Examination of the Exchange Rate and Import Price Pass-through to Inflation: A View from Nigeria

We examine the effect of exchange rate and import price pass-through to inflation in Nigeria using headline inflation and import price data, with the aid of a non-recursive Structural Vector Autoregression model. Our results indicate mostly incomplete ERPT and IPPT to inflation. Specifically, we found that (i) the ERPT to the INF is incomplete at all horizons. (ii) IPPT to the INF is incomplete at all horizons. (iii)IPPT to inflation is relatively more rapid than the ERPT to inflation. The findings further suggest that the monetary authority should be wary of using devaluation of the domestic currency as a way of propping up the economy as that would not only aggravate domestic inflation but likely to also increase the ERPT. Similarly, harmonizing the disparate exchange rate windows in the economy might reduce import price pass-through to domestic inflation. Also, the size and speed of both ERPT and IPPT from the study suggest that relevant authorities need to strengthen domestic industries and instill confidence in consumers, to reduce reliance on imports.


INTRODUCTION
Over the last 20 years, the Nigerian economy has experienced spikes in its inflation mostly due to 'imported inflation', which is a result of significant dependence on imported items. Imported inflation may be caused by an increase in the prices of with high imports (Ogundipe and Egbetokun, 2013;Bada et al, 2016;Çiftçi and Yılmaz, 2018).
This study contributes to the existing literature on ERPT, especially in the EMDEs, and specifically in Nigeria where exchange rate movements had been quite volatile in the past decade. The study assessed the effect of exchange rate and import price passthrough to inflation in Nigeria with three specific objectives: a) the completeness or otherwise of the exchange rate pass-through to inflation, b) the magnitude of exchange rate and import price pass-through to inflation, and, c) the speed of exchange rate and import price pass-through to the general price level. The analysis is based on a structural Vector Autoregressive (SVAR) model with a non-recursive identification scheme to recover the exogeneous import price and exchange rate shocks.
A summary of our empirical results reveals that the exchange rate and import price pass-through to inflation are incomplete at all horizons. Also, import price pass-through to inflation is relatively more rapid than the exchange rate pass-through to inflation.
The rest of the paper is organized as follows. A review of the relevant theoretical and empirical literature is presented in section two. The model specification and results of the model estimation are contained in section three and section four respectively, while section five presented the conclusions.

Literature Review
The theoretical literature on the exchange rate pass-through is drawn from the monetary theory to exchange rate determination, the law of one price and the purchasing power parity theory. Subsequently, there is an interplay between the exchange rate and a country's price level, in that the level of inflation and the dynamics associated with it influence the purchasing power of a currency. Further, depending on the extent to which a nation depends on imported goods and services, its domestic inflation could be impacted through the exchange rate, a phenomenon that is known as exchange rate pass-through (ERPT). Goldberg and Knetter (1999) define exchange rate pass-through as the "percentage change in import prices caused by a 1 percent change in the bilateral currency exchange rate between an exporting and importing countries". By implication, the depth and speed of exchange rate pass-through are, therefore, dependent on the extent to which a nation relies on foreign goods or services.
The literature on exchange rate pass-through gained prominence in the 1970s in response to an increase in the price of oil which generated inflationary shocks. In high inflation environments, the concern is expressed by central banks on the movements of the exchange rate and its reflection on prices because of currency depreciation. A low pass-through gives a central bank a higher degree of independence when it conducts its monetary policy operations and it makes it possible for a central bank to implement an inflation-targeting framework. However, in countries with a higher degree of exchange rate pass-through (countries with high imports), changes in prices of imports can result in a much larger change in the consumer price index.
Exchange rate volatility influences exchange rate pass-through even to investment decisions as high volatility will tend to make them more cautious given their profit motive. Ca'zorzi et al (2007) and McCarthy (2007) examined the exchange rate and import price pass-through in emerging markets and industrial countries and found ERPT to be lower in countries with higher volatility, but also higher aggregate demand.
As such, the size and speed of the exchange rate pass-through depend on factors such as expectation regarding the length of currency depreciation and the level of aggregate demand. The depreciation of the currency is expected to be reflected in higher prices of imported goods. If the depreciation is not fully reflected in the prices of the imported goods, the exchange rate pass-through to prices is incomplete. An incomplete pass-through reflects the partial transmission of exchange rate changes into prices and affects Macroeconomic policy, as noted by Shitile and Usman (2020).
