Page | 1
EMPIRICAL ANALYSIS OF THE DOMESTIC SAVING
BEHAVIOUR IN R
WANDA
.
Joseph BASABOSE
Master thesis, 15 Credits MASTER OF ECONOMICS
Page | 2
Abstract
This study examines the relationship between gross domestic savings, exports of goods and services, foreign direct investment, population growth rate, final expenditure, and gross domestic income in Rwanda for the period that stretches from1988-2018. The Johansen co-integration test indicated the presence of a co-integrating relationship between variables. Furthermore, the VECM coefficients revealed that there is a positive significant relationship between gross domestic product, exports, and foreign direct investment and gross domestic savings, but final expenditure and the population growth affect the domestic savings negatively. On the other hand, in the short-run, the exports of goods and services affect domestic savings positively whereas income affects the domestic savings negatively but significantly. Also, the impulse response function results show that the final consumption expenditure can explain the major variations in saving growth in Rwanda.
Page | 3 Table of Contents
Abstract ... 2
1. Introduction ... 5
2. Literature Review... 7
2.1. The theoretical framework ... 7
2.1.1. The Keynesian Theory of Absolute Income Hypothesis. ... 8
2.1.2. Permanent income hypothesis ... 8
2.1.3. The life Cycle Theory of Consumption ... 9
2.1.4. The Random Walk Theory of Consumption ... 10
2.3 Empirical Literature Review ... 11
3. Overview of the Rwandan Economy ... 15
3. Data and Methodology ... 16
3.1. The data description ... 16
3.2. Methodology ... 20
3.2.1. Model Specification ... 20
3.2.2. Dickey-Fuller Test ... 22
3.2.3. Lag-Order Selection model ... 23
3.2.4. Johansen Cointegrating Test ... 23
3.2.5. Vector Error Correction Model (VECM) ... 23
3.2.6. Granger Causality for VECM ... 25
4. Results and Discussions ... 25
4.1. Unit root test ... 25
4.2. Long-run equation ... 27
4.3. Vector error correction model ... 29
Page | 4
4.4.1 Stability condition test for VECM ... 30
4.4.2 Lagrange multiplier ... 31
4.4.3. Normality test for VECM ... 31
4.5. Impulse Response Function ... 32
4.6. Forecasting with VECM... 34
4.7. Granger causality test for VECM ... 35
5. Conclusion ... 36
Page | 5
1. Introduction
Over the years of history, the savings behavior has been a subject-matter not only of macroeconomic concern but also of policy relevance. The theoretical and empirical literature provides compelling evidence suggesting that savings are a product of a constellation of several economic and demographic factors that are capable of engendering sustainable economic growth (Aremadu, 2009).
Many economists studied consumption and saving and explained the determinants of saving behavior. Firstly, some of the important theories related to consumption and savings are Keynesian consumption theory, lifecycle hypothesis (LCH), and permanent income hypothesis (PIH). The Keynesian consumption theory argues that if the disposable income is high, the domestic savings also will be high. Secondly, many empirical studies laid their emphasis on analyzing the determinants of saving ( Kudaisi, 2013), Adelakun (2015). Saving function or propensity to save relates to the level of saving to the level of income (Aremadu, 2009). It is the desire or tendency of the economic agents to save at a given level of income. Thus, saving is a function of income (Agrawal et al., 2010).
Since the independence of Rwanda, a low saving rate has been observed which has resulted in a low economic growth rate over time. The low saving rate reflects the consumption preference of all economic agents. Since Rwanda as a highly populated country relays on the people that continue having a high consumption rate, its policymakers failed to design effective policies to provide some incentives for savings so that it motivates individuals to change their consumption behavior. Also a lack of education and availability financial institutions facilities whereby people prefer to spend money on useless customs and traditions such as hoarding up until the year 2003 whereby Rwanda economy started a new strategic plan leading to growth known as Vision 2020. This set of economic policies intended to focus on increasing the domestic savings instead of relying on foreign aids and loans to sustain its economic growth by augmenting investment in physical and human capital (Uwizeyimana, 2019).
The World bank report 2020 entitled 'Future Drivers of Growth in Rwanda', showed that Rwanda's aspiration for upper-middle-income by 2035 and high income by 2050 calls for stretch targets for future growth rates. This will require average annual growth of above 10%. To reach
Page | 6 this target again, other important policies are likely to be implemented in form of continuous investment in education and innovation, high level of savings and investment, technological innovations towards competitiveness, political and social consensus on reforms, attracting FDI, and growing exports.
Rwanda has developed policies that guide its domestic resource mobilization effort, aiming at increasing the level of capital accumulation. While the country registered encouraging results overall in terms of total government revenue as a proportion of GDP, peaking at 24.1 percent in 2018, Rwanda recognizes the need to enhance domestic resource mobilization and sustain progress in both medium and long term (African Development Bank, 2010).
Few empirical studies are available in the literature on saving behavior of Rwanda. Even though, it is difficult to point out the exact factors responsible for the low saving rate in Rwanda. Most of the documents are reports from MINECOFIN, UNCTAD, Finescope, and World Bank. The common factor of all reports is the low level of savings in Rwanda and the lack of saving culture. The studies on savings suffered from weaknesses due to poor estimation techniques, to a short span of data, and the selection of irrelevant variables in their models (Iragena, 2015). This study is an attempt to bridge the research gap by analyzing the short and long-run causal relationship between the preselected factors of saving behavior in Rwanda.
The main objective of this study is to assess the performance of domestic saving and its determinants as well as to empirically investigate the short and long-run relationships among them in Rwanda. From 1988 to 2018, the domestic savings in Rwanda have been affected by preselected factors such as foreign direct investments, exports of goods and services, population growth rate, government expenditure, and gross domestic product in both the short and long-run. Moreover, to explain the empirical results found in this study, it is important to highlight the responses to domestic savings after different disturbances and shocks that would have affected predictor variables in this model.
For instance, after a traumatic shock known as the Rwandan genocide that devastated the whole sectors of activities in the country, the government of Rwanda formulated a set of policies known as Vision 2020 to boost up the economy. To transform this vision into reality, the government of Rwanda needed adequate investment where savings is a primary factor. Therefore, we need to
Page | 7 identify which factors contribute to the domestic savings in Rwanda. This study examines, from an empirical point of view, the determinants of domestic savings in Rwanda for the period 1988-2018.
Generally, saving behavior in Rwanda seems to be a new topic of interest, only a few types of research have been carried out since (see Byiringiro & Qian, 2017, Iragena, 2015). This study seeks to answer the following questions:
• What are the determinants of domestic saving in Rwanda?
• How do these factors affect the short and long run saving behavior of the Rwandan economy?
• Is there any causal relationship between domestic saving and its determinants?
This study is of great importance as it analyzes the relationship between the variables using econometric techniques, appropriate selection of time span, and the use of relevant variables in the estimation of the model. To assess the possible short and long-run relationship between domestic saving and its determinants, VECM was selected as a suitable approach in this study. VECM allows also investigating the short-run dynamics by Granger causality test and the long-run equilibrium relationships by analyzing the Impulse response functions. We have also to consider that, one such long-run relationship is captured by the error correction term known as the speed of adjustment (Cahyono et al., 2019).
