Oil Price Shock and Regime Switching Behaviour of Exchange Rate in Nigeria


 This study examines the relationship between oil prices and exchange rate in Nigeria by viewing this relationship in another dimension which is the ability of exchange rate to move from one regime to the other. The period of investigation spanned the period 1980–2017. The regime switching characteristics of exchange rate were examined with the Markov Switching Model technique. The regime switching test suggests that there are two exchange rate regimes of managed float and fixed regimes. It was found that the probability of exchange rate to move from a managed float regime to a fixed regime was very low as compared to switching from fixed to managed float regimes. In fact, the expected duration of transitions is about 4 years for managed float but 9 years for fixed exchange rate regime. Both oil price and exchange rate move in opposite direction; despite the regime changes.


Introduction
trade balance model focuses on the relationship that exist between crude oil prices and exchange rate changes. In a world constituted of the Organisation for Petroleum Exporting Countries (OPEC), America, and Germany, the trade balance model presupposes that exchange rate need not change as a result of increase in the price of oil. The reason adduced is that the revenue generated from the increase in the price of oil will be used by OPEC to import goods from America and Germany. The prediction of Krugman (1983) serves as the proposition of this study to check whether in Nigeria, the same stance holds. Specifically, oil price increased from $57 in 2007 first quarter to $118 in 2008 third quarter. During the same period, the Naira-Dollar exchange rate also appreciated from 128 Naira per dollar to 118 Naira per dollar. Consequently, oil price dropped to $44 in 2009 first quarter. During this period, the Naira-Dollar exchange rate exchange rate got depreciated to 147 Naira per dollar. However, exchange rate instability has been very alarming over the years, which has in turn affected the economy in one way or the other. This occurred through lack of confidence on the economy by foreign investors which leads to the reduction in inflow of capital, worsening of the country's balance of payment and other mechanism through which exchange rate instability affects the economy.
The overall intuition is that the instability of exchange rate is of a great concern to the economy as it slows down and hampers the development of the economy. While the Central Bank of Nigeria (CBN) has tremendously activated policies to stabilize this instability over time, the results are still not satisfactory. The question that this study seeks to answer is that is there a relationship between changing oil price and exchange rate fluctuations? Hence, this study seeks to look at oil price and exchange rate relationship; especially with a focus on the various exchange rate regimes in the country. While many studies have investigated the oil priceexchange rate nexus for different countries and have provided various justifications for their studies, this study will be the first to employ a theoretical framework which is that of Krugman (1983) that considers oil price and other variables affecting exchange rate. Most of the previous studies have examined solely oil price and exchange rate dynamics without considering other factors affecting exchange rate. This is being captured in the modified model by including other factors affecting exchange rate but not mentioned in Krugman (1983) model as control variables. Also, this study will be the first to view the oil price-exchange rate nexus in terms of regime switching in Nigeria by using the Markov switching model to estimate the relationship. The study also looked at the relationship through the use of high frequency quarterly data. This data frequency will assists in capturing the various regime switching episodes of exchange rate in tandem with changing oil prices in Nigeria. In addition to this introductory section, this study will further be discussed in four other sections. Section 2.0 considers the review of theoretical and empirical literature while section 3.0 provides analytical framework for empirical investigation. Section 4.0 detailed the estimations while section 5.0 captures the conclusion and the recommendations for policy formulations.