The law of one price (LOOP) lays the foundation for the relationship between exchange rate and inflation. The law states that in the absence of trade frictions and under a system of free competition and flexible pricing, identical goods sold at different places must be sold at the same unit price when expressed in the same currency. Hence, when price changes in the home currency market it would have an equal change in price at the foreign market despite it being two different countries.
The monetary approach to exchange rate determination principally relies on Krugman's (1986)  The literature of models on 'industrial organization' has attempted to explain the nexus between inflation and exchange rate through import penetration, oligopolistic competition, market concentration, and the degree of substitution between foreign and domestic goods produced. Dohner (1984) attempts to explain the divergence in the prices of traded goods across markets using a dynamic model of pricing by forward-looking and profit-maximizing exporters. The model assumes that consumers adjust slowly to price changes. He finds that the level of pass-through is determined through the speed and expectation of consumers of the duration of the exchange rate changes. This conforms with Kreinin et al (1987) who provide evidence that industry characteristics determine the extent to which exchange rate movements are passed on to the dollar price of foreign goods. Krugman (1986) in his work entitled "pricing to Market", explains that the reason for incomplete exchange rate passthrough to prices of imported goods is due to the behavior of firms. Dornbusch (1987) developed a static model to explain the degree of pass-through regarding the competition between firms, both foreign and domestic. The analysis revealed than an incomplete pass-through can occur even if goods are perfect substitutes. Fisher (1989) also lays out a model of exchange rate pass-through using a partial equilibrium model in which firms (domestic and foreign) set their prices based on the expected exchange rate. The study discovered that the changes in the exchange rate could lead to changes in import prices. However, the degree of passthrough depended on the market structure existing in domestic and foreign markets.
On market structures, Baldwin (1988) uses a model sunk market-entry cost where temporary fluctuations in the exchange rate alter the domestic market structure to influence the pass-through of the exchange rate to the prices of imports. Obstfeld and Rogoff (1995) using a micro-founded dynamic general equilibrium model, introduce nominal rigidities and market imperfections. They found that purchasing power parity was always still maintained, and the pass-through was complete. Also, Devereux (1996, 2000) developed an extended version of the Obstfeld-Rogoff model allowing for pricing-to-market. they only differ from Obstfeld and Rogoff (1995) model by changing the assumption on the pricing strategy of firms, whereas, Obstfeld and Rogoff (1995) assume nominal prices are set in producers' currencies. Therefore, a fluctuation in the nominal exchange rate cause equal feedback in prices of imported goods, i.e. the pass-through in the short-run exchange rate is then complete. The implication for policy is that flexible exchange rate regimes act as a substitute for flexible nominal prices, and therefore help to achieve relative price adjustments, making it a more desirable exchange rate regime. However, Devereux (1996, 2000) propose a model in which a segment of firms can set prices in the foreign currency market. This diminishes the effect of exchange rate volatility on domestic prices.
In recent times, the literature on exchange rate pass-through has begun taking the view that imports are intermediate goods that undergo non-traded production or distribution processes before being consumed. This process might weaken the impact of exchange rate volatility on prices. Subsequently, the exchange rate changes only affect the final goods price, and the pass-through to consumer prices is likely to be small.
The commitment of central banks to maintain a low inflation environment play a critical role in firms transmitting their prices. Using a microeconomic model of staggered pricing, Taylor (2000) produced a theoretical framework where the degree of pass-through depends on the inflation environment. He finds that a lower passthrough is caused by lower perceived persistence of cost changes. Additionally, the author finds a positive correlation between the persistence and level of inflation in the USA. The paper concludes that low inflation causes low pass-through. Drawing on Taylor (2000), the links between pass-through and inflation has been further examined by (Gagnon and Ihrig, 2004) who carry out an analysis of twenty industrialized countries. They concluded that the pass-through wilted in countries whose central banks have adopted inflation targeting since the 1990s.
