




































Economy 
ISSN(E) : 2313-8181  
ISSN(P) : 2518-0118 
Vol. 3, No. 2, 74-78, 2016 
www.asianonlinejournals.com/index.php/Economy 
 

 
 

 

 

 

 

74 

 

The Effects of Inflation and its Risk on Interest Rate: An 

Empirical Evidence from Nigeria 

 
Amaefula C. G1    

 

1
Department of Mathematical, Computer and Physical 

Science, Faculty of Science, Federal University Otuoke, 
Yenagoa, Bayelsa State, Nigeria 

 
Abstract 

The paper examines the effects of inflation and its risk on interest rate in Nigeria. The data sets cover the 

period of 1995:M1 to 2014:M12. ARCH (1) and GARCH (1, 1) were used to measure inflation risk and 

the result indicates that GARCH(1, 1) measures inflation risk better than ARCH(1) model based on 

Schwarz Information Criterion (SIC), and adopting multiple regression method, the result reveals that 

inflation and inflation risk exact negative and positive impacts on interest rate respectively, but none is 

significant. This result implies that the direction of this interest rate by monetary policy rate (MPR) is 

not proactive enough to curb the rising inflationary pressure in Nigeria. Hence, there is a need for more 

proactive monetary policy rate that can cut back the rising inflationary pressure.   
 

Keywords: ARCH (1), GARCH (1, 1), Multiple regression, SIC, Inflation and interest rate. 
 
Contents 
1. Introduction ......................................................................................................................................................................... 75 

2. Literature Review ................................................................................................................................................................ 75 

3. Materials and Method ......................................................................................................................................................... 75 

4. Data Analysis and Results ................................................................................................................................................... 76 

5. Conclusion and Policy Implications .................................................................................................................................... 77 

References ................................................................................................................................................................................ 78 

 

 
Citation | Amaefula C. G. (2016). The Effects of Inflation and its Risk on Interest Rate: An Empirical Evidence from Nigeria. Economy, 3(2): 74-78. 

DOI: 10.20448/journal.502/2016.3.2/502.2.74.78         

ISSN(E) : 2313-8181   

ISSN(P) : 2518-0118 

Licensed: This work is licensed under a Creative Commons Attribution 3.0 License  

Funding: This study received no specific financial support. 

Competing Interests: The author declares that there are no conflicts of interests regarding the publication of this paper. 

Transparency: The author confirms that the manuscript is an honest, accurate, and transparent account of the study was reported; that no 

vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. 

Ethical: 

History: 

This study follows all ethical practices during writing.  

Received: 12 September 2015/ Revised: 29 December 2015/ Accepted: 22 February 2016/ Published: 27 June 2016  

Publisher: Asian Online Journal Publishing Group 

 
 

 

 

 

 

 

 

 

 

 

 

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Economy, 2016, 3(2):74-78 

 

 

 

 

75 

 

1. Introduction 
Inflation is considered to be one of the key economic targets and keeping inflation evenly low means a stable 

economic environment for investment, and therefore, creates the benign atmosphere for the best possible level of 

economic growth for a long period of time. Prior to 1986 in Nigeria, there was administrative fixing of interest rates, 

which failed to achieve the desired policy objective of promoting among other things, investment and growth in the 

real sector as a result of rising inflationary pressure necessitated by real low interest rates, thus discouraging savings 

and as such, the financial sector remained grossly underdeveloped. But with the deregulation of the financial sector 

in 1986 and the introduction of market determined interest rate and implementation of full deregulation of interest 

rate in 1996, banks were allowed to set their deposit and lending rates according to market condition. 

The Monetary Policy Rate (MPR) was the principal instrument used to control the direction of interest rates and 

anchor inflation expectations in the economy. Most measures of inflation moderated throughout the period in 

response to the policy measures implemented by the Bank. Year-on-year headline inflation decreased to 8.0 per cent 

in December 2013, from 8.4 per cent in June 2013 and 12.0 per cent in December 2012. Food inflation also declined 

marginally to 9.3 per cent from 9.6 per cent over the same period. However, core inflation rose from 5.5 per cent to 

7.9 per cent between June and December 2013 continued to contribute significantly to the robust performance of the 

economy after the shock of the global financial crisis in 2008 (on the one hand and the domestic banking crisis of 

2009 on the other). In spite of these developments, output remained relatively high while inflation decelerated in 

2013 (Central Bank of Nigeria, 2014). 