Literature Review
The theoretical relationship between oil price and exchange rate has been well espoused in the literature. The theoretical literature has recorded four (4) major theories. These are the Dutch disease phenomenon, the Hotelling (1931) theory of exhaustible resource, Dornbusch (1976) Overshooting hypothesis and the portfolio-balancing theory of Krugman (1983). The Dutch disease phenomenon was first coined by the Economist magazine in 1977 but later popularised by Corden and Neary (1983). The theory is primarily associated with a natural resource discovery that resulted in a large influx of foreign currency into a country, including foreign direct investment, foreign aid or a substantial increase in natural resource price. The theory predicted that a resource boom affects the rest of the economy through two channels. The first is the resource movement effect and the second is the spending effect. With an increasing return to marginal productivity of labour in the energy sector, wages in this sector increases and further attracts labour from manufacturing and other tradable sectors into the energy sector. The productivity of the other sectors fall due to absence of labour factor. Given that the marginal productivity of labour in the energy sector brings about a boom and more income to the economy, the spending effect emerge through increase importation and domestic absorption for both tradable and non-tradables. The real exchange rate appreciates as the prices and wages of non-tradables increase relative to tradables due to the price internationalization of the tradable goods (Corden and Neary, 1983).
The Hotelling theory is a decision theory of non-renewable energy resource. According to Hotelling (1931), the future value of non-renewable energy has to be compared to its discounted present value before decision as to whether sales should be made today or in the later future could be decided. The theory presumed that the owners of non-renewable resources will only produce a supply of their basic commodity if it can yield more than available financial instruments. The theory posited that the major driving force for sales decision of non-renewable energy resource is profit maximization under a perfect cum efficient market condition. In addition, Dornbusch (1976) introduced a theory of exchange rate overshooting. This theory was later extended by Driskill and McCafferty (1982). Later, Turnovsky and Bhandari (1982) refined the Driskill and McCafferty (1982) extension. The basic theory explains an over-reaction of monetary policy-inducement to exchange rate volatility and that short-term effect of this volatility would exceed its long-term effect. This occurs due to prices and wage stickiness in the short-run and that as time passes, prices and wages become 'unsticky' and this dissipate the initial over-reaction for the long-run situation at a new equilibrium position for all markets. The additions made by Driskill and McCafferty (1982) and the refinement done by Turnovsky and Bhandari (1982) were to further interrogate the origin of shock that hits the economy through the exchange rate volatility. The former found that trade balance and relative prices were correlated with the spot and forward exchange rates while the latter concluded that the balance of payment position is a determining factor.
Lastly, the Krugman's (1983) theory of portfolio balancing is a dynamic partial equilibrium model that explains how increase in the international price of oil influences the exchange rate. As a restrictive theory, it assumes three stakeholders of the United States of America, Germany and the Organisation of Petroleum Exporting Countries (OPEC) and it posited that there exists thresholds for appreciation and depreciation of domestic currency consequent upon oil price increases.
According to Krugman (1983), there are perfect counteracting effects between oil price increases and importation of goods that leave the domestic currency unaffected in the long-run situation.
The increase in oil price leads to appreciation of domestic currency and this increase income. The increase in income leads to increases in consumption and importation increases. The increased importation leads to depreciation of domestic currency that perfectly commensurate the initial appreciation. An extension to the Krugman's (1983) portfolio balancing theory was carried out by Caprio and Clark (1981). The duo modelled the effect of oil price shocks as a wealth transfer between oil-exporting and oil-importing countries. This extension reinforces that exchange rate will only remain same if perfect asset preference holds between the importing and exporting countries. Otherwise, the counteracting effects will not hold.
Empirically, the effect of oil price shock on exchange rate is different in oil exporting and oil importing countries. When oil price increases, the exchange rate of an oil exporting country tends to appreciate as it now gains more inflow of income, while that of an oil importing country tends to depreciate as a result of the increase in its outflow in relation to its inflow. This gives an insight into how the review of empirical literature can be captured. The empirical literature is therefore divided into four categories. The first category capturing studies that have been done in net oil exporting countries, the second category capturing that of net oil importing countries, the third category capturing studies that encompasses both net oil importing and net oil exporting countries, while the fourth category hinged on measurement distinctions of the relationship. Prominent among the studies that investigated for net oil exporting countries were those of Adeniyi, Omisakin, Yaqub, and Oyinlola (2012), M and Aimer (2016), Alzyoud, Wang, and Basso (2018), Wu and Yu (2017), Eugene (2016), Ogundipe, Ojeaga, and Ogundipe (2014), Babatunde, (2015), Englama, Duke, Ogunleye, and Isma'il, (2010), Benhabib, Mohammed, and Maliki (2014), Hashimova (2017), Hasanov, Mikayilov, Bulut, Suleymanov, andAliyev (2017) Dawson and Jennifer (2007) all confirmed that an increase in oil prices leads to depreciation of the exchange rate. Ahmed, Qaiser and Yaseen (2016) reported that negative shock in oil price and exchange rate have larger effect on their volatilities than positive shocks. Brahmasrene, Huang and Sissoko (2014) view this relationship in another form as it was obtained that exchange rate shock has a significant negative impact on crude oil prices while impulse response of exchange rate variable to a crude oil price shock was statistically insignificant. Ji, Liu, and Fan (2018) observed that there is a significant risk spillover from crude oil to the Chinese and US exchange rate markets. Coudert, Mignon and Penot (2005) found that there is a long-term relationship between oil price and the US exchange rate. The approach according to them outperforms its counterparts, in the case of small samples among its other advantages, such as: being easy to perform just by using OLS; estimating long-and shortrun coefficients, simultaneously; applicability regardless of regressors being I(1) and I(0) or a mixture of them. It is of this that a view of regime switching behavior of exchange rate should be presented to capture the relationship between oil price and exchange rate volatility in a new dimension.