The rest of the study is organized in the following manner: Section Two reviews the empirical literature on saving behavior and gives an overview of the Rwandan economy. Section Three presents data and model specification and contains econometric methodology. Section Four provides empirical results and discussions. Finally, Section five concludes.
2. Literature Review
2.1. The theoretical framework
Many economists had in the past studied the relationship between savings and economic growth. Particularly, they analyzed the factors that affect saving as a determinant of economic growth. While some of the studies were mainly theoretical arguments, others applied empirical statistical and econometric procedures (Schmidt-Hebbel & Salimano, 1994; Loayza and Hevia, 2012).
Page | 8 Thus, the findings helped to design a set of recommendations addressed to policymakers. So, the review of the previous literature serves to elaborate and to understand the determinants of saving at micro and macroeconomic levels of activities in both developed and developing countries. There are three main theoretical approaches to consumption and saving: Keynesian consumption theory, the life-cycle, and permanent-income hypothesis (Raut & Virmani, 1989).
2.1.1. The Keynesian Theory of Absolute Income Hypothesis.
According to Froyen (1998), Keynes in his theory argues that consumption is a key element in income determination. Based on the fundamental psychological law, men are disposed to increase their consumption as their income increases but not as much as an increase in their income. According to his psychological law, the Keynesian consumption function equals:
C =a + bYDa >0, 0 < b < 1 (2.1)
C is real consumption and YD is real disposable income, which is equal to GNP minus taxes. The
intercept is a, it measures the consumption at zero levels of income. The parameter b is the Marginal Propensity to Consume (MPC) which measures the increase in consumption per unit increase in the disposable income (𝛥C/𝛥YD). The ratio of consumption to income is termed as the
Average Propensity to Consume, which is written as follows
(2.2)
The APC is greater than the MPC, by the amount a/Y. Hence the APC declines as Income increases. This implies that as income of the households rises; they consume a small fraction of income, which means that their larger portion of income is saved. The Marginal Propensity to Save (APS) is a larger fraction of income equals (1-APC), or
APS=1-a/YD-b=-a/Y+(1-b) (2.3)
If the disposable income (YD) is equal to zero, saving is negative or very low, and generally, the
income-savings relationship is not proportional. The theory assumes that rich people save more than poor people, other things hold constant (Froyen, 1998).
2.1.2. Permanent income hypothesis
The permanent income hypothesis (PIH) is a post-Keynesian consumption theory, developed by Milton Freidman in the year 1957. In this model, it is assumed that households’ marginal propensity to consume is fixed. Although this view is incompatible, it applies to an unforeseen
Page | 9 change in expectations or unexpected large loss of financial assets. Such circumstances would likely affect households’ willingness to spend. Besides, the households' willingness to spend might fluctuate or is more likely to change over time (Froyen, 1998).
The consumption is proportional to permanent income function: C=kYp
(2.4). Here, Yp
is a permanent income, and k is the factor of proportionality (k > 0). Permanent income is an expected average long term income from both "human and non-human wealth", which is both expected labor income (human capital) and the expected earnings from assets holdings (non-human wealth). It assumes also a random element to consumption known as transitory consumption. The measured income can be written as Y=Yp
+Yt
(2.5)
According to PIH, it is only the permanent income that influences consumption. Even though consumption is a transitory component of consumption, but it is independent of transitory income. According to him, individuals in each period adjust their estimates of permanent income by a fraction j of the discrepancy between actual income in the current period and the prior period’s estimates of permanent income. It is shown by the following equation:
Yp
t=Ypt-1+ j (Yt-Ypt-1) (0 <j <1) (2.6)
This equation confirms the backward-looking expectation theorem, which states that individuals revise their estimates of permanent income based on how the last periods’ actual income differed from the last period’s estimate of permanent income (Froyen, 1998).
The PIH can explain the confusion about the consumption-income relationship both in the short and long run. In short-run, years of high income will be the ones of positive transitory components of income. But in the long-run, this relation is approximately proportional, given equation (2.4), with a constant APC equal to k. Lastly, considering that consumption rises only with an increase in permanent income, in the high-income years the ratio of consumption to measured income will be low (Froyen, 1998).
2.1.3. The life Cycle Theory of Consumption
According to Froyen (1998), the Life Cycle Hypothesis was developed by Albert Ando, Richard Brumberg, and Franco Modigliani in 1963. The main aim of saving in the LCH is to accumulate savings for retirement. Moreover, the LCH deals with consumption-saving decisions and suggests that economic agents consciously make a great effort to maximize their present value of lifetime utility, by distributing consumption over the lifetime
Page | 10 In addition to this, individual or the household level of consumption does not only depend on the current income but also more importantly on the long-run expected earnings. Individuals are assumed to plan their expenditures based on the expected income over their lifetime. Besides, individuals plan to continue lifetime earnings in T equal installments (Froyen, 1998). Hence, the following consumption equation simplifies the model:
Ct=1/T[Y1
t+(N-1)Y1e+At] (2.7)
LCH suggests also that the consumption would be quite unresponsive to change in current income (Y1
t) that did not also change the average expected future income. From equation (2.7),
the following expression is derived; 𝛥Ct/𝛥Y1t=1/T (2.8)
Therefore, an income that was expected to persist through the working years would mean that the expected annual labor income (Y1e)
also rose and the effect of the consumption would be much greater as shown by the equation:
𝛥Ct/𝛥Y1t + 𝛥Ct/𝛥Y1e = [1/T +N-1/T] =N/T (2.9)
The LCH accounts for the dependence of consumption and saving behavior of the individual’s position in life. The young who enters the labor force have a relatively lower income and possibly a negative saving rate. Then, in middle age income may vary and the saving level also increases. In retirement which the last stage of life causes income to fall and might call upon the period of the dissaving (negative rate of saving).
When considering the analysis of LCH by the previous researchers, the following are the important predictions revealed, that individuals maintain their standard of consumption throughout their lifetime period (Tesha, 2013). LCH suggests that GDP growth will increase aggregate savings because it increases the lifetime earnings and savings of younger age groups compared to older age groups. Thus, countries with higher GDP growth rates are expected to have higher savings than countries with lower growth rates (Athukorala and Sen, 2004).