Critical role in determining ERPT is played by the composition of a country's import basket in determining the pass-through, and this assumption has been confirmed by Campa and Goldberg (2005) who conclude that changes in the pass-through are mainly caused by changes in the composition of a country's import basket. They stress that moving away from energy which has a high pass-through to manufactured goods which the pass-through is comparatively low will reduce the pass-through to import prices, leading to lower prices for consumers. Campa and Goldberg (2005), one of the commonly cited papers in the literature on the subject matter, analyzed pass-through elasticities for 23 OECD countries using quarterly data from 1975 to 2003. The authors showed that there was a partial passthrough effect of the exchange rate on import prices in the short-run, particularly in manufacturing companies. Also, OECD countries that had lower rates of the exchange rate and inflation volatility had a lower pass-through impact on import prices. For example, they found that the United States had one of the lowest pass-through elasticities, at approximately 25 percent in the short run and 40 percent in the long run.
The Authors observed that changes in pass-through effects in import prices could be associated with shifts in the composition of the import components in these OECD countries.
Some studies have carried out an empirical analysis of the subject matter in Nigeria using an SVAR. Leading the way is Zubair et al (2008) who find the the ERPT to be incomplete while it takes eight quarters for the full impact of the pass-throught to be felt. Ogundipe and Egbetokun (2013) adopted the SVAR approach for the period 1970-2008 in estimating the pass-through effect of the exchange rate to inflation in Nigeria. The Authors found a substantially large pass-through from the exchange rate to inflation and asserted that the depreciation of the currency over the period influenced the results. They further observed that when the depreciation of the currency is persistent, the attendant increase in costs gets passed on to consumers by firms and importers. The Authors also noted that the large share of imports in the consumption basket coupled with high and persistent inflation in Nigeria during the examined period could explain the degree of exchange rate pass-through. Similarly, Bada et al (2016) examined the exchange rate pass-through to import and consumer prices for the period 1995 -2015. The study also found that the pass-through from the exchange rate to inflation was incomplete in Nigeria, utilizing the Johansen approach to cointegration and a vector error correction model. Also, the exchange rate passthrough was found to be higher in import prices than in consumer prices.

Model Specification
The objective of this paper is to determine the impact of changes in the exchange rate and import price on prices along the value chains, i.e. the general price level in the economy, given domestic monetary policy influence. Our focus rests on three objectives: a) the completeness or otherwise of the ERPT to inflation, b) the magnitude of ERTP and IPPT to inflation, and, c) the speed of ERPT and IPPT to the general price level. The paper follows (Choudhri et al, 2002;Gueorguiev, 2003;McCarthy, 2007;Ito & K, 2008;and Jiang & Kim, 2013) who also have investigated ERPT through structural analysis. Similarly, SVAR, through its two potent tools, impulse response and variance decompositions, is capable of individually or collectively providing more information in regards to the impact of macroeconomic shocks and policy innovations (Aarle et al, 2003).
In the model, the pass-through from the exchange rate to prices is occasioned by supply and demand shocks and assessed through the consumer price index. We, however, being conscious of the country's propensity for the consumption of foreignproduced goods, decided to see the effect of changes in import prices alongside those of exchange rate on inflation.
All the data were sourced from the Central Bank of Nigeria database. We adopted a non-recursive identification system to recover exogenous monetary policy shocks and exchange rate shocks. According to Jiang & Kim, (2013), a VAR analysis of the ERPT makes it easier to account for the feedback between exchange rate and other prices; it allows for a proper investigation of the effect of exchange rate shocks and monetary policy shocks on domestic inflation in an integrated framework, and lastly, it simplifies the task of tracking the ERPT into a set of domestic prices along the distribution chain in a single framework.
Our VAR model takes the following general form: Where (L) represents the path order matrix polynomial in the lag operator, L; to the extent that ( ) = 0 − 1 − 2 2 − − ⋯ − ; where 0 = non-singular matrix normalized to 1 on the diagonal and explains the contemporaneous relationships between the endogenous variables in the 1 vector , in an 1 vector of structural disturbances. In association with this, the reduced form VAR is estimated as Where ( ) is an n th order matrix polynomial in the lag operator ; is an 1 vector of reduced form disturbances.
