In most cases, empirical approaches to assessing real exchange rate misalignment are based on small, usually reduced-forms of equation-econometric models. In these models the real exchange rate is defined as the relative price of tradable to non-tradable goods that, simultaneously, are compatible with the attainment of internal and external equilibrium (Edwards,1998). As a basis for these analyses, many authors (Clark and Macdonald, 1988; Edwards and Savastano, 1999) developed theoretical models from which a reduced-form for the equilibrium real exchange rate (ERER) was derived. This reduced-form relates the long-run

Real Exchange Rate Misalignt and Trade Flows in Nigeria (1960-2013): 49-65 equilibrium real exchange rate to a set of variables, called the real exchange rate “fundamentals.” These “fundamentals” usually include the terms of trade, output growth (or productivity differentials), the country’s openness to international trade, import tariffs and government spending. While some authors (Elbadawi and Soto, 1994; Baffes et al., 1997) have tried to use a relatively large number of “fundamentals” in their regression equations, others have restricted their analyses to a small number of variables. The majority of single equation models follow a four-step approach for assessing real exchange rate misalignment. In the first step, historical data are used to estimate a (reduced- form) real exchange rate equation. The equation usually expresses the real exchange rate as the function of some economic fundamentals. Most recent studies have estimated this equation using co integration techniques. The second step usually (but not always) consists of computing “normal” or “sustainable” values for the fundamentals. This is typically done by decomposing the fundamentals into “permanent” and “transitory” components using various techniques, such as the Hodrick Prescot filtration approach and the moving average method. The third step consists of using the fitted values which are interpreted as the long-run sustainable values of the fundamentals, and the estimated regression coefficients to construct an “equilibrium” path for the real exchange rate. An important property of this approach is that, in contrast with simple PPP-based calculations, it generates an estimated equilibrium real exchange rate that does not have to be constant over time. Indeed, to the extent that there are changes in the fundamentals, the estimated index of the equilibrium real exchange rate obtained from the equation will vary through time. In the fourth and final step, the degree of misalignment is computed as the difference, at any moment in time, between the equilibrium and the actual real exchange rate. 2.2

A number of authors have examined the effects of real exchange rate misalignment on trade flows. In most of the literature reviewed, the results obtained were similar, despite the use of different methodologies in their regression. For instance, Jongwanich (2009) examined the impact of the real exchange rate misalignment on export performance in developing Asia. His reduced-form model for export performance regressed the total volume of export on variables like the real exchange rate, FDI, real income, domestic production capacity and an index of real exchange rate misalignment. He employed a general-tospecific modeling procedure which was considered appropriate because the set of variables used were made up of a series of stationary and non-stationary data. The technique employed was the Johansen co-integration method. The WU-Hausman test for simultaneity, according to him, suggests no evidence of simultaneity. All variables were measured in natural logarithm, to enable regression coefficients to be interpreted as elasticities. The result revealed a negative impact of misalignment on export performance in developing Asia. Also the work of Gala and Lucinda (2006) for the European Union, investigated the impacts of real exchange rate misalignment on the trade flows in the region. The work employed the gravity model that controls simultaneity bias. In the model, the volume of trade between two countries increases with the product of their GDPs and decreases with their geographical distances. Using a pooled OLS method of regression, it was observed that, exchange rate misalignment has a negative effect on international trade. Gala (2007) investigated the impact of exchange rate misalignment and volatility on Malaysian trade flows. The study used the reduced-form equation method to construct real exchange rate misalignment, and the GARCH (1,1) method to construct the exchange rate volatility. He specified a simple regression model for the volume of export and import. The volume of export was expressed to depend on the real exchange rate, foreign GDP and an index of misalignment, while, import demand was specified to depend on the real exchange rate, domestic GDP and an index of misalignment. Using the full information likelihood technique to estimate the two models, it was observed that, real exchange rate misalignment has adverse effects on both the volume of export and the import of Malaysia. In their work, Olimov and Sirajiddinov (2008) examined the effects of the real exchange rate volatility and misalignment on foreign trade flows in Uzbekistan. The paper employed the two-step Engle-Granger technique to compute import demand and export supply price elasticities. In particular, a separate log-linear specification of long-run export and import equations that have among others as explanatory variables; RGDP, real exchange rate, measure of real exchange rate volatility and index of real exchange rate misalignment. The results obtained using the-cointegration technique was that the real exchange rate misalignment had depressing effects on the volume of trade, especially exports in Uzbeskistan. In Nigeria, Agu (2002) examined the position for equilibrium exchange rates for Nigeria using the single equation procedure. Misalignment was found to be higher during the regulation period. The work proceeded to ascertain the influence of the misalignment and volatility of the RER on the trade balance, and capital account. His trade balance and capital account equations have as explanatory variables, terms of trade, openness of the economy, nominal effective exchange rate and an index of real exchange rate misalignment. He uses the OLS method for estimation. It was observed that the real exchange rate misalignment impeded both the trade balance and the capital account. 2.2

 below:

3. Research Methodology In line with previous studiesexchange on the subject mattertime, (Baffes al., 1997:2-8; Where R rate over gn etrepresents totalJ t is the real effective   Px*  2007:59-60, Rtprevious , etc), ,this OPEN , Madopts , et 1 an .......... .......... 3.1 exchange rate expr Dosse, study equilibrium real In line with studies on* the subject matter (Baffes et the al.,....country’s 1997:2-8;  g nis, NKI captures terms of tra expenditure, NKI net capital Pm inflow, P*2 x/P* m   Jimoh, 2006:89; Dosse, 2007:59-60, etc), this study adopts an equilibrium real below: the openness of the economy, exchange rate expression as statedM below: 2 represents broad money supply, while, e t-1 is the Where Rt is the real effective exchange rate over time, gn represen nominal effective .  exchange  Px* israte captures the country’s term expenditure, NKI net capital P*x/P*m.... .........................................3.1  R g NKI , , , M 2 , einflow, 3.1 * , OPEN t t 1 ....................  n Pm   broad money supply, while, et thebehavioral economy, M As a firstthe stepopenness to obtainofthe equilibrium exchange rate (BEER) from equ 2 represents is the real effective rate over n time, gn represents to Where t Rt effective nominal exchange rate exchange . this approach, line previous works that studytheassumed that total with government expenditure, NKIhave is netused capital inflow, P* /P* this captures Where R is the real effective exchange rate over time, g represents x m the country’s terms of expenditure, NKI is net capital inflow, P*x/P*m captures country’s terms of trade, by OPEN is the openness of the economy, M2 represents relationship delivered theory was in log-linear transformation of the variables. T Asopenness a first step toet-1 obtain behavioral equilibrium exchange (BEER) broad money supply, while, is the the lagged the of nominal effective exchange broad money supply, rate while, et-1 is t the of the economy, M 2 represents 3.1 is written as: rate. line with previous worksrate that. have used this approach, this study assum nominal effective exchange

As a first step to obtain the behavioral equilibrium exchange rate (BEER) from equation in line with.......... previous works that..... have this of the var delivered by theory was in3log-linear transformation LogR  relationship  , H3.1, .......... .......... .2used this approach, t   t .......... As a first to obtain relationship the behavioral equilibrium exchange study tassumed thatstep the long-run delivered by theory was inrate log-(BEER) from 3.1 is written as:variables. Thus equation 3.1 is written as: linear transformation of the line with previous works that have used this approach, this study assumed th

Where Hrelationship of theby values forwas theinfundamentals, μt is the disturbance term t is the vector , theory log-linear transformation of the variables ...................................................................3.2 LogRt  delivered H t  t .......... .......... .......... ............... 3.2

3.1 is the written as: that cause the exchange rate to diverge from its equilibrium to the theory, shocks

Where Ht is vector of the values for for the the fundamentals, μt is μthe is the vector of the values fundamentals, Where Ht,the t is the disturba LogR Heventual .......... ..... 3cause .2 the exchange run should produce convergence to.......... the that relationship. A specification that t  t  t .......... disturbance term. According to the theory,.......... the shocks rate to diverge its equilibrium thecause short-run should produce to thefrom theory, the shocks in that the exchange rate toeventual diverge from its equ notion is thetodynamic error-correction model. This thus, this expressed 3.2 as fo convergence the relationship. A specification that captures notion isequation the

Ht is the model. vector This of the values for theequation fundamentals, μt is the disturbance te dynamic Where error-correction thus, expressed 3.2 as follows:

run should produce eventual convergence to the relationship. A specificat to the theory, the shocks that rate to diverge from its equilibri p cause the exchange p

, dynamic error-correction model. , This thus, expressed equation LogRt notion  log isRtthe 3.3 .....3.3 ......... 1   H t 1    i LogRt  i  i H t  j   t ..........

i 1 convergence to i  0the relationship. A specification th run should produce eventual

 dynamic  model. This thus, expressed P* error-correction notionH is the equation 3.2 Where vectorofof fundamentals, , NKI Where the vector errora t is the ....... t LogR log, Rx * ,OPEN  , H, M 2 ,et 1  isis the LogR fundamentals,  , H and  v..........  gn t

m tP and vt isthe error term with mean zero and stationary over time.p p term with mean zero and stationary over time.