2.1.4. The Random Walk Theory of Consumption
The theories of PIH and LCH talked above assume that consumers have certainty about their future income. In practice, these two hypotheses are not predictable with a high degree of certainty. It means that there is uncertainty about the future; hence this set of doubt caused Robert Hall in 1978 to develop a new theory of consumption by incorporating elements of uncertainty in both LCH and PIH to derive a new theory known as the random walk theory of
Page | 11 consumption (Dwivedi, 2010). The consumer chooses to consume in each period, it means that in period t-1, t, t+1, etc, so that they maximize their lifetime utility with the condition that lifetime utility equals their lifetime resources or income. The utility maximization condition is equalizing the marginal utility gained in each time. It can be specified as follows:
MU(Ct-1)=MU(Ct)=MU(Ct+1) (2.10)
When introducing uncertainty in this equation of the consumer utility, this latter will be no longer be certain to maximize his or her lifetime utility. Robert Hall applied the rational expectations theory to explain the consumer under uncertainty. This theory is to equalize the marginal utility in period t with the expected marginal utility in period t+1. Thus, the modified rule for utility maximization is given as E[MU(Ct+1)] = MU(Ct), this implies that the reliable
utility (U) depends on the total consumption. So, the rule of utility maximization will be written as: E[(Ct+1)]= (Ct) (2.11)
However, the expected value of consumption E[(Ct+1)] is not observable, Robert Hall applied the
theory of rational expectations to the theory of consumption. According to him, the observed consumption behavior can be written: Ct+1=Ct+δ (2.12) Where δ is expected consumption due to sudden or surprise rise is income. This theory states that there is uncertainty about future income, it may increase or decrease over time. When individuals get an unexpected rise in their income, their consumption also increases, and when income declines the consumption is reduced. This kind of change is unpredictable. Hence, the change in consumption in case of uncertainty is random (Dwivedi, 2010).
2.3 Empirical Literature Review
Several empirical studies examined the determinants of savings in both developed and developing countries by the use of different methods. Most studies used techniques like cointegration and error correction models when analyzing the long-run relationship of the determinants of saving. A greater number of studies investigated empirically the determinants of domestic savings rate shed light on the relationship between domestic savings and its determinants in different countries around the world ( Touny, (2008); Ahmad & Marwan, (2010); Ismail and Rashid, (2013); Yohannes, (2014); Ogbokor, (2014); Ahmad, (2011);
Page | 12 (2018);) With the sake to attain the purpose of these researches, various statistical and econometric procedures were utilized.
Ismael and Rashid (2013) conducted a study on the relationship between household saving and various socio-economic and demographic variables in Pakistan by applying the Johansen cointegration procedures. Furthermore, Error Correction Model is also estimated to find out the convergence of the model towards equilibrium. The results show that there exists a long-run relationship between household saving and the variables used in the study, while the result of the Error Correction Model reveals that about 45% convergence towards equilibrium takes place every year.
Kudaisi (2013) investigated the determinants of domestic savings in West Africa using panel data collected from 1980-2006. The theoretical foundation for this study is a random walk Hypothesis, generalized ordinary squares, and fixed-effect model, used as econometric tools. The results showed that the dependency ratio, the interest rate is negative and insignificant on domestic savings. But the growth of GDP is positive and statistically insignificant. Moreover, the government budget surplus and inflation rate are found to be statistically significant and the development of the West Africa financial market has a positive effect on savings. Finally, the real interest rate and terms of trade have an insignificant impact.
Ahmad & Mahmood (2013) worked on macroeconomic determinants of domestic Savings in Pakistan. The co-integration using Autoregressive Distributed Lag Model (ARDL) bound testing
approach for co-integration techniques to check the robustness for long-run relationship and error
correction Mechanism. They found that per capita income inversely related to domestic savings rate, both in the long-run and as well in the short-run significantly. The exchange rate and inflation rate harm savings. Moreover, trade openness is positively associated with national savings in Pakistan.
Ogbokor (2014) the purpose of this study was to empirically establish the determinants of savings in Namibia through the use of co-integration and error correction mechanisms for the period stretches from 1991 to 2012. Here, macroeconomic quarterly data sets were used. The results of the co-integration tests suggest that there is a long-run relationship between savings and the explanatory variables used in the study. Thus, inflation and income have a positive
Page | 13 impact on savings, while the population growth rate has negative effects on savings. Further, deposit rate and financial deepening have no significant effect on savings. Finally, the need to achieve a higher rate of savings in Namibia implying income levels cannot be overstretched. Elias & Worku (2015) analyzed the causal relationship between economic growth and savings in two East African countries Uganda and Ethiopia using time series data (1981-2014), using VECM and Johansen's Co-integration approach. The results confirmed that there is a significant relationship between domestic savings and economic growth in the case of Ethiopia and Uganda. The results of Granger Causality showed the presence of unidirectional causality between economic growth and gross domestic savings in Ethiopia and Uganda. The gross domestic product does Granger cause gross domestic savings in both countries. Olesia (2015) intended to indicate the causal relationship that exists between savings and economic growth in Albania on time series collected from 1992- 2012. Johansen Co-integration Test and VECM were used. The results showed a positive relationship between savings and economic growth in conjunction with the corresponding role of FDI toward growth. He suggested to the government to pay special attention to FDI policies to make positively affect the economic growth of the country.
Adelakun (2015) used time-series data within twenty-nine years in Nigeria to examine the relationship between savings, investment, and economic growth using co-integration and VECM. The result exhibited a positive relationship between savings, investment, and economic growth. The inflation rate contributed negatively to saving, while interest rate positively affects saving. Iragena (2015) investigated the relationship between savings and its determinants in Rwanda, using VECM and Granger causality testing approaches to check the robustness for long-run relationship and Error Correction Model (ECM) for short-run dynamics during 1978-2012. The findings revealed that the per capita income inversely related to national saving in the short-run and positively related in the long-run. Capital formation has a positive effect on national saving both in the short and long-run. The consumption and interest rate have an inverse relation with savings in the short and long-run, however, inflation has a positive influence on savings both in the long and short-run in Rwanda.
Moussavou(2017) analyzed the determinants of the domestic savings in Congo-Brazzaville. The results obtained from the VECM show that in the long term, the terms of the exchange, the rate of inflation, the real interest rates, the gross domestic product per capita and the financial
Page | 14 deepening moved of a period, explain the domestic savings. On one hand, terms of the exchange, per capita GDP, and the financial deepening moved of two periods, affect the domestic savings. On the other hand in the long-run, these results show that the terms of the exchange, the inflation rate, and the real interest rates influence the domestic savings in Congo-Brazzaville.
Beshir (2017) used the co-integration and vector error correction model (VECM) to examine the factors affecting savings, real GDS, and the causal relationship between the Gross Domestic Savings (GDS) for Ethiopia of time series data. Results showed that gross domestic savings in Ethiopia are affected by age dependency ratio, real exchange rate, real interest rate, real gross domestic product, foreign capital inflow, and money supply both in the short and long run. The elasticity of the exchange rate concerning domestic savings is high and significant in the long run. This implied that continuous depreciation of the real exchange rate has a direct impact on domestic savings encouragement.
Byiringiro &Yu (2017) analyzed the Responsiveness of National Savings to the Monetary Policy and Economic Growth Strategies in Rwanda, where they used Keynesian Economic Model, Johansen co-integration test, the Dynamic Error Correlation Model, and Vector autoregressive estimates, on the time series data collected (1980-2015). Findings revealed that economic growth strategies increase national savings, through Foreign Direct Investment as it is significant in the short and long run while the other two variables (Exports and Deposits Interest rate) are only significant in the long-run.