In the recent years, interest rate has been raised to curtail the growing rate of inflation. The effect of inflation risk 

on interest rate has not been given much attention resulting to scanty literature on the subject matter. However,  this 

paper differs from previous papers in the following dimensions; firstly, it investigates whether direct relationship 

exist between interest rate relative to inflation and inflation risk in Nigeria as found in other countries. Secondly, it 

measures inflation risk via the framework of autoregressive conditional heteroscedasticity models and selects the 

subclass of ARCH models that best describe inflation uncertainty. 

The rest of the paper is organized as follows; section 2 deals with the literature review, section 3 presents the 

materials and method, section 4 presents the data analysis and results and section 5 deals with the conclusion and 

policy implications. 

 

2. Literature Review 
Earlier studies have shown that inflation uncertainty have positive relationship with interest rate. Many 

researchers like Fama and Schwert (1977); Mishkin (1981); Fama and Gibbons (1982) and Chan (1994) have 

provided empirical evidence for the positive relationship between expected inflation variation and the t-bill rates 

under different specifications such as asset pricing models.  

Gul and Ekinci (2006) investigated the interaction between nominal interest rates and inflation for Turkey over 

the period of 1984-2003. Their result supports the idea that there is a long-run relationship between interest rates and 

inflation for Turkish markets. They also find that causality exists in only one direction from nominal interest rates to 

inflation. Kugler (1982) investigated the dynamic relationship between short term interest rates and inflation for the 

US, the UK, France, Germany, and Switzerland for the period 1974-1980. The result strongly suggests the variation 

of the nominal interest rate and inflation help to predict the ex ante real interest rate. 

Umoru and Oseme (2013) examined the relationship between inflationary expectations and the variations in 

interest rate in Nigeria using the Generalized Method of   Moment (GMM) estimator and their result indicated that 

the effect of interest rate variation on expected inflation in Nigeria is negative and significant. Berument (1999) 

studied the effect of inflation and uncertainty on interest rates in the  UK with quarterly data from 1958:4 to 1994:4 

and the result showed that both expected inflation and conditional variability of inflation positively affect the UK 

three-month treasury- bill rate. 

Herwartz and Reimers (2006) employed a VEC model to examine the relationship between inflation and interest 

rates for 114 economies over a 45 year period using monthly data.  

Interest rates and inflation are found to exhibit a long-run equilibrium relationship for numerous economic states. 

However, in states with large positive changes of inflation, high inflation risk or high interest rates, a long-run 

equilibrium relationship may not exist.  

 

3. Materials and Method 
This section provides information on source of data collection, variable measurement and definition, model 

specification and method of unit root test. 

 

3.1. Source of Data Collection 
The data sets on monthly consumer price index (CPI) and deposit rate were obtained from published Central 

Bank of Nigeria (CBN) statistical bulletin of 2013 and March 2015. The data sets cover the period of 1995:M1 to 

2014:M12. 

 

3.2. Variable Measurement and Definition 
One of the most commonly used surrogate to inflation is the CPI hence, this paper used CPI to measure inflation 

and monthly deposit rate (DR) is used to measure interest rate.  And the variables are defined using first difference of 

natural logarithm of present and previous values of each variable multiplied by 100 and are presented as follows; 

Inflation rate is defined as 100log
1











t

t

t
CPI

CPI
ifr , interest rate is defined as 100log

1











t

t

t
DR

DR
itr . 

Moreover, since inflation risk is not directly observable, the better describing Conditional Heteroscedasticity model 



Economy, 2016, 3(2):74-78 

 

 

 

 

76 

 

between Autoregressive Conditional Heteroscedasticity (ARCH (1)) Model and Generalized ARCH (1, 1) model 

were adopted to measure inflation risk. In other words, inflation risk is measured using inflation volatility 

(conditional variance). 

According to Engle (1982) given the mean equation of inflation as 
tt  inf the ARCH(1) is of the form; 

2

1

2




tt
        (1) 

were the nonnegativeness and stationarity of 2

t  are guaranteed for ω > 0, 0  for and .1  Hence, 2

t  

becomes a function of the previous squared shock, large shocks of either sign tend to be preceded by large shock and 

vice versa.  Though the ARCH (1) model can capture the stylized facts of volatility clustering and excess kurtosis, its 

short coming is that, it is unlikely that the model accommodates for the features related to the autocorrelation 

function of squared disturbances 2

t . And according Bollerslev (1986) GARCH(1, 1) is of the form; 

2

1

2

1

2




ttt
      (2) 

Where ),,0( 2 vt
t

  ,  the tail parameter v > 2 and t-distribution approaches normal distribution if v

. According to the property of GARCH model, 1)(  and  1 ,0  
 
show that the model is covariance 

stationary.  Again, a large 2

1-t

2

1 or      t   gives rise to a large 2

t . This means that a large 2

1t   tends to be followed 

by another large 2

t , generating again, the well-known behavior of volatility clustering in financial time series. 

