### Revisiting The Fisher Hypothesis: The Case Of India

### CHAPTER 1 - INTRODUCTION

### 1.1 CONTEXT OF THE STUDY

In 1930 Irving Fisher investigated the relationship between the nominal interest rate, the real interest rate and expected rates of inflation. He discovered that a long-run equilibrium relationship existed between the nominal rate of inflation and expected rate of inflation. More commonly referred to as the Fisher effect, Fisher (1930) found that a one percent increase in the rate of inflation would be reflected by a one percent increase in the nominal interest rate leaving the real rate of interest unchanged.

The fact that the Fisher hypothesis involves such key macroeconomic variables such as interest rates and inflation has led to numerous empirical analyses. A key motivation behind many of these studies relates to how the fisher hypothesis affects monetary policy and monetary neutrality models of any country. As Carneiro, Divino and Rocha (2002) point out, validation of the Fisher effect would imply that real interest rates are unaffected by anticipated changes to either money supply, or the rate of inflation. Nussair (2009), Peng (2009) and Hawtrey (1997) highlight the importance of understanding the behaviour of real interest rates with regards to not only intertemporal savings and investment decisions, but also other fundamental variables such as exchange rates through its influence on trade and capital flows.

The Fisher hypothesis has endured years of empirical testing, however, the vast majority of the studies have utilised data from major developed countries such as the USA, UK and Australia, and have yielded mixed results.

### 1.2 OBJECTIVES OF THE STUDY

In comparison, the amount of empirical studies of the Fisher effect in developed countries is far greater than the amount of studies that exist for the Fisher effect in developing countries.

India is one of the most well-known developing counties in the world, combined with the country's phenomenally high economic growth rate and Therefore, this study seeks to extend the recent work of Balachandra (2008) by testing for the Fisher effect in a developing economy, and centres on testing in India. The methodology utilised follows

The data is analysed over the period

This study is organized as follows:

### CHAPTER 2 – THEORY & LITERATURE REVIEW

### 2.1 THEORY

In 1930 Irving Fisher investigated the relationship between UK interest rates and inflation. In his analysis of the relationship he decomposed interest rates into nominal interest rates and real rates of interest. The connection of all three variables is described below:

### = - (1.1)

With:

( ) = Real interest rate, simply defined as the improvement in purchasing power

= Nominal rate of interest, simply defined as the rate of interest paid by banks

( ) = Rate of inflation, simply defined as the general rise in price levels in the economy. It states that the real rate of interest reflects the difference between the nominal interest rate and the rate of inflation. Rearranging the equation produces:

### = + (1.2)

More accurately, because future rates of inflation cannot be predicted, expected rates of inflation are used, therefore the equation becomes:

### = + (1.3)

The above Fisher equation shows that the summation of the real rate of interest ( ) and the expected rate of inflation ( ) can be expressed as the nominal rate of interest ( ). The equation implies that changes in real interest rates and/or expected rates of inflation would change the nominal rate of interest.

Fisher (1930) puts forward that because capital productivity and technological constraints are the most significant factors that affect real interest rates, major changes in nominal rates of interest should reflect increases in expected inflation and unstable prices.

In a practical context, using rational expectations and the theory of efficient capital markets the fisher equation can encompass the actions of rational agents such as savers. Most savers would understand the risk associated with an expected reduction in their future purchasing power, and the negative effect it