Methodology
The theoretical framework for this study is the Krugman (1983) model. The model is anchored on a trade balance portfolio model of exchange rate determination. The basic model predicts that for a small economy with capital mobility, changes in oil price yields a counteracting effect on exchange rate movement in country through trade adjustment mechanisms. The domestic currency earlier appreciates on the attendant increase in oil price and later depreciates due to increased imports necessitated by increased income. For an oil-exporting country with an exogenously fixed international price of oil denoted as 0 , the trade balance model can be specified as; The trade balance of the oil-exporting country is denoted as ; Price of oil is represented by 0 , while 0 represents the total quantity of oil supplied by OPEC; Represents export of other commodities to America and Germany excluding oil; Represents import of other commodities from America and Germany excluding oil.
Since OPEC fixes price of oil exogenously, exchange rate will only determine the export and import of other goods given as; is the total quantities of exported goods, is the total quantities of imported goods, and represents exchange rate.
Including capital movement OPEC will invest in America and Germany Where 0 represents capital flow to America and Germany − = .
Where is the net export of other goods excluding oil A few modifications were done to the basic model in order to reflect the reality of the contemporary global oil market. The restrictive assumption of USA and Germany as the only trading partners is relaxed. The world now consists of all countries of the world such that any variable with respect to America and Germany will now be for the whole world. By definition, the variables in equation (6) are now redefined thus; is the trade balance of Nigeria and the rest of the world; 0 now is the net capital flow of Nigeria.
Re-specifying equation (8) gives; Deflating the whole variables with trade balance, we have the theoretical model for this study as; The empirical model for this study becomes; Both interest rate and inflation rate are introduced as control variables in the model Represents interest rate, while represents inflation rate The study looks at the relationship between oil prices and exchange rate in Nigeria, and the period properties of the variables. Also, the data stability test would be carried out in order to test for the stationary of the data; this would be done using the Augmented Dickey Fuller (ADF) test. The framework for the test can be specified as; Describes the first difference of and the term m is the lag length of the augmented terms for while is the error term. The above equation allows for testing of the variable to be a stationary series. The null hypothesis in the ADF test is that has a unit root or is non-stationary.
The technique of estimation is the Markov switching model of Hamilton (1989) also known as the regime switching model, is one of the most popular nonlinear time series models in the literature.
This model involves multiple structures (equations) that can characterize the time series behaviors in different regimes. By permitting switching between these structures, this model is able to capture more complex dynamic patterns. A novel feature of the Markov switching model is that the switching mechanism is controlled by an unobservable state variable that follows a first-order Markov chain. In particular, the Markovian property regulates that the current value of the state variable depends on its immediate past value. As such, a structure may prevail for a random period of time, and it will be replaced by another structure when a switching takes place (Kuan 2002 where = 1,2, … . . , denotes the unobserved state indicator which follows an ergodic k-state Markov process and is a zero-mean random variable which is identically and independently distributed over time. The number of states, k, is assumed to be finite. The methodology has been used in empirical work by Engel and Hamilton (1990).The second Markov switching model allows for state-independent autoregressive dynamics:

Descriptive Statistics and Statistical Properties
The statistical properties of the variables included for the model are presented in Table 2. These include both summary statistics such as mean, standard deviation, and skewness. Also, formal statistics of kurtosis and Jarque-bera tests were conducted.  This section starts by looking at the trend analyses of the variables in the model. The price of crude oil at quarterly basis, the official exchange rate also quarterly, and the trend of both of them together. The graphical trend is firstly presented then followed by the tabular trend. The Naira and the unwillingness of OPEC to stabilize the oil markets. Some part of it intended to reduce its production, but the leaders mainly Saudi Arabia, UAE, and other Gulf allies refused to cut their production. However, Iraq was the only country that not only maintained its supply, but actually increased it. This resulted in an oversupply of oil, which in turn placed downward pressure on crude oil prices for the long term. Also US saw this as an opportunity and increased its production which further led to the decline in crude oil prices.
The trend in Figure 1 is very instructive about the behavior of exchange rate in Nigeria. Exchange

Data Stability Condition
Before the estimation proper, the data stability test is being carried out to check for the stationarity of the data. The test considered in this study is the Augmented Dickey Fuller (ADF) test as shown in table 2. The statistics obtained shows that MPR, NET CAPITAL FLOW, and TRADE BALANCE are of order I(0), which implies that the data are pure and raw and are stationary at level. Log (CPI), EXCHANGE RATE, and OIL PRICE are of order I(1) and this implies that the data are purified, that is not pure and raw which calls for integrating the variables. This implies that the data are stationary at first difference.  Note: (*, **, ***) implies that the series is non-unit root at 1%, 5%, and 10% level.
After the data stability test has been carried out, the next thing is to estimate the Markov Switching Model. Theoretically, exchange rate can be into two regime, which are; the floating and the fixed regime. The floating regime can thereby be into two categories, namely; the free float regime and the managed float regime. The fixed regime also known as the pegged exchange rate regime is when transactions about exchange rate takes place at an exchange rate determined by solely by the monetary authority. The exchange rate might be fixed by legislation or intervention in the currency market. The monetary authority might buy or sell currencies according to the needs of the country, or may take policy decisions to appreciate or depreciate the national currency. In most fixed exchange rate regime, the monetary authority holds foreign currency reserves in order to intervene in the foreign exchange market, when demand and supply of foreign exchange are not equal at the fixed rate. The floating regime, also known as the flexible regime is when the exchange rate is left to be determined by the forces of demand and supply. The floating regime can be into the free float and the managed float. The free float regime implies that the market forces of the demand and supply of foreign exchange determines the exchange rate.
The managed float regime also known as the dirty float regime is when the exchange rate is basically determined by the free forces of demand and supply of exchange rate, but the monetary authority intervenes from time to time to control excessive fluctuations in exchange rate. By using the Markov switching model, the type of exchange rate regime can be known through the coefficient. If the coefficient of state is zero, it implies a free floating exchange rate regime. If the coefficient of the state is larger let's say 100 upward, the exchange rate regime can be identified as a fixed regime. But if the coefficient is not too large and not zero, but tending towards zero, the exchange rate regime can be identified to be a managed float, let's say like 30 to 0.