Asghar and Nadeem (2015) examined both short-run and long-run causal relationship between national savings and its selected determinants in Pakistan for the period 1984-2014. Using the Johansen cointegration and Vector Error Correction Model (VECM), the results of the study indicate that foreign remittances, economic stability, and population have a positive impact on savings while government stability and income inequality affect negatively savings. Using the Toda Yamamoto Causality test the study indicates that there is bidirectional causality between income inequality and foreign remittances, income inequality and population size, government stability and population size, savings, and income inequality.
Ogren (2018) examined the determinants of the saving behavior in 15 OECD countries, using panel data from 1995-2016. The findings showed that factors such as uncertainty unemployment
Page | 15 as precautionary savings and the intensity of fiscal policy are found to have a significant effect on the level of total household income. There are other determinants, like demographic factors which contribute less to the explanation of unemployment but not inflation of the level of saving. An overview of the above studies shows that different variables and estimation techniques had been used to investigate the relationship between factors that determine savings in different economies. Additionally, after their findings, they recommended future researches to use econometric analysis by using appropriate variables, data, and the latest estimation techniques. The results of this study may be helpful for policymakers to design and implement policies consistent with the economic conditions established also in Rwanda. Hence, this study tried to analyze the short-run and long-run saving behavior in Rwanda using recent advances in dynamic modeling and software packages.
3. Overview of the Rwandan Economy
Rwanda is a small landlocked country located in the central East of Africa. Rwanda is a rural agrarian country with agriculture accounting for about 65% of export earnings, with some mineral and agro-processing factories. Rwanda is an overpopulated country where about 12 million inhabitants are distributed on a small surface which is 26,338 km2
. The main sources of products for exports are tourism, minerals, coffee, and tea. Although Rwanda processes a fertile ecosystem, still food production as well as other industrial products are imported from abroad (Central Intelligence Agency, 2019).
The Rwandan economy had been affected by the economic crisis of the mid-1980s, followed by the 1990s and Genocide that contributed to the destruction of its progress and achievements. The 1994 genocide did not only result in the unparalleled loss of human lives and disruption of the social framework, but also the virtual destruction of the already weak economy and socio-economic institutions. Real GDP in 1996 remained at only 72% of its 1990 level. Five years later, over 60% of households lived below the poverty line, compared to about 40% in 1985. The post-genocide government's commitment was to achieve a rapid economic recovery; with prudent fiscal and monetary policies, liberalization of the economy, and institutional capacity building (African Development Group, 2010).
Page | 16 Figure 1: Gross Domestic Product Growth rate in Rwanda (1988-2018)
Source: Author using the data from the World Bank database
The Rwandan GDP growth rate increased from 1994 to 1998 (see graph 2). After a temporary setback in 2003 (when the real GDP growth rate fell to 2.9%), high rates of growth have been recorded since 2004. Since 2005, Rwanda’s annual real GDP growth has exceeded 7 % each year except in 2007 when it dropped to 7.7%. In 2008, the economy experienced its first double-digit real growth rate in over five years, at 11.6%. In 2015, 39% of the population lived below the poverty line, according to government statistics, compared to 57% in 2006 (African Development Group, 2010).
The political economy factors support the Government of Rwanda’s enthusiastic need to maximize Domestic Resources Mobilization. The Rwandan leaders need their country to become a regional leader in information communication technologies and aims to reach an upper-middle-income by 2035 and high-income country by 2050, which requires the future growth rates by capitalizing on the service industry in conjunction with other economic policies like poverty eradication, education, infrastructure, and foreign and domestic investment (Central Intelligence Agency Report, 2019).
3. Data and Methodology
3.1. The data description
In most cases, time-series data are trended over time; this makes it difficult to forecast economic time-series with macroeconomic variables. Sometimes it may be difficult to see whether a series is stochastic or deterministic or a mixture of these states (Koski, 2016). The main disadvantage
Page | 17 of the time-series method is that it is vulnerable to changes in general conditions that may be relevant to the phenomenon of the study. Hence, it is necessary to combine different tests and procedures when analyzing limited and noisy data (Gujarati and Porter, 2009))
The empirical analysis of this study is based on the determinants of the savings in Rwanda, the annual time series data is the secondary data used in this study. Furthermore, the dependent and the explanatory variables are given with a brief description in the table below, to make the data understandable. The time-series data for all variables stretches from 1988– 2018, collected from the World Bank online database.
Table 3.1. Explanation of the Variables
Variables Description Measurement Source
(GDS) Gross Domestic Saving GDP minus final consumption expenditure (total consumption). Data are presented US Dollar.
World Bank
(FCE) Final Consumption expenditure It is the sum of the (private) households’ final consumption expenditure and the general government final consumption. It is measured in the US dollar. It is calculated annually.
World Bank
(EDS) Export of goods and services The sum of all goods and services exported on the international market. Data are calculated in the current US dollar.
World bank
(GDP) Gross Domestic Product It is the sum of all gross value added by all residents in the economy plus any product taxes and minus any subsidies. It is in the US dollar.
World Bank
(TOP) Total Population It counts all population within the country within a year, without considering their legal status or citizenship.
World Bank
(FDI) Foreign Direct Investment It is the sum of equity capital reinvestment of earnings, and other short and long-term capital inflows as in the balance of payment. It is in the US dollar.
Word Bank
Source: World Bank
Before engaging any regression analysis, it is a good idea for a researcher to run a summary statistics of a data set, because it gives an idea on the measures of shape of a distribution. The components of distribution are composed by its average value in its mean, its standard deviation,
Page | 18 the skewness which measures mathematically how a distribution deviates from symmetry, and the kurtosis measures the variance of a variable from an extreme value (Stock & Watson, 2012). Again, in economic analysis and forecasting, variables must be transformed into logarithms to stabilize the variance of the series (Lütkepohl & Kratzig (2012).The reason why the variables in this study have been transformed into logarithms.
Table 3.2: The descriptive statistics of data
Source: author
The results from table 3.2 exhibit the presence of six variables, and 31 observations, the lowest mean of the overall distribution is 19.5 and a high standard deviation of all distributions is 2.8. Table 3.2 shows the measurement of normality test results show that apart from log GDS and logTOP, the remaining variables in the model have positive and non-zero skewness values. Again, all kurtosis values in these distributions have low kurtosis since their values are less than three. After checking the skewness and kurtosis for all six variables of the model within this study, the results exposed their distributions to be asymmetric and not having a bell-shaped format. As a conclusion, the variables in this study are not normally distributed.
