674942 INCOME 0.252578*** 0.066819 3.780009 INFLATION -0.026247 0.056157 -0.467349 SAVINGS -0.073103 0.075386 -0.969716 R-squared 0.250544 Mean dependent var 1.349000 Adjusted R-squared 0.218988 S.D. dependent var 1.710071 S.E. of Regression 1.511273 Akaike info criterion 3.712489 Sum squared resid 216.9750 Schwarz criterion 3.842747 Log likelihood -180.6244 Hannan-Quinn criter 3.765207 F-statistic 7.939647 Durbin-Watson stat 1.243255 Prob(F-statistic) 0.000014
Notes: *significant at 10%, **significant at 5%, ***significant at 1% (Table 9: Result from main estimated time series model)
As seen in table 9 the coefficient of repo rate is recorded to be –0.3183 and the p-value is 0.0000, the coefficient appears to be statistically significant at the five percent significance level. According to the beta coefficient of the repo rate variable, the sign and value suggest that there is a negative relationship between private consumption and repo rate. In the theoretical framework section 2, neo classical macro theory states that there should be a negative relationship between interest rates and private consumption. Hence the repo rate variable appears to be in line with theory. The beta coefficients are in level and have the value of –0.3183 would suggest that a one unit increase in the repo rate would lead to a 0.3183 unit decrease in private consumption. However, the coefficients value will not be vital in our conclusion since we recognize that the model can produce misleading results. From the diagnostics test we know that the model suffers from positive autocorrelation. Autocorrelation appears frequently in time series data and the estimated model in this thesis is developed from time series data. When autocorrelation is present the error terms in the regression model are no longer independent. Uncontrolled autocorrelation could cause the parameter estimate to be biased. The consequence of autocorrelation will eventually make the hypothesis testing unreliable. The R-square is 0.2505 hence the fit would suggest that the independent variables explain the variations in the dependent variable by roughly 25% (Gujarati, 2003).
In table 9 the coefficient of income is recorded to be 0.2526 and the p-value is 0.0000, the coefficient appears to be statistically significant at the five percent significance level and the one percent significance level. According to the beta coefficient of the income variable, the sign and value suggest that there is a positive relationship between income and private consumption. In the theoretical framework section 2, neo classical macro theory states that there should be a positive relationship between income and private consumption. Hence the income variable appears to be in line with theory. The coefficient of inflation is recorded
to be -0.0262 and the p-value is 0.6413 the coefficient appears to be statistically insignificant at the five percent significance level. According to the beta coefficient of the inflation variable, the sign and value suggest that there is a negative relationship, however the variable is insignificant according to the p-value, thus it is not meaningful to further interpret the sign of the coefficient. The parameter estimate is insignificant, one explanation could be that the variables repo rate and income are highly intercorrelated with private consumption, as seen in the correlation matrix in table A5 in the appendix. Intercorrelation between explanatory variables are called multicollinearity. In our diagnostic test we conducted a variance inflation factors, the test suggested that there should not be a multicollinearity problem, however a single tests dose not per definition ensure absolute certainty. Another risk is that the variable is redundant. The empirical model is derived from the IS-LM consumption function where the theory states that the inflation variable is the expected inflation and not the actual inflation, which we use as a proxy variable and this could be a problem since predicting the future inflation would require forecasting models. The coefficient of savings is recorded to be -0.0731 and the p-value is 0.3347 the coefficient appears to be statistically insignificant at the five percent significance level. Since the savings variable is not significant it does not make sense to interpret the sign of the coefficient. Savings might also suffer from the correlation problem and redundancy as mentioned above. Another issue could be caused based on how the IS-LM model exactly specify wealth. The savings variable is based on actual household savings in millions of SEK, however we could suffer from omitted variable bias. The omitted variable bias could be in the form of omitting certain assets that is not captured in the net savings.
The null hypothesis stated that the repo rates have no significant negative relationship with private consumption from 1995-2019 in Sweden. And the alternative hypothesis stated that repo rate has a significant negative relationship with private consumption from 1995-2019 in Sweden. Since the p-value for repo is 0.0000 we reject the null hypothesis and conclude that repo rate has a significant negative relationship with private consumption from 1995-2019 in Sweden.