Model Estimations and Discussion of findings
Results obtained show that there are two regimes of exchange rate in Nigeria. The first regime (State 1) has 10.602 coefficients. This implies that the state is a managed float regime while the second regime (State 2) has coefficients of 152.4682; which implies that state 2 is a fixed exchange rate regime. The significance of the two regimes are significant are further reinforces the presence of two regimes of exchange rate in Nigeria. After detecting for the number of states and the types that they are, the next thing is to know the transition probabilities and the intuition behind it. This can be seen as the probability of exchange rate moving from a managed float regime to a fixed float regime, and vice versa. P11 is the probability of exchange rate moving from a managed float regime to a managed float regime. It can be seen that the probability of exchange rate moving from a managed float regime to a manage float regime is 99.34%, which depicts a higher chance of staying in the managed float regime. On the other hand, P12 is the probability of exchange rate moving from a managed float regime to a fixed regime. The probability is 0.66%, which is very low which depicts a very low chance of switching to fixed regime. Also, P21 is the probability of exchange rate moving from a fixed regime to a managed float regime. The probability is 0.67%, which depicts a low chance of exchange rate moving from the fixed regime to the managed float regime. More so, P22 is this probability of exchange rate moving from a fixed regime to a fixed regime. The probability is 99.33%, which implies that exchange rate has a higher chance of staying in the fixed regime.   The transition probabilities of exchange rate were also examined. P11; this is the probability of exchange rate moving from a managed float regime to a managed float regime. It can be seen that the probability of exchange rate moving from a managed float regime to a manage float regime is 93.58%, which depicts a higher chance of staying in the managed float regime. P12 relates to the probability of exchange rate moving from a managed float regime to a fixed regime. The probability is 6.42%, which is very low which depicts a very low chance of switching to fixed regime. P21 is the probability of exchange rate moving from a fixed regime to a managed float regime. The probability is 2.72%, which depicts a low chance of exchange rate moving from the fixed regime to the managed float regime. P22 is the probability of exchange rate moving from a fixed regime to a managed-float regime. The probability is 97.28%, which implies that exchange rate has a higher chance of staying in the fixed regime.

Conclusion and Policy Suggestion
This study examines the relationship between oil prices and exchange rate by viewing this relationship in another dimension which is the ability of exchange rate to move from one regime to the other. It is of evidence that exchange rate can be into two states or let's say regimes, which are; the state of a managed float regime and a fixed regime. And it was found that the probability of exchange rate to move from a managed float regime to a fixed regime very low, and also the chance of exchange rate moving from a fixed exchange rate regime to a managed float regime is very low. It was also obtained that exchange rate is expected to stay 15.57 quarters in the managed float regime which is 3.9 years, while exchange rate is expected to stay 36.76 quarters in the fixed regime which is 9.2 years. It was also observed that exchange rate and oil price exhibits a negative relationship; that is, they move in opposite directions whereby when oil prices increase, the exchange rate will reduce which implies appreciation of the currency. It was found that a 1% increase in oil price will lead to a 0.20% appreciation in the Naira Dollar exchange rate. This clearly implies the fact that Nigeria is an oil exporting country, and an increase in oil price will transfer wealth from oil importing countries to exporting countries. By the implication of the results obtained, the following suggestions are recommended for policy direction.
First, the revenue generated from oil should be channeled into creation of necessary and adequate infrastructural facilities in order to encourage small industries in producing locally made goods.
By this, the importation of goods will reduce and the trade balance becomes favourable. Secondly, interest rate should be closely monitored by the central bank, in order to command inflow from abroad increasing the net cash inflow into the country. Thirdly, policies should be harnessed together. In Nigeria, there is a problem of new administration coming with new policies which contradicts the policy of the previous administrations. This is because political party tends to show off with their policies, and this neglects the policies of the previous terms. New government should therefore further with the achievement of good policies started by previous administration.

*Availability of data and material
The data for this study are available on request.

*Competing interests
It is instructive to note that there is no competing interesting for this study. The two authors with corresponding email addresses provided here are the contributed to the completion of this manuscript.

*Funding
Not Applicable