Relationships between Eq (1) and eq (2) could be expressed as follows: Being a short-run SVAR, identification is obtained by placing restrictions on the nonsingular matrices A and B. Given that there are ( +1) 2 free parameters in , this allows for as many as possible parameters to be estimated in the A and B matrices. Given a 2 2K parameters in A and B, the sequential position for identification requires that 2 2 − 1 2 ( + 1) restrictions be imposed, implying that our five variables would require thirty-five (35) restrictions based on literature and economic theory to achieve proper identification of the structural parameters. This is appropriate considering the short-run nature of our model and the absence of exogenous variables.
Our VAR model comprises of a vector of five endogenous variables, , where connotes monetary policy rate; represents the exchange rate, a more realistic measure of the interest rates available in the real sector; is consumer price index; import price index; is the nominal effective exchange rate, and is global oil price.
The selection of these variables follows both Jiang & Kim (2013) and McCarthy (2007) but without the intermediate prices as in Jiang & Kim (2013), due to unavailability of these data within the selected periods.
The choice of inclusion of these variables: nominal effective exchange rate, the consumer price index, and the import price, is to enable us to evaluate the extent of the ERPT into domestic prices along the distribution chain. The money stock as represented by the broad money and interest rate as proxied by the monetary policy rate is included for two reasons, (1) to gauge monetary policy reaction to contemporaneous or previous exchange rate movements, and (2) given the fact that monetary policy has a significant influence on exchange rates and domestic inflation.
International oil price was included as a veritable proxy for global activity, and with contemporaneous feedback into the supply side of the Nigerian economy via the two domestic prices.
While Nigeria is considered the largest open economy in Africa, albeit a small to medium-sized in a global context, the country's monetary policy decisions have no effect whatsoever on the global interest rate, global oil prices are considered to be contemporaneously exogenous in terms of the domestic economy. Import price index and inflation, as represented are included to serve as a proxy for the demand-side factors.
In our VAR model, we imposed a non-recursive identification scheme only on the contemporaneous structural parameters, 0 . Our identification scheme based on = 0 is summarized in the following equations.  inflation. According to Sims & Zha (1998), as cited by Jiang & Kim (2013), monetary policy, despite our data, cannot respond immediately to price developments due to information lags, and neither can it respond to developments in the global oil market.
Given this reality, we suppressed the monetary policy reaction to import prices and changes to global oil prices, but we allow it to affect inflation.
For the exchange rate equation, we reckoned that changes in the bilateral exchange rate are caused, among other factors, change in interest rate, change in inflation rate and change in a country's current account position, and changes to global oil price movements, but not necessarily vice-versa, as such, we excluded contemporaneously the policy rate, inflation, import prices, and commodity prices. For the inflation equation, we assumed that exchange rate shocks and import prices would affect investors' perception contemporaneously, but the effects of interest rate and commodity price changes would come with a lag because of economic agent's initial cautious response and possible planning delays (Sims & Zha, 1998). The real activity in our model is assumed to be affected by inflation and the nominal exchange rate with a one-period lag, (Jiang & Kim, 2013), as such we allowed commodity prices to affect exchange rate contemporaneously, given that Nigeria's bulk of the country's foreign exchange reserve comes from oil export. It's pertinent to mention that our structural model is overidentified with contemporaneous restrictions as shown in equation (5). This implies that our equation contains more zero restrictions than required for our model to be just identified.

Pre-Estimation Tests
Stationarity Test: The results displayed in  (1) -11.642*** -8.231*** -2.651 -1.171 -11.609*** -8.227*** Notes: ***denotes rejection of the null hypothesis of unit roots at a 1% level of significance. Both the Augmented Dickey-Fuller (1981, ADF) and Phillip-Peron (1988, PP) tests were conducted, following (Jenkins and Katircioglu, 2011) and per (Enders and Granger, 1998). Tests were carried out with the aid of E-Views 11 Table 2 depicts the lag length criteria that we followed in choosing the optimal lag length for our VAR analysis. As can be seen, of the five criteria, one recommended a single lag, i.e., SC, while another (FPE) recommended twelve. However, LR, AIC, and HQ supported three lags. While using one lag resulted in serial correlation in the VAR residuals, hence not capable of adequately modeling persistence in the data, twelve lags rendered the SVAR model unstable with resultants explosive impulse responses.