5.2 Estimated Results NIR
Dependent Variable: PRIVATE_CONSUMPTION Method: Least Squares
Sample: 1 100
Included Observations: 100
Variable Coefficient std. Error t-statistic C 1.523022*** 0.334440 4.553944 REPO -0.336079*** 0.086537 -3.883660 INCOME 0.254652*** 0.067419 3.777176 INFLATION -0.025973 0.056427 -0.460295 SAVINGS -0.074362 0.075834 -0.980590 DUMMY -0.160938 0.480358 -0.335037 R-squared 0.251438 Mean dependent var 1.349000 Adjusted R-squared 0.211621 S.D. dependent var 1.710071
Log likelihood -180.5648 Hannan-Quinn criter 3.794557 F-statistic 6.314812 Durbin-Watson stat 1.245995 Prob(F-statistic) 0.000043
Notes: *significant at 10%, **significant at 5%, ***significant at 1% (Table 10: Estimated Model with dummy variable)
In table 10 the coefficient of repo rate is recorded to be –0.3361 and the p-value is 0.0002, the coefficient appears to be statistically significant at the five percent significance level. According to the beta coefficient of the repo rate variable, the sign and value suggest that there is a negative relationship between private consumption and repo rate. This is in line with what the main regression suggests. Hence the repo rate variable appears to be in line with theory. The beta coefficients are in level and have the value of –0.3361 would suggest that a one unit increase in the repo rate would lead to a 0.3361 unit decrease in private consumption. As mentioned in the main regression the coefficients value will not be vital in our conclusion since we recognize that the model can produce misleading results. The model in table 10 is based on main regression, thus we assume that the dummy-model also suffers from positive autocorrelation, the issues regarding positive autocorrelation is mentioned above. The R-square is 0.2514 hence the fit would suggest that the independent variables explain the variations in the dependent variable by roughly 25% (Gujarati, 2003).
As seen in table 10 the coefficient of income is recorded to be 0.2547 and the p-value is 0.0003, the coefficient appears to be statistically significant at the five percent significance level. According to the beta coefficient of the income variable, the sign and value suggest that there is a positive relationship between income and private consumption. This relationship could also be seen in the main regression; hence the result suggests that this income variable follows predicted neo classical theory. The coefficient of inflation is recorded to be -0.0260 and the p-value is 0.6464 the coefficient appears to be statistically insignificant at the five percent significance level. According to the beta coefficient of the inflation variable, the sign and value suggest that there is a negative relationship between inflation and private consumption. However, the coefficient is insignificant thus there is little meaning to further analyse the sign. This discovery was found in the main regression where we discuss potential reasons for the insignificant result. The coefficient of savings is recorded to be -0.0744 and the p-value is 0.3293 the coefficient appears to be statistically insignificant at the five percent significance level. The same discovery was found in the main regression where we discuss potential reasons for the insignificant result. The coefficient of the dummy variable is recorded to be -0.1609 and the p-value is 0.7383 the coefficient appears to be statistically insignificant at the five percent significance level. The dummy variable is included for the interest of investigating whether negative repo rate is different from positive repo rate on the private consumption level. As a p-value of 0.7383 suggests rejecting the null hypothesis in section 2 is not proper. Thus, this result suggest that the negative repo rate is not different from positive repo rates on private consumption in Sweden from 1995-2019.
5.3 Limitations and Weaknesses
According to Durbin Watson statistic the empirical model suffers from some degree of positive autocorrelation. The weakness of the model with positive autocorrelation is that the error term is dependent on each other over time. In Gujarati (2003), it is suggested that autocorrelation can cause the standard errors of OLS estimates misleading,
and that hypothesis testing might become unreliable (Gujarati, 2003). Since positive auto correlation is present, we must recognize that this is a weakness in our empirical model. Hence one must be aware that the estimate can produce misleading information.
Aggregation bias could possibly be a weakness in this study. The selection of the time unit of the data is often dictated by data availability. The data used in this study was primarily only available in the time unit of quarterly data. To keep the time unit homogenous some variables have been manipulated to be presented as quarterly data. Specifically, data that that was only available with the time unit of monthly data have been aggregated to quarterly data. By aggregating data, one may fail to account for heterogeneity within the model which means that by aggregating data some information is lost. This loss of data may result in reduced accuracy of forecasting and estimation (Moody's Analytics, 2016). To elaborate further we conducted some tests where we could see that the aggregated data point did not match any of the data points from the monthly data since the quarterly data is just the average from the monthly data, thus one can clearly observe that the aggregation method does not capture heterogeneity in the data set. It is also important to recognize that the data that was only available in quarterly data from statistics Sweden also suffers from aggregation bias, since in the end the economy is made up from a large amount of micro decisions, hence looking at an aggregated macro perspective we can only capture general trends in the economy (SCB, 2020).
Central limit theory states that when the number of data points in the variables are large these variables may follow a normal distribution. A general rule suggest that the sample size should be equal or larger than 30 data points. At this level, the normal distribution is still not very smooth. The data used in this thesis are chosen from year 1995 to 2019 based on data availability and allowing us to size up the data set. Using yearly data would have not satisfied the general rule to achieve central limit theory, thus quarterly data is a better alternative (Montgomery, 2014). However, the data set in this thesis is still quite small at 100 observations. We have tested for normality in the data set and according to the Jarque-bera test we have normality thought the graphical representation is still not smooth. More data means more information hence we recognize that 100 observations are sufficient but could be a limitation in producing more accurate estimates.
If one or more relevant variables which can determine the regressor are not included in the regression model, there will be an omitted variable bias. We suspect that our model suffers from some degree of omitted variable bias, since we could not capture expected future income in our time series data. There is also the possibility that the model suffers from unknown omitted variable bias, meaning that we have failed to include unknown explanatory variables. The model in the thesis is derived from the consumption function of the IS-LM framework. As mentioned above it is believed that there might be some other determinant independent variable that are not included on a scientific perspective, hence one weakness of the selected model is omitted variable bias (Howland, 2006).