Variables Obs Mean Std. Dev. Min Max Skewness Kurtosis logGDS 31 19.47169 2.813052 4.60517 20.91888 0.000 0.0000 logFDI 31 16.67455 2.591257 6.907755 19.56726 0.007 0.0013 logTOP 31 2.012412 0.8237146 -1.453388 2.715881 0.000 0.0000 logGDP 31 21.85564 0.70588 20.44042 22.97548 0.5682 0.3500 logEGS 31 19.47054 1.078302 17.67621 21.23392 0.4985 0.0012 logFCE 31 21.84363 0.6427146 20.83589 22.89648 0.2939 0.0023
Page | 19 Figure 2: The trends of the growth rate of GDS,
FCE, GDP, FDI, EGS and TOP in Rwanda (1988-2018)
Source: Author
The figures above show the individual trends for the variables of interest in this study whereby all variables fluctuate and show the same direction over time. From the year 1990 to 2000, all variables show a decline in their trends, probably because Rwanda was in a period of war and insecurity that devastated the country and all sectors of activities were affected.
After the year 1995, all the variables experienced an upsurge. This confirms that the economy was recovering, probably due to government policy rehabilitation and new policies established and implemented. From the year 2000 up until 2018, it was not the case for a growth rate of the domestic saving as well as the population growth rate which has been stable, while on the other hand, the growth of the remaining variables kept on fluctuating over time(see figure 2).
Page | 20
3.2. Methodology
The current study estimates the relationship between domestic saving and its predetermined independent variables. The following is a brief description of the main methodological procedures of the study. In this section, different used methods are also explained. The Augmented Dickey-Fuller test was utilized for the unit root test of the variables. Johansen co-integration test was used to check for the possible long-run relationship among variables. These procedures are necessary to determine the suitability and usefulness of VECM as the real approach, to reach the purpose of this study.
3.2.1. Model Specification
The model for this study is based on the random walk hypothesis. The variables chosen in our model are resulting from economic factors and governmental policies which are assumed to affect consumption both in past, current, and future households, corporate, and government income. The latter might be important factors that determine domestic saving behavior in Rwanda. The Random walk theorem by Robert Hall in 1978 was chosen in this study because it states that consumers change their consumption whenever they are informed about their lifetime resources, hence the changes in consumption are unpredictable. The fundamental idea is that anything that affects consumption will similarly determine savings (Manamba, 2014).
In this study based on the above arguments, the Gross Domestic Savings is a response variable while predictor variables are GDP which is a proxy for Income, Foreign Direct Investment (FDI), Final Consumption Expenditure (FCE), Total Population and Exports of Goods and services (EGS). The current study considers the following model when estimating the determinants of Domestic Savings in Rwanda. All variables measured in this model, have been transformed into logarithms because whenever logs are applied, the empirical distributions behave better (Woodridge, 2016).
logGDS=f(logGDP,logFCE,logEGS,logFDI,logTOP) (3.1) The model is presented as follows:
logGDS= 𝛽 0+ 𝛽 1 logGDP+𝛽2logFCE+𝛽3logEGS+𝛽4logFDI+log 𝛽5TOP +et (3.2)
(-/+) (+/-) (+/-) (+/-) (-) The intercept stands as a constant (𝛽0,), the coefficients of each independent in the model (𝛽 0, 𝛽
Page | 21 considering the expected relationship between the dependent variable and the explanatory variables: LCH and PIH showed that the growth rate of income determines domestic saving (Hall, 1978). According to LCH, when the income of active workers increases, the lifetime resources devoted to consumption and saving are expected to increase.
Again, PIH shows that increased growth would imply higher anticipated future income, which would induce people to dissave for expecting future earnings. In this case, higher current income growth also reduces aggregate savings. Therefore, the effect of GDP in this study vis-à-vis the domestic saving can take a negative or positive value, depending on a given situation of an economy (Ademe, 2012).
Foreign direct investment and domestic savings rates may have a positive or negative relationship. Dhar and Roy (1996) conducted a study by taking the sample in some countries and the negative net flows of FDI in Singapore have been accompanied by an upward movement in the savings rate. On the contrary, the results obtained for the sample countries of Latin America and Africa do not support the view that FDI is generally accompanied by improvements in the savings rates of host countries. This, in other words, implies that FDI would have a limited role in raising the growth potential of the host countries. Lalwani, (2002) suggested that the effect of FDI on domestic savings and investment has been cautious because it may have a positive or negative (statistically significant influence on savings on national economies of the developing countries. Therefore; this study expects the coefficient of FDI towards domestic savings to be negative or positive.
Exports of goods and services are considered as the foreign demand for a country's product. These transactions yield the amount of money in the foreign currency which will increase the ability to produce or to consume and save the extra money in form of the local currency, which would increase the domestic saving. Consequently, this will impact positively domestic saving.
The FCE is the sum of the households' final consumption expenditure and the general government final consumption. The LCH states that consumption of households affects domestic savings negatively. On the other hand, Government consumption affects domestic savings from two directions. The firstly, the increase in government consumption reduces the amount of saving directly through a reduction in government saving and boost up inflation which is a tool for economic stabilization and reducing the purchasing power of money kept for consumption (Ademe, 2012). Thus, higher government consumption harms domestic saving.
Page | 22 Secondly, government consumption increases on developmental projects. Hence, this higher level of job creation induces higher government spending, but which can result in increased domestic savings in the long-run (Chaudhry et al., 2010). Consequently, government consumption can affect domestic savings significantly and the sign of coefficient may be positive or negative.
The population growth rate is generally known to have two conflicting effects on domestic savings. On one side, it can reduce domestic savings as it leads to a higher level of young dependency ratio, but on the other side, if well stabilized it can also increase savings by increasing the number labor force entering the working part of the life cycle and hence the number of prospective savers(Cook, 2016). In this study, the domestic savings are expected to be impacted negatively, since Rwanda is an overpopulated country and has high young dependency ratio.
3.2.2.Dickey-Fuller Test
Generally, time-series data are not stationary which means that they usually exhibit unit root which can be removed by differencing. When variables exhibit a unit root, it indicates that the expected value is non-constant or that the variance is changing over time, either increasing or decreasing (Studenmund, 2014). This causes the regression model to be incorrect while the R2
and t scores show the opposite, leading to spurious results of the regression (Khamsi, 2016). A series that contains stochastic trends is non-stationary and violates OLS assumptions (Stock &Watson, 2012).
The common practice of including the time or trend variable in the regression model to data is valid only for stationary time series. When variables are non-stationary, it is most of the time alleviated by taking the first difference. Whenever the t-distribution is not normally distributed, the Dickey-Fuller table is used to determine the overall fit (Khamsi, 2016). This study used the Augmented Dickey-Fuller (ADF) test, which follows the same features as the Dickey-Fuller statistic, by adding the lagged value of the dependent variables (Gujarati & Porter, 2009). ADF test aims at checking for the presence of a unit root in a time series.
Under the null hypothesis, a unit root is rejected in favor of the alternative to be stationary. It is known that when time series have a unit root, it means that this series under consideration is non-stationary. Thus, once the data are differenced, they may be transformed to become stationary. The random walk stochastic trends can be eliminated by the first difference of the
Page | 23 series (Stock & Watson, 2012). After, dealing with the problem of stationarity in this model; the following step is to check if there is any relationship between or among variables of interest.
