Interest Rates and Growth of Private Domestic Investment in Kenya; Vector Autoregressive Econometric Approach

This study sought to determine the relationship between short term interest rate, long term interest rate, and private domestic investment in Kenya using time series quarterly data spanning 1997 to 2018. Vector autoregressive model was used to estimate the relationship. The findings show that the central bank rate and lending rate significantly impact private domestic investment. The results emphasize the role of interest rate policy and monetary policy in driving domestic private investment in Kenya. The findings of this study will be of benefit to policy makers through provision of data-based evidence that will be used as a guide while making appropriate policies to encourage growth of private domestic investment in the country leading to economic growth.

year. According to endogenous growth models, private investments is the engine for economic growth and development (salai, 1997;Romer, 1990). From a similar theoretical perspective, the 10% growth envisioned in vision 2010 is anchored on the increase in private and public investment. Specifically, private investment was expected to rise from 15.6% of GDP in 2006/07 to 22.9% in 2012/13, and to over 24% of GDP during the period 2020/21 to 2030 (KIPPRA, 2017). The projected growth rate is minimal at 2.3 in 2020, due to COVID-19 shock which has crippled economic performance in almost all the sectors. This comes in the wake of a diminishing growth impetus as exemplified by 5.4% in the 2019 growth rate from 6.4% (KIPPRA, 2020).

Figure 1. Economic Growth and Private Domestic Investment Trend
Source: World Development Indicators.
Empirical research work also underscores the role of private investment in driving economic growth and development. Investment is one of the very important macroeconomic variables since the capacity of an economy depends not only on labor but also on the capacity available to produce goods and services (Nghifenwa, 2013). This is in line with Bosco and Emerence (2016) argument that the rate of growth of an economy is proportional to the rate of investment. With increasing burdens on public finances, a higher investment ratio would need to come almost totally from the private investment (Mohan & Kapur, 2015).
The private sector plays a major role in the overall macro-economic development of any country, in the current development strategy private investment is acknowledged as a major source of promoting income and employment through enlarged production and productivity (Mbaye, 2014). According to Michael and Aikaeli (2014) enhancing domestic investment indicates more domestic capital formation  1997Q1 1998Q2 1999Q3 2000Q4 2002Q1 2003Q2 2004Q3 2005Q4 2007Q1 2008Q2 2009Q3 2010Q4 2012Q1 2013Q2 2014Q3 2015Q4 2017Q1 2018Q2 in the economy, which is quite healthy to economic performance since it moderates productive resources/ capital leakages. Governments of developing countries, Kenya inclusive are now considering the potential of private sector involvement in their economies and more in terms of private investment, despite these efforts private investment has remained low in most developing countries (Bosco & Emerence, 2016).

Economic Growth and Private Domestic Investment; Historical Perspective
The Kenyan economy has over the years experienced low and sharp fluctuations. Kenya's economic performance has been declining rather sharply since its independence in 1963. In the 1980s, the government adopted fiscal discipline that was aimed at borrowing that is more prudent. Through these measures, confidence may have been restored in the economy regarding prospects thus slightly contributing to increased investment in 1986 and 1987. Through a raft of fiscal measures, Kenya sought to shift from a government-controlled economy to a market-driven one in  Kenya, 2002Kenya, , 2003Kiptui, 2005).   transmission mechanism as revealed by (Cheng, 2006). In the third quarters of 2002, the looser  monetary policy stance came into force, with nominal short-term interest rates beginning to fall below 10 percent and continuing to fall to less than 1 percent in 2004. Corresponding to these developments are accelerated growth rates for the money supply in the economy. Monetary policy tightening is witnessed in 2010 amid the rising inflation and rising interest rates. The rates fall subsequently, and much more after 2016 in response to interest rate capping policy.
For Kenya to achieve vision 2030 and create sustainable development, for growth and employment, the decline in private investments must be tamed. To induce private investment, monetary and fiscal policymakers need to know the relationship between private investment and interest rates. This study sought to determine the relationship between private domestic investment and both long term and short term interest rates using quarterly time series data spanning 1997 to 2018.