5.4 Additional Empirical Tests Using Market Rates
The following test should be viewed as additional tests where we connect stated theory with the additional test results. These tests have not been filtered, structured, and analysed in the same manner as the main regressions. We will not discuss diagnostic tests and limitations regarding these models since they are supposed to provide a foundation for further discussion. We find it also quite interesting to include this section to see the difference between market rates and repo rates. However, since this test is to some degree biased, we choose not to draw any conclusions.
The theory section explains how the repo rate affects markets rates according to the Swedish central bank. We also know that the repo rate is a reference rate to the interbank rate STIBOR. Thus, consumers are not directly affected by the repo rate since consumers interact with market rates directly. Market rates however is expected to be directly affected by the repo rate (Riksbanken, 2020). From our data set we can plot the time series data of repo rate and market rates in Fig A15. Fig A15 graphically exhibits that repo rate and market rates follow the same trend. This is in line with what the Swedish central bank suggests. In table A16 we ran a multiple linear regression where we investigate the significance level also, thus we have both some graphical representation and a statistical representation that supports what the Swedish central bank suggests. If we assume that the defined market rate is directly affected by the repo rate, we could substitute the repo rate with market rates and run a regression based on the IS-LM consumption function using the same idea as the main regression in the methodology section. The results are presented in Table A17. Due to data shortage this time series data starts in 2008 quarter one and ends in 2019 quarter four. Every variable is statistically significant. The sign relationship dose not match what the IS-LM suggest. The R-square is 50% which is twice as high from the main regression.
6. Conclusions
Sweden and other developed countries have seen declining repo rates and relatively low inflation in the new millennium (Jobst & Lin , 2016). The decline in repo rates have led to some debates in the economic community on whether low rates are a problem or not. After the financial crisis in year 2008 many countries applied a wide array of quantitative easing that was initially aimed to stimulate the economy (White, 2019). Quantitative easing has also been applied in the most recent economic shock namely the covid19 pandemic to mitigate economic damage (Riksbanken, 2020).
The main test conclude that repo rate does have significant negative impact on private consumption. Our result is line with classical theory. Though there are weakness with the empirical model the result illustrates that repo rates from 1995 to 2019 has a significant impact on the private consumption in the relative years in Sweden. The findings are in line with classical theory such as the IS-LM theoretical framework. In William Whites conference notes regarding the effects of ultra-low interest rates on banks and the economy, there are concerns about the unintended or unknown consequences of long-term wide adoption of negative interest rates. Such as reduced efficiency for stimulating the economy and increased lending and borrowing causing instability in the financial markets (White, 2019).
Given the significant results in the first test we wanted to control for the periods where the repo rate shift from positive to negative. This method would allow us to see if the result would change. However as seen in the result segment we saw that even if we isolate periods with negative interest rates the repo rate is still significant and retain the predicted relationship as suggested from classical theory. Due to limitations in the model we are not drawing any specific conclusions, however if these results where to be true we could see that negative repo rates possesses the same properties as positive repo rates which contradicts the hypotheses drawn in William Whites notes in favour of neo classical theory. An article from the economist suggest that negative interest rates have been a success for Sweden and that there seems to be an “irrational fear of negative interest rates”. The article further suggests that the demand for increased interest rates might be coming from the public that is either uneducated in the matter or fear that lower interest rates might weaken the domestic currency (The Economist, 2019). Our test focuses on private consumption thus negative interest rates might not be so different from positive interest rates when we are specifically analysing domestic consumption. Though negative interest rates might have effects in other places in the economy such as domestic currency making import more expensive or increased journeys abroad. According to the empirical results of this paper there seems to be no deviation from neo-classical theory. The effect repo rates have on private consumption seems to behave as expected from classical theory whether the rate is positive or negative. According to our results the evidence point to that negative interest rate policy is indifferent from any other policy change with positive interest rates. We must remember that this would only apply to private consumption, hence negative interest rate policies can still have significant impact on other places in the economy, such the domestic currency as discussed above.
In this study we fail to obtain the expected income variable due to the complexity of accurately forecasting future expected income. This is the main reason why the model has the occurrence of omitted variable bias. For future study, a proper method to capture the expected future income is preferred. By including the expected future income variable, a more precise regression output is expected. As discussed in the weakness and limitation part, relatively small sample size is one of the weakness in the thesis. It is recommended that using a larger sample size to obtain a more accurate output result could provide more insight, hence in the future there might be more data available to conduct a similar study but with a greater number of data points that would represent this new era of low interest rates. In IS-LM model, wealth is suggested to be one explanatory variable for private consumption. However, in the thesis, aggregated account savings in millions are used as a proxy variable to replace the wide definition of wealth. In deep consideration, account savings is just one variable of wealth. Wealth is more than just account savings, it includes other assets such as real estate, ownership of cars, stocks, and other securities. These parameters are not included in the regression model due to complexity, but we want to highlight the consideration that our proxy variable for wealth might be too weak. Thus, this is also a form of omitted variable bias. Using only savings as a proxy to wealth might be one reason the savings variable turned out to be insignificant in the estimated model. In a future study a more detailed proxy to wealth should be included for better and more precise analysis.