Given this consideration and the monthly nature of our data, we included three lags in the SVAR model, following some empirical studies in which VAR was estimated with monthly data. The AIC and HQ statistics supported our choice of 3 lag as can be seen in table 3. Consequently, we did not observe evidence of serial correlation in the VAR residuals and the stability condition for the VAR model is satisfied.

0.20
The sample period is 2010M01 -2018M12 2 The column displays the specified order of serial correlation for our reduced-form VAR residuals 3 Report of multivariate LM test statistics for the VAR residuals for serial correlation up to the order reported in the third column. 5 The column indicates the stability or otherwise of the VAR model. In order words, it shows whether the roots of the characteristic polynomial for the estimated VAR are greater than 1 in absolute values. The "Yes" indicates that the VAR model satisfies the stability condition.

Results of Estimation
In this section, we report our impulse response functions, then, we looked at the exchange rate pass-through elasticities, followed by the variance decomposition, and finally, we take a look at the historical decomposition.
In The market-determined CPI elasticity, however, is surprisingly negative, a seemingly a posteriori outcome, indicating that market prices react negatively to interest rate movement rather than changes in the money stock.
In   In response to a positive one standard deviation innovation import equation, the monetary policy rate drops drastically dropped for in the first two months, then gradually rose for the next 10 months, before it began to soften in the 12 th month.
Consequently, the exchange rate rose through to the 12 th month before retracting and leveling up at a lower level. Inflation on its own, responded with a lag, declining in the first month before assuming a gradual ascent through to the 11 th month. Except for the one month lagged responses of inflation and bilateral exchange rate, these responses follow a conventional view or a priori outcome, in that, a rise in the prices of imports is expected to be accompanied by a depreciation of the domestic bilateral exchange rate, as a result of higher demand for the domestic currency to offset the increased gap. In effect, the results are generally in accord with theoretical expectation, in that a weakened bilateral exchange rate of the domestic currency induces higher prices in the domestic market, and ultimately attracts higher costs of fund. Higher demand for local currency is expected to be accompanied by an increase in interest rates and vice versa. The response of import prices to its own shock is negative and immediate up to the 16 th month, after which it levels up. Global output responded by declining for the first three months, then, started to rise, albeit at a statistically insignificant rate.
We now study the impact of the exchange rate and imports price changes on prices along the distribution chain by following (Kim W. J. 2007) who argued that only the ERPT from a structural VAR can capture the unbiased exchange rate pass-through when one or more of the import price variables is endogenous. Accordingly, we also estimated the exchange rate pass-through elasticity coefficient through the structural VAR's impulse response or the normalization of our inflation responses to the exchange rate and import price shock through the response of the exchange rate and import price to their own shocks within the same horizon.
The dynamic pass-through elasticity could be stated in the following form: , Where , + represents the cumulative pass-through between month and month + ; ē , + represents the cumulative change in the price level between the corresponding months. Table 5 presents the estimated pass-through elasticities for our two analytical price measures for up to 36 months horizon. As can be seen, the ERPT and import price pass-through to the inflation are incomplete at all horizons. The magnitude (0.006 to 0.084) indicates the extent at which the inflation moves with the nominal exchange rate, and the range (0.061 to 0.23), the extent at which inflation moves with import prices. While the general price level appears to move less than onefor-one with the nominal exchange rate, the rate of movement with import prices is higher than the rate at which inflation moves with the exchange rate. This is in line with (McCarthy, 2007), and invariably points to the high extent at which foreign-made goods have infused the country's landscape or consumers' preference for imported goods. Another reason why exchange rate infusion into inflation might appear low is that the available exchange rate data is that of the official exchange rate window, with data on the parallel market mostly inexistent, as such, most transactions in the foreign exchange market usually go unreported or underreported. Secondly, the impact of exchange rate depreciation in the country could have been muffled by the price stickiness in some sectors of the economy that resulted from government subsidy and menu costs.
Similarly, the pass-through to inflation from import prices is observed to be higher than to EXPT at all horizons, a phenomenon that is also evidenced by the impulse response analysis. However, both the import price pass-through to inflation and exchange rate pass-through reach their maximum within the first 12 months and ranges from 0.025 to 0.177, for the IPPT and 0.010 to 0.094 (in absolute term) for the ERPT. Incidentally, most of the impacts from import prices are felt within 12 months, while most for the ERPT is within 18 months. Almost half of the changes in the exchange rate is passed to the inflation within the first 3 months, the corresponding share for import price pass-through is about one-third. One reasonable assumption that can be deduced for the rapid pass-through is the insufficient industrial capacity in the country given the huge population, to the extent that citizens rely more on foreign-produced goods to sate their consumption appetites. Another reason could be attributed to the lack of an efficient foreign exchange forward market where investors can hedge against exchange rate risks (Lafleche, 1996;Kim W. J., 2007).

Table 5. Estimated ERPT and Import Price Pass-through Coefficients, 2010M01 -2018M12
To further assess the impact of different shocks on movements in domestic prices, we estimated the forecast error variance decomposition (FEVD)analysis for the SVAR model.  For the imports, contributions to the forecast error variance came largely from its own shock, while exchange rate contribution came a distant second, and oil prices came third throughout the forecast horizons. It is quite noteworthy that for both the NEER and IMPI, own innovation is the most significant source of fluctuation at all forecast horizons, comprising 99 percent and 89 percent, respectively at the peak before shrinking to 20 percent and 38 percent at the tail end of the horizon. Another very important point to note here is the fact that the impact of import prices on inflation is greater than that of the exchange rate on inflation. This is in line with the results obtained from the ERPT and impulse response functions.

Conclusion
This paper examines the effect of the exchange rate and import price pass-through to inflation in Nigeria. The analysis is based on a structural VAR model with a non-recursive identification scheme to recover exogeneous import price and exchange rate shocks.
Our results indicate mostly incomplete ERPT and IPPT to inflation. Specifically, we found that (i) the ERPT to the INF is incomplete at all horizons. (ii) IPPT to the INF is incomplete at all horizons. (iii)IPPT to inflation is relatively more rapid than the ERPT to inflation.
As in most economies, exchange rate stability constitutes a significant part of price stability in Nigeria. Our results, although, revealed that the size and speed of the exchange rate pass-through (ERPT) to inflation is less than that of import prices, meaning that a positive one standard deviation shock to the exchange rate and import prices tends to elicit a positive but disproportional response in inflation. Put another way, the rate of reaction of inflation to a one percentage point change in the exchange rate is less than the rate of reaction inflation exhibits to a one percentage change in import prices. In effect, the response of inflation to shocks coming from import prices is higher than that of those coming from the exchange rate. In response, monetary policy stance turned contractionary for the first two periods, then loosened up slightly before it normalized about 7 months later. The implication here is that monetary policy can offset only a part of the effect of exchange rate shock on domestic inflation.
The results also showed that ERPT and import price pass-through to inflation are incomplete at all horizons. The magnitude (0.010 to 0.094) indicates the extent to which the inflation moves with the nominal exchange rate, and the range (0.025 to 0.177), the extent of co-movement between inflation and import prices. In both cases, is less than one-for-one with the exchange rate. The rate of movement with import prices is higher than the rate at which inflation moves with the exchange rate. This invariably points to the rather high rate of infusion of foreign-made goods into the Nigerian landscape. Another reason why exchange rate infusion into inflation might appear lower is that the available exchange rate data is that of the official window, with data on the parallel market mostly inexistent, leading to most transactions in the foreign exchange market being unreported or underreported.
Consequently, the ability to achieve harmonization across disparate exchange rates and maintain stability in the exchange rate market is essential to achieving the central bank's price stability mandate. That role of the exchange rate in stabilizing prices across the entire price spectrum cannot be supplanted just by targeting money growth, as in the current framework. It is also clear that prevailing domestic inflation had some extemporaneous effects on the pass-through of import prices. Also, the findings revealed that the monetary authority should exercise caution in using devaluation of the domestic currency to promote economic growth, as that would not only exacerbate domestic inflation but also likely increase the ERPT. This is even more so, given that exchange rate devaluation is unlikely to improve the country's chances in the international market vis-à-vis its exports.