Literature Review
The neoclassical flexible accelerator theory is the widely accepted general theory of investment behavior and empirical tests of the model using data from several industrial countries have been quite successful (Altaleb & Alokor (2012). The basic assumption of the flexible accelerator principle is that investment is a function of the level of output and the user cost of capital. The user cost of capital is, however, dependent on the price of capital goods, the real interest rate, and the rate of depreciation of capital assets. This theory also links monetary and fiscal policy adjustment to investment (Olweny & Chiluwe, 2012). If expansiary fiscal policy (high government spending and low personal tax policy) is combined with a tax policy such as a greater investment tax credit will promote private investment.
Secondly, the expansionary fiscal policy raises the level of income and expected output of the firms and will, therefore, raise the level of desired capital stock and hence stimulate investment. On the other hand, expansionary monetary policy lowers interest rate which would reduce the rental cost of capital and will increase the desired capital stock (Mundia, 2015;Hassan, 2015). The monetary policy conduct and transmission mechanism link long term and short term interest rates to investment behavior.
Empirical evidence in line with this theory is shown by Altaleb and Alokor (2012)  Predominantly, the studies find interest rates as key in explaining investment behavior.
Interest rate is the price borrowers' pay for the use of the money they borrow from a lender/financial institution or fee paid on borrowed assets (Crowley, 2007). According to Kithinji and Waweru (2007), interest can be thought of as "rent of money". The interest rate as a price of money reflects market information regarding the expected change in the purchasing power of money or future inflation (Ngugi, 2001). Kidwell et al. (2016) characterize interest rates as the percent of important charged by the loan specialist for the utilization of its money. Interest rates are commonly noted on an annual premise, known as the annual rate (APR). The advantages acquired could incorporate money, shopper products, and substantial resources, for example, a vehicle or building. Interest is a rental, or renting charge to the borrower, for the utilization of a benefit. Because of a substantial resource, similar to a vehicle or building, the interest rate is also known as the rent rate (Andolfatto & Varley, 2016).
The Keynesian and Monetarists see on interest rates command the discussion on whether changes in interest rates affect private investment. One school proposes that it has a negligible effect on private investment while the other school recommends that adjustments in interest rates significantly affect investment (Becker, 2017). Haberler (2017) offers another huge perspective when she expresses that the genuine interest rate is the price at which the supply of and interest for capital are compared where capital is provided using sparing and is requested for investment. The Keynesian school trusts that interest rate is principally a monetary wonder that is dictated by the supply of and interest for money.
Among this school, changes in interest rates have an insignificant effect on investment. This study seeks, therefore, to understand the relationship between the short term, long-term interest rates, and domestic private investment in Kenya using econometric model.

Preliminary Data Analysis
The study used quarterly time series data spanning 1997 to 2018. The time-series data were obtained from the World Bank and the Central Bank of Kenya. In the preliminary analysis, the study computes the summary statistics comprising of measures of central tendency, measures of dispersion, and a test for normality as presented in Table 1 below. All the variables are normally distributed with the central bank rate showing the highest level of volatility, followed by the T-bill rate and Repo rate with standard deviations at 5.18, 5.12, and 4.84 respectively.
The average central bank rate remained at 11.1%, a fair indication that the sample period was inflationary stable. The lending rate is 16.9%, 5% above the central bank rate which implies that most of the sample period was before the lending rate capping policy in 2016 where the rate was pegged 4% above the central bank rate.