3.2.3.Lag-Order Selection model
In economics, the dependence of a variable Y (response variable) on another X (predictor variable) is rarely instantaneous. Very often Y responds to X with a lapse of time. Such a lapse of time is called a lag (Stock & Watson, 2012). Therefore, the researcher must be careful when choosing the lag length in a model considering the types of data used.
When determining the optimal lag length, this is done by considering the relevant information criteria such as Akaike’s information criteria (AIC) or Schwarz’s Bayesian information criteria (SBIC). By using information criteria, the empirical issue is somewhat resolved since the information criteria with the lowest value are the ones preferred (Stock & Watson, 2012).
3.2.4. Johansen Cointegrating Test
Two economic series are co-integrated if they have a long-run relationship or equilibrium relationship between them (Gujarati & Porter, 2009). Regarding the need to test for cointegration among the time series variables, two approaches can be used viz: Engle-Granger approach which is useful in a simple model with two variables and Johansen’s co-integration approach which is suitable for a multivariate series (Wakyereza, 2019). Since the Engle-Granger approach is a single-equation-model-based approach and our model uses more than two variables, the Johansen co-integration methodology becomes convenient to this study.
3.2.5. Vector Error Correction Model (VECM)
It is recommended to use an ordinary VAR in the first difference if variables in a data set are not cointegrated (Anoruo and Ahmad, 2001). But if they are co-integrated, then a VECM, which
combines levels and differences, can be estimated instead of a VAR in levels (Maitra, 2019). For
this reason, VECM which allows series to be tested in both levels and differences can provide more information that is canceled out when first differencing for a standard VAR model took place. Therefore, VECM allows analyzing the short-run dynamics and long-run equilibrium relationships in a data set (Khamsi, 2016). A VECM is an augmented version of a vector autoregressive model (VAR) which includes a lagged error correction term for the sake of measuring the long-run relationship (Khamsi, 2016).
Page | 24 Sims (1980) proposed the VAR model framework as the standard tool in macroeconomic modeling. In this application, VARs are used to model the underlying structure of the economy (Stock and Watson, 2012).VAR (p) is represented as follows:
Yt=c iyt-1 𝜑yt-1 ut, t =1,…,T (3.4)
Where yt is a k × 1 vector of variables, c is a k × 1 vector of parameters, 𝜑" is k × k coefficients
matrices containing the short-run dynamic parameters and ut is a k × 1 vector of white noise
disturbances, or the residual or stochastic error. The ut has mean zero, covariance matrix Ω and
i.i.d. normal over time. Since all the variables have a unit root and there is cointegration, the best alternative is to choose VECM.
The latter is a restricted VAR model with cointegration restrictions built into the specification that restricts the long-run behavior of the endogenous variables to converge to their cointegrating relationship by an ECT (Stock &Watson, 2011; Gujarati & Porter, 2006). By not considering the deterministic trend terms, the multivariate VECM can be written as follows:𝛥Yt=c i𝛥yt-1 𝜑Et-1 ut, t = 1 , ...T (3.5)
The ECT is represented by𝛥Yt =yt-yt-1, Et-1, and 𝜑 is the speed of adjustment coefficient of the
correction. The dependent variable is a function of its lag, function of the lagged values of the other regressor in the model, an error correction term, and a stochastic error (Stock and Watson, 2012).
VECM is obtained VAR Model must be differenced which means that a lag is lost and the VECM will be estimated by (p–1) across the entire Model. Everything on the LHS up to the coefficient of the correction (𝜑) represents the short-run dynamics. The ECT (Et-1) is what
contains the long-run information that is derived from the cointegrating relationship using OLS regression. The ECT is defined by the following equation: Et-1=yt-1-a-δxt-1. Where the long-run
cointegrating relationship between x and y is shown by the parameters a and δ.
The coefficient of the correction captures the speed at which the dependent variable converges to the long-run equilibrium after changes in the explanatory variables (Stock and Watson 2012). It is known as the speed of adjustment. If the data are once differenced and cointegrated, they may lose the long-run information and estimate only the short-run model is possible. In this case, the use of VECM is an alternative option, because it is advantageous that you may at the same time model both short-run and long-run relationships among variables (Barunik, 2011).
Page | 25 It is often noted that the usage of VECM allows for short-run dynamics and long-run equilibrium relationships within the model with many variables. Dibooglu & Enders (1995) suggested that the dynamic relationships among the variables can be best understood by examining the impulse response function (IRF).
IRF measures the effect of a shock to an endogenous variable on itself or another endogenous variable (Lutkepohl, 2005). When the IRF from the innovation in one variable to another decrease to zero as time goes on, the innovation to the first variable is said to have a transitory effect on the second variable, but if the IRF does not go to zero, the effect is said to be permanent. Lastly, the study may make a forecast for the variables within the model since the cointegrating VECMs are used to produce forecasts of both the first-differenced variables and the levels of the variables (Stata, 2016).
3.2.6. Granger Causality for VECM
VECM is a special case of the VAR model that uses applications that increase the possibility of measuring the interaction between variables known as Granger causality. The latter is used to determine the direction of causality -the unidirectional, bidirectional relationship-or independence between variables. This model aims to decide whether the past value of independent variables, helps to predict the value of the explanatory variable. For instance, A granger causes B, otherwise, it can be called A non-granger causes B (Ahmad, 2015).
4. Results and Discussions
4.1. Unit root test
Unit root refers to an auto-regression with the largest root which is equal to one (Stock & Watson, 2012). The first step in cointegration analysis involves testing the presence of non-stationarity (unit root) and looking for the order of integration. The existence of a unit roots in time series data implies that the mean, variance, and covariance of the variable is time-variant (Ademe, 2012). This study uses the ADF test to check the presence of any stochastic trend. A random walk stochastic trend can be removed by the first difference exercise (Stock &Watson, 2012).ADF test sets a selection criterion that the null hypothesis of a unit root is rejected in favor of the stationary alternative in each case if the t-statistic is lesser than the critical value; also the p-value is less than the critical value of 5% (Chipote & Makhetha-Kosi, 2014). Table 4.1 shows the ADF results as follows:
Page | 26 Table 4.1: ADF test results of the unit root
Order of integration
Variables T-statistics
(5%)Crit.
value P-value Test results Series integrated of order I(0)
logGDS -2.204 -2.986 0.2049 Non-Stationary logGDP -0.220 -2.986 0.9361 Non-Stationary logFCE -0.339 -2.986 0.9790 Non-Stationary logEGS -0.338 -2.986 0.9790 Non-Stationary logFDI -2.447 -2.986 0.1128 Non-Stationary logTOP -2.079 -2.986 0.2530 Non-Stationary Unit root test results at the first difference
Order of integration
Variables T-statistics 5%Crit. value P-value Test results Series integrated of order I(1)
logGDS-d1 -6.643 -3.584 0.0000 Stationary logGDP-d1 -6.479 -3.584 0.0000 Stationary logFCE-d1 -5236 -3.584 0.0001 Stationary logEGS-d1 -5.295 -3.584 0.0001 Stationary logFDI-d1 -8.764 -3.584 0.0000 Stationary logTOP-d1 -4.038 -3.584 0.0003 Stationary Source: Author
At first sight, the study opted for the ADF test to check the series and it is observed that the variables were non-stationary at levels. However, after the first difference, we found both the series to become stationary (table 4.1). Therefore, there is a possibility to investigate the existence of a long-run relationship among the variables by the use of Johansen cointegration testing procedures.
Before conducting the Johansen cointegration test, it is necessary to choose the optimal lag length of the model. The most popular of the information criteria are the Akaike information criteria (AIC), and Bayesian information criteria (BIC) (Stock and Watson, 2012).
Table 4.2.The information criteria selection
Lag LL LR FPE AIC HQIC SBIC
0 -59.3054 5.1e-06 4.83744 4.92307 5.1254 1 72.4172 263.45 4.6e-09 -2.25313 -1.65374 -.237381 2 167.107 189.38 9.2e-11 -6.60051 -5.48736 -2.85698 3 297.621 261.03 3.9e-13 -13.6015 -11.9746 -8.13023 4 2387.69 4180.1* 1.9e-76* -165.755* -163.614* -158.556* Source: Author
Page | 27 Since the value proposed by both AIC, HQIC is lag 4, the optimal lag length in this study is four (see table 4.2). According to Johansen co-integration test, the hypothesis is highlighted as follows; H0: there is no cointegration and H1 states that H0 is not true. The decision criterion is to
compare the trace statistics and its corresponding critical values at a 5% level of significance; the rejection occurs when the trace statistics are higher than the critical value; hence, the H0 is
rejected in favor of H1.
Table 4.3: The results from the Johansen test for co-integration
Johansen tests for co-integration Number of observation 29
Trend: constant Lag 4
Sample: 1990 -2018
Max. rank Parms All Eigenvalue Trace 5%Critical Value
0 30 20.091373 . 151.3231 68.52 1 39 61.443587 0.94226 68.6186 47.21 2 46 81.252015 0.74490 29.0018* 29.68 3 51 90.325954 0.46516 10.8539 15.41 4 54 95.673028 0.30841 0.1598 3.76 5 55 95.752905 0.00549 Source: Author
The results in table 4.3 of both trace and Eigenvalue tests revealed that there are two cointegrating equations. This suggests that there is a long-run relationship between the variables used in this study. The relationship among logGDS, logGDP, logFDI, logTOP, logFCE, and logEGS is not spurious and they move together in the long-run between the periods (1988-2018).
VECM is a special case of VAR which takes into account the cointegrating relations among variables (Dhuria and Chetty, 2018). It has taken the first difference of the variables of interest in this study, such that they are represented as logGDS, logGDP, logFDI, logTOP, D-logEGS and-logFCE. Further, the R-squares value of all these six variables is good enough to justify their causality and p-values indicate also their level of significance.
4.2. Long-run equation
Table 4.4 shows the results of the regression equations by taking the D-logGDS as the dependent and the lagged values as the logGDP, logFDI, logTOP, logEGS and logFCE. The _ce1 and _ce2 show the presence of two cointegrating equations. And since the first one has a negative coefficient and significant p-values, then, VECM shows a long-term causality among variables of interest in this model. On the other hand, the second one has a negative coefficient but it is statically insignificant and it is not discussed in this study.
Page | 28 The estimated normalized equation is presented as follows:
logGDS = 0.74logFDI+0.65logGDP +0.65logEGS –4.3logFCE–1.12logTOP (4.1) In Table 4.4, all coefficients were significant at 5% level of significance. The variables are in logarithms and the first cointegrating vector is estimated, the coefficients can be interpreted as long-run elasticity. Thus, a 1% increase of foreign direct investment is likely to increase the domestic savings by 0.74% and this estimate is statistically significant. Similarly, a 1% increase in the export of goods and services will yield an increase of 0.62% of domestic savings; this coefficient is significant at a 5% level of significance. Moreover, a 1% increase in income is likely to increase the domestic savings rate by 0.65%, this coefficient is statistically significant. For a 1% increase in final consumption expenditure, there will be 4.3% decreases in domestic savings, this coefficient is statistically significant. Lastly, a 1% increase in population growth rate generates a decrease of 1.12% in the domestic saving rate. The size of the population impacted negatively the domestic savings in Rwanda and, this affects negatively the domestic savings since the income earned is highly consumed. Generally, the result of the logGDS equation as shown above is found to be satisfactory since it has the expected sign.
Table 4.4 Normalized Cointegrating Coefficients
_ce1
Beta Coefficients Std. Err. Z p>|z|
LogGDS 1 . . LogTOP -1.127016 .0677661 -16.63 0.000 LogFDI 1.542091 .2127573 7.25 0.000 LogEGS .6208437 .1282977 4.84 0.000 LogGDP .651584 1.246647 0.52 0.001 LogFCE -4.377406 1.012949 -4.32 0.000 _cons 14.90603 . . . _ce2 LogGDS 1 . . . LogTOP 0 (omitted) LogFDI .0747099 .0525027 1.42 0.155 LogEGS -1.453601 1.058228 -1.37 0.170 LogGDP 3.611463 7.285665 0.50 0.620 LogFCE 6.947943 7.112722 0.98 0.329 _cons -138.7467 . . . Source: Author
Having identified the cointegrating vector using Johansen procedures, equation (4.1) shows the long-run dynamics of the domestic saving in Rwanda. The long-run equation suggested that logFDI; logEDS, logGDP, are positively affecting domestic savings in the long-run. But, on the other hand, logFCE and logTOP has a negative influence on domestic saving in the long-run. The results are statistically significant for all variables (see table 4.4). Again, these results coincide with the "a priori "expectations of this study.
Page | 29
4.3. Vector error correction model
Nabila and Nadeem, (2016) suggested that the most important element in the short-run analysis is the error correction term (ECT). It is super important in an econometric analysis when ECT has a negative sign and statistically significant. This indicates the presence of a cointegrating relationship among the variables and the presence of a stable long-run equilibrium path. This state shows also that the deviation from the long-run equilibrium is corrected gradually through a series of partial short-run adjustments.
The results in Table 4.5 showed that the error correction terms denoted as [(_ce1) and (_ce2)] of the equations of domestic saving carry negative signs. The speed of adjustment in the first equation is approximately 20 percent per period towards the long-run equilibrium. This means that there is a slow speed of adjustment of domestic saving which may reflect a little pressure on the variable in restoring to the equilibrium in the long run due to any shocks or disturbance (Chipote & Asrat, 2016). Also, the speed of adjustment in the second equation is 80 percent, but the second equation has a negative sign, it is statistically insignificant.