LogRt   log Rt 1   , H t 1    i LogRt  i  i, H t  j   t ...................3.3 i 1

The study estimated equation 3.3 by first testing for the unit root properties of all the variables using the ADF statistic, then, tested for the existence of co-integration relationship between the set of fundamentals and the real effective exchange rate using the Johansen co-

The study then estimated the co-integrated equation using the Johan likelihood methodology. Criteria such as Alkaike information criteria (AIC),

The study estimated equation 3.3 by first testing for the unit root properties (SC) and Likelihood ratio (LR) were usedforforthelag-length and model of all the variables using the ADF statistic, then, tested existence of of variables cointegration relationship between the set of fundamentals and the real effective exchange rate usingThe the Johansen co-integration approach. The co-integration co-integrating vector from equation 3.3 represents the equilibriu vector among them could then be interpreted as the equilibrium (long-run) relationship.rate. In order to make the BEER result comparable to other methods such as The study then estimated the co-integrated equation using the Johansen’s maximum-likelihood methodology. Criteria such asthe Alkaike information equilibrium exchange rate (FEER), real exchange ratecriteria fundamentals identifie (AIC), Schwatz criteria (SC) and Likelihood ratio (LR) were used for lag-length of variables were and model selection. separated into transitory and permanent components. The study employ The co-integrating vector from equation 3.3 represents the equilibrium real exchange rate. In order make the result other methods Prescott filter tomethod toBEER separate thecomparable values oftothe fundamentals into transitor such as the fundamental equilibrium exchange rate (FEER), the real exchange rate fundamentals identified in equation 3.3 were separated into transitory components. and permanent components. The study employed the Hodrick–Prescott filter method to separate the values of the fundamentals into transitory and permanent components.Therefore, the real exchange rate misalignment malt  is measured as: Therefore, the real exchange rate misalignment (malt) is measured as:

Where, Rt is the real effective exchange rate over time and R*t represents the real effective

R  R  equilibrium exchange mal  ratet over ttime.* 100.......................................................3.4 *

Rt

The above tests were carried out to avoid the problem of spurious regression and enable

Where, R is the real effective exchange rate over time and R* represents t the to have their long-run values. rate The over idea of the error-correctiont model (equation 3.3) theestimates real effective equilibrium exchange time.

The above tests were carried out to avoid the problem of spurious regression and enable the estimates to have their long-run values. The idea of the coefficients error-correction (equation 3.3) would produce the dynamic estimates run of the model variables. of the variables by giving the both short-run and the long-run coefficients of the variables. In order to determine the effect of real exchange rate misalignment on trade balance in In order to determine the effect of real exchange rate misalignment on trade in Nigeria, an augmented based on existing literature Nigeria, anbalance augmented model based on existing model literature (Bahmani-oshooee, 1998:6-9; Olimov (Bahmani-oshooee, 1998:6-9; Olimov and Sirajiddinov, 2008:10- 16) was employed. The model is stated16) as follows: and Sirajiddinov, 2008:10was employed. The model is stated as follows: would produce the dynamic estimates of the variables by giving the both short-run and the longln

Misalignment(%)

1960 -0.674 2.675 -125.18 1965 2.968 2.923 1.53 1970 1.697 2.111 -19.61 1975 0.801 1.311 -30.73 1980 0.802 1.252 -35.90 1985 1.115 0.161 5.88 1986 1.304 1.365 -4.50 1990 2.736 2.142 27.71 1994 3.451 3.764 -8.31 1995 3.479 3.874 -10.20 2000 4.997 4.687 6.60 2005 5.244 4.908 6.85 2006 5.235 5.108 2.47 2007 5.200 5.928 -12.28 2008 5.175 5.673 -8.76 2009 5.390 5.232 3.02 2010 5.524 5.421 0.10 2011 5.637 5.565 0.07 2012 5.651 5.687 0.04 2013 6.117 6.312 0.19 NB: (1) A positive value of misalignment implies currency undervaluation while a negative value signifies overvaluation of currency.

(2) REER and PEER are in their logarithm values. (3) Exponential values of log(REER) log(PEERHP) give back the actual values.

signs) in the years 1965, 1985, 1990, 2000, 2005, 2006, 2009, 2010, 2011, 2012 and 2013. The currency was overvalued in the years 1960, 1970, 1975, 1980, 1986, 1994, 1995, 2007 and 2008.

The study employed the BEER approach to obtain equilibrium real effective exchange rate over the period 1960-2011 in Nigeria. The differences between the ideal values of the real effective exchange rate and the actual real effective exchange rate (in absolute terms) gave the misalignment indicators. The effects of the real effective exchange rate misalignment indicators on trade flows were later examined. The estimates of the results confirmed the adverse effects on trade flows in Nigeria. The appropriate policy recommendation from this study is that, since the regression result obtained indicates higher misalignment of exchange rate in the fixed exchange rate regimes and vice versa for the flexible regimes in the country, thus, to minimize the extent of real exchange rate misalignment, adequate flexibility is required. Thus, the study recommends a flexible exchange rate system for the country. This could be done by reducing the government’s frequent intervention in the foreign exchange market. Moreover, once, the extent of the real exchange rate misalignment is minimized or curtailed, the adverse effects it has on the trade flows of the country will also be reduced. Thus, an appropriate choice of the exchange rate regime will minimize the effect of misalignment on various components of trade. Author information Ibrahim Waheed (Ph.d),Department of economics, PMB 1601 Adewole estate, Alhikmah university, Ilorin, Kwara state. Nigeria