Test for Stationarity
When dealing with macroeconomic time series data it is important to determine the order of integration or non-stationarity properties of the series. If a vector y t is integrated of order d (i.e., y t , ~ I (d)), then the variables in y t need to be differenced d times to induce stationarity. If the individual series has a stochastic trend it means that the variable of this series does not revert to average or long-run values after a shock strikes and its distribution does not have a constant mean and variance meaning the time series data contain a unit root. Therefore, the unit root test is necessary to avoid spurious results from the regression analysis. The study applied Augmented Dicky-Fuller (ADF) and Phillips-Perron (PP) tests for unit roots. Where the results contradict, the study relied on PP test given its superiority to other tests.  The great advantage of the Philips-Perron test is that it is non-parametric, i.e., it does not require to select the level of serial correlation as in ADF and therefore is more reliable and conclusive than the ADF test (Biometrika, 1988

Vector Auto-regression (VAR)
Vector Auto-regression (VAR) model is a theory-free method used for the estimation of economic relationships (Sims, 1980). According to Stock and Watson (2001) , a VAR model of order p (VAR(p)) can be written as: zero-mean error term. Explicitly we seek to estimate the following set of equations in VAR.
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.2 VAR Stability
To determine the stability of the system, and Autoregressive (AR) unit root test was conducted to test for the stability of the model. According to the autoregressive unit root test, the inverse roots of the AR characteristics polynomial of the model, take place within the unit circle. Accordingly, if all AR inverse roots are within the unit circle, the system is either stable or steady; if at least one of them is on or outside the unit circle, the system cannot be stable (Koyunce, 2014). For the AR roots graph, an estimated model is stable if all roots have modules less than one and lie inside the unit circle (Mutuku & Omwenga 2018). The result AR unit root test presented in Figure 3 below showed that all the inverse roots are within the unit circle, implying that the VAR model meets stability conditions. The tests done for suitability and stability and stability of the model, reveal that impulse response and variance decomposition will be consistent.

Heteroscedasticity and Serial Correlation Tests
To investigate the appropriateness of the estimated VAR model, Heteroscedasticity and serial correlation tests were performed. For the Breusch-Pagan Godfrey heteroscedasticity test, the null hypothesis was no heteroscedasticity (homoscedasticity). For Breasch-Godfrey serial correlation LM tests, the null hypothesis was no serial correlation. The results of these tests are highlighted in Table 4 below. The findings suggest that there is neither serial correlation nor the heteroscedastic problem.

VAR Estimation
The standard practice in VAR analysis is to report results from impulse responses and forecast error variance decomposition (see Stock & Watson, 2001;Cyrus, 2014).

Impulse Response Function
Impulse  Figure 4 shows that a shock in the central bank rate may significantly last for 4 quarters before the impact decays. A shock in the repo rate has no significant effect on the central bank rate. However, a shock in the t-bill rate tends to increase the central bank rate for 4 quarters. This is explained by monetary policy operation mechanism since an increased central bank rate meant to reduce financial market liquidity may be accompanied by an increased t-bill rate to mop up the market of excess liquidity. Such a policy instrument combination is essential in a price unstable environment.

Variance Decomposition
The forecast error variance decomposition is the percentage in forecasting a variable due to specific shock at a given horizon (

Long-run Model
In this section, the study estimated a simple model to determine the static relationship between domestic private investment and interest rates. Since the lending rate is closely related to the short term interest rates, multicollinearity is expected in the OLS model. To avoid this problem, the estimation is done in two phases. In the first phase, we estimated the model with the only lending rate as the explanatory variable.
The findings show that an increase in the lending rate negatively and significantly reduces private domestic investment. Controlling for the short term interest rates in the second phase of estimation, the findings show that an increase in the central bank rate significantly reduces private domestic investment. This echoes the earlier findings in this study. The commercial lending rate is the cost of loans which could be the main source of investment financing. The lending rate is majorly determined based on the central bank rate which is the rate at which loans to commercial banks are discounted by the Central Bank as the lender of last resort. The relationship between the T-bill rate, the repo rate, and domestic private investment which is expected given that the two rates are the basis of pricing government securities in which the private sector invests in for portfolio diversification.

Conclusion
This study sought to model the relationship between private domestic investment and long-term and short-term interest rates. The analysis reveals that the commercial bank lending rate and the central bank rate are the main drives of private domestic investment. This is consistently evident in impulse response functions, variance decomposition, and the OLS model estimated in this study. The results underscore the essence of monetary and interest rate policy in driving domestic private investment, a critical aspect for Kenya in attaining the vision 2030.