Table 4.5 VECM estimation results
D_logGDS Coefficients Std. Err. Z P>|z| _ce1 -.200622 .1008046 -1.99 0.047 _ce2 -.8030782 2.719073 -0.30 0.768 logFDI LD. -1.393827 .8388544 -1.66 0.097 L2D. -3.071651 .4606221 -6.67 0.000 L3D. -1.844272 .2922663 -6.31 0.000 logGDP LD. 4.527466 18.11566 0.25 0.803 L2D. -42.11996 12.71952 -3.31 0.001 L3D. 7.109892 10.7525 0.66 0.508 logEGS LD. -.4287527 2.019262 -0.21 0.832 L2D. 12.82015 2.033958 6.30 0.000 L3D. 6.719846 1.689354 3.98 0.100 logFCE LD. -6.412694 16.93001 -0.38 0.705 L2D. -.189128 2.125115 -0.09 0.929 L3D. 5.428293 10.87794 0.50 0.618 logTOP LD. -10.32635 6.005656 -1.72 0.086 L2D. 5.045797 7.355659 0.69 0.493 L3D. -3.392108 3.531269 -0.96 0.337 _cons -.0165508 0.3300182 -0.05 0.960 Source: Author
Page | 30 Table 4.5 Results indicated that the short-run causality is evident in the case of the second lag of logGDP and logEGS with the level of significance less than 5%. Again, apart from logFDI, other variables at their levels are statistically insignificant in determining domestic saving at a 5% level of significance in the short-run. The lagged income has a significant negative short-run influence with a coefficient value of -42.1 suggesting that a 1% increase brings 42.1% declines in the domestic savings rate. Similarly, the lagged exports of goods and services have a statistically significant positive effect on the domestic saving rate suggesting that a 1% increase in export of goods and services will yield 12.8% of the domestic savings rate. It can be concluded for the results in table 4.5 that only the exports of goods and services and gross domestic products have a short-term influence on the domestic savings rate. The population growth rates, the foreign direct investment growth rate, have no short-run impact on the domestic saving in Rwanda. The outcome of the study indicates that there is a negative relationship between income and savings in the short-run in Rwanda as also confirmed by Iragena (2015).
4.4. The diagnostic checks after VECM
The diagnostic checks are very important to the model because they validate the parameter evaluation outcomes achieved by the estimated model (Chipote and Asrat, 2014).
4.4.1 Stability condition test for VECM
This comes into existence because if there is a problem in the residuals from the estimated model; it indicates that the model is not efficient such that parameter estimates from the model may be biased. Therefore, the stability conditions and normality tests are used to check the suitability of the model.
In this study, we should also evaluate the stability of the estimated VECM. For a K-variable model with r cointegrating relationships, the companion matrix will have K−r unit Eigenvalues. For keeping the stability of the model, the moduli of the remaining r Eigenvalues should be strictly less than unity. But regrettably, there is no general distribution theory that can justify this statement(stata,2016).
Page | 31 Table 4.6 Eigenvalue stability condition
Eigenvalue Modulus 1 1 1 1 1 1 -.6799772 .679977 .2166295 + .6315584i .667678 .2166295 - .6315584i .667678 .5342596 .53426 -.2359902 + .3759558i .443885 -.2359902 - .3759558i .443885 -.2476268 .247627
The VECM specification imposes 3 unit
Figure 3. Roots of the companion matrix
Source: Author
The results in table 4.6 showed that there are three of the roots that are unit. The footer of the table shows that the specified VECM imposes three-unit moduli on the companion matrix. Figure 3 of the Eigenvalues shows that none of the remaining eigenvalues are closer to the unit circle. Although the information is the same as in the table, the graph visualizes how close the root with modulus 0.67 is to the unit circle. Thus, Johansen cointegrating test is adopted. The model meets the stability condition.
4.4.2 Lagrange multiplier
Among the diagnostic test, the common are the ones used to test for autocorrelation and test for normality. It is important to apply Lagrange Multiplier diagnostic to test after VECM such to use an active model. The null hypothesis states that no-autocorrelation is present at the lag order. The results in table 4.7, show that there is no presence of autocorrelation, from lag one up to lag 4, the p-values are insignificant which means that the null hypothesis is accepted. Hence, this model is free of the problem of autocorrelation.
Table 4.7.Lagrange multiplier
Lag chi2 Df Prob > chi2
1 37.2079 36 0.41323 2 44.8544 36 0.14786 3 40.9762 36 0.26134 4 43.4549 36 0.18360 Ho: No Autocorrelation Source: Author
4.4.3. Normality test for VECM
The test of normality of VECM is used within this study using Jarque–Bera test. The Null hypothesis states that the residuals in the model are normally distributed.
Page | 32 Table 4.8. Jarque- Bera test Results
Equation Chi Df Pro chi2
D_logGDS 3.386 2 0.18398 D_logGDP 2.618 2 0.27003 D_logFCE 7.280 2 0.02625 D_logEGS 12.048 2 0.00242 D_logFDI 33.811 2 0.00000 D_logTOP 0.790 2 0.67381 ALL 59.932 12 0.00000 Source: Author
The residuals of the model were checked for the existence of serial correlation and normal distribution. The results revealed that the variables residuals are not serially correlated. However, only logGDS, logGDP and logTOP variables in this study are characterized by normally distributed residuals but it is the case for the remaining variables. But in the model as a whole, the residuals are not normally distributed (see table 4.8).
4.5. Impulse Response Function
IRFs describe how the innovations to one variable affect another variable after a given number of periods. The impacts of shocks from a stationary VAR tend to vanish over time; IRFs from a cointegrating VECM do not always vanish. Besides, orthogonalized IRFs can be constructed for VECMs. However, the presence of the integrated variables (unit moduli) in the VECM representation implies that shocks may be permanent as well as transitory (Stata, 2016). The results were estimated for 10 periods (steps) to check the persistence of shock during the long-run. The impulse response plots are given with zero lines, generally, when responses are below the zero line then responses are statistically insignificant while when responses are above this line then responses are statistically significant (Ahmad, 2015).
The observed responses of domestic savings to the shocks in explanatory variables are given in figure5. It can be seen in figures 1 to 5 that domestic savings respond immediately to the shocks in all explanatory variables. Moreover, domestic savings respond positively to the shocks in foreign direct investment, the export of goods and services, income, and population growth whereas savings respond negatively to final consumption expenditure.
Page | 33 Figure 4: Result of Impulse Response with VECM
Source: Author
Impulse response function based on VECM is used to analyze the dynamic effects of the model responding to certain shocks as well as how the effects are among the six variables within 10 periods (steps). Figure 4 indicates that an orthogonalized shock to exports of goods and services, income, and population growth have a permanent effect on domestic saving but again the orthogonalized shock to foreign direct investment and final consumption expenditure has a transitory effect on domestic savings in Rwanda. According to this model, unexpected shocks that are local to exports of goods and services, income, foreign direct investment, and population growth will have a permanent effect on domestic savings, while unexpected shocks to and final consumption expenditure that is local will have a transitory effect on domestic savings in Rwanda.
Figure 4 suggests that domestic savings respond positively to the shock of exports of goods and services, reaches to the highest level in period one, and declines gradually up to the sixth period. This suggests that the domestic savings level increases because probably individuals have more