 

3.3. ERS Unit Root Test 
Elliot Rothenberg, and Stock Point Optimal (Elliott et al., 1996) Test is a unit root test that is based on the quasi-

differencing regression 

      ttt aaxdayd  


 //       (3) 

where, 














 1 t if       y

1  t if                  
)/(

1t t

t

t
ay

y
ayd      (4) 

and tx  contains either a constant, or a constant and trend, )(a is the OLS estimates from this regression and t   is 

the residual. Let  )(ˆ)( 2 aaSSR t be the sum squared residuals function. The ERS  fea i  e  point opti a  te t 

 tati ti   of the nu   that       again t the a ternative that      , i  then defined a   

   0/))1()(( fSSRaaSSRPT             (5)  

where,  

 

 

 








t

T
a

,1  xif              7/5.131

1  xif                  /71

t

t
 (6) 

and 0f  is an estimator of the residual spectrum at frequency zero. The estimator 0f can be estimated using 

autoregressive spectral density estimator at frequency zero based upon the residual variance and estimated 

coefficients from the auxiliary regression. 

tptptttt uyyxyy    111 '.            (7) 

The AR spectral estimator of the frequency zero spectrums is defined as 

  )ˆˆˆ1/(ˆ
21

2

0 puf            (8)  

and  Tutu /ˆ 22  is the residual variance and ̂ ’  are e ti ate  fro  the auxi iary regre  ion.  

 

3.4. Model Specification 
The model specification for the effects of inflation and its risk on interest rate is based on multiple regression and 

it is given as follows 

ttifrtt
eifritr  2

.210
      (9) 

Where )2,1,0( i
i

  are parameter coefficients, 
2

.tifr
  is the conditional variance of inflation (inflation risk) 

and 
t

e  is the disturbance term and ),0(~ 2Ne
t

. 

 

4. Data Analysis and Results 
This section presents the Unit root test as shown in Table 1 below. Table 2 presents the analysis of conditional 

variance of inflation as a measure of inflation risk via ARCH(1) and GARCH(1, 1) models and selects the 

appropriate model that describes inflation risk using SIC and Table 3 gives the estimates of the effects of inflation 

and inflation risk on interest rate as specified in Equation (7). 

 

 

 

 

 



Economy, 2016, 3(2):74-78 

 

 

 

 

77 

 

Table-1. ERS Unit Root Test Analysis 

Variable 

 

Test 

 

Deterministic 

Terms 

Lags Test 

value 

critical values Remarks 

         1% 5%                       

t
ifr  ERS 

 

C 0  0.935938 1.925600 3.187550 I(0) 

C, t 0  1.297306  4.032450 5.652200 I(0) 

t
itr  ERS C 1  0.281204 1.925600  3.187550 I(0) 

C, t 1 1.039423 4.032450  5.652200 I(0) 
                       Source: Computed by the author 

 

Table 1 shows the result of ERS unit root test of inflation and interest rate. The lag orders used were suggested 

by Schwarz information criterion. The result indicates that inflation and interest rate are both integrated order zero, 

that is I(0), which shows that both variables are stationary. 

 
Table-2. Estimates of inflation volatility (risk) and Diagnostic test using ARCH(1) and GARCH(1, 1) 

Statistics Coefficient z-Statistic Prob. Remarks 

ARCH(1) Conditional Variance Equation   

C 0.000167 9.805471 0.0000 Significant at 1% 

2

1t
  0.409637 3.119283 0.0018 Significant at 1% 

Diagnostic test  

ARCH(LM 15lag) 0.280289  0.9966 No ARCH in the squared residuals up to 15th lag 

Ljung-Box 

Q-statistics 4.6614  0.995 

No serial correlation in the squared residuals up to 15th lag 

SIC -5.306162    

GARCH(1, 1) Conditional Variance Equation  

C 1.27E-08 0.044802 0.9643  

2

1t
  0.226103 5.137666 0.0000 

Significant at 1% 

2

1t
  0.780375 29.56277 0.0000 

Significant at 1% 

     

ARCH(LM 15lag) 0.211851  0.9993 No ARCH in the squared residuals up to 15th lag 

Ljung-Box 

Q-statistics 3.5950  0.999 

No serial correlation in the squared residuals up to 15th lag 

SIC -5.534332    

        Source: Computed by the author 

 

The comparison of the conditional variance of inflation as estimated  using ARCH(1) and GARCH(1, 1) indicate 

that there is neither ARCH nor serial correlation in the squared residuals up to lag 15. However, comparing the two 

models using SIC precludes that the GARCH(1,1) measure of inflation risk is preferable. 

 

4.1. Results and Discussion 

The result of model specification of Equation (9) is presented below. The values in brackets are the p-values. 

Estimation is via OLS 

0016.0R , 2.059763 stat Watson -Durbin    

   (0.8182)        (0.5539)     (0.9114)    value-p

[0.2301]  [-0.5928]   [-0.1114]  

2
.

5905.21718.00008.0         

2 





Statistict

t
e

tifrt
ifr

t
itr 

 

 

The estimated regression model above shows that inflation has an insignificant negative effect on interest rate. 

This result differs from the findings of Berument (1999); Fama and Schwert (1977); Mishkin (1981); Fama and 

Gibbons (1982) and Chan (1994) who find positive relation between inflation and interest rate. And inflation risk 

(measured using conditional variance of inflation) has positive influence on interest rate, but is not significant. This 

finding agrees with that of Berument (1999) in the UK, though the effect of inflation risk in Nigeria is not 

statistically significant. The Durbin-Watson Statistic is approximately 2 suggesting absence of serial correlation in 

the model. 

The R² value of 0.0016 is very low; indicating about 0.2% variation in interest rate is explained by inflation and 

inflation risk. This result shows that other macroeconomic factors rather than inflation and inflation risk explained 

about 99.8% variation in interest rate. 

 

5. Conclusion and Policy Implications 
This paper examines the effects of inflation and inflation risk on interest rate in Nigeria. The result reveals that 

inflation and inflation risk exact negative and positive impacts on interest rate respectively, but none is significant. 

The negative effect of inflation rate on interest rate is an indication of indirect relationship between the two variables. 

Inflation risk although not significant, has a direct relation with interest rate. 

The insignificant effects of inflation and inflation risk on interest rate and a very low R² value imply that interest 

rate variation is influence by other macroeconomic factors rather than changes in inflation and inflation risk. 

However, the result also implies that building a measure to curb inflationary pressure based on monthly deposit rate 



Economy, 2016, 3(2):74-78 

 

 

 

 

78 

 

may not be realistic. Hence, a more practical direction of interest rate that can cut back the rising inflation by our 

MPR becomes a necessity.  

 The findings of this paper also provide a lead way for further investigation on which measure of interest rate has 

strong relationship with inflation in Nigeria. This is essential for the purpose of practical monetary policy that can 

control inflationary pleasure.  

 

References 
Berument, H., 1999. The impact inflation uncertainty on interest rates in the UK. Scottish Journal of Political Economy, 46(2): 207- 218. 
Bollerslev, T., 1986. Generalized autoregressive conditonal heteroscedasticity. Journal of Econometrics, 31(3): 307-327. 

Central Bank of Nigeria, 2014. Monetary policy review. Available from www.cbn.gov.ng. 

Chan, L.K.C., 1994. Consumption, inflation risk, and real interest rate: An empirical analysis. Journal of Business, 67(1): 69-96. 

Elliott, G., T.J. Rothenberg and J.H. Stock, 1996. Efficient test for an autoregressive unit root. Econometrica, 64(4): 813-836. 
Engle, R.F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 

50(1): 987-1007. 

Fama, E. and M. Gibbons, 1982. Inflation, real returns and capital investment. Journal of Monetary Economics, 9(3): 297-323. 

Fama, E. and G. Schwert, 1977. Asset returns and inflation. Journal of Financial Economics, 5(2): 115–146. 
Gul, E. and A. Ekinci, 2006. The causal relationship between nominal interest rate and inflation: The case of Turkey. Scientific Journal of 

Administrative Development, 4(21): 54-69. 

Herwartz, H. and H. Reimers, 2006. Modelling the fisher hypothesis: World wide evidence. German Economic Review, 7(1): 65-86. 

Kugler, P., 1982. The dynamic relationship between interest rates and inflation: An empirical investigation. Empirical Economics, 7(1): 25–
137. 

Mishkin, F.S., 1981. The real interest rate. An empirical investigation. Carnegie-Rochester Conference Series on Public Policy, 15(1): 151-200. 

Umoru, D. and S.A. Oseme, 2013. Inflation expectations and interest rate variation in Nigeria: An econometric assessment of the evidence. 

International Journal of Development and Economic Sustainability, 1(2): 1-12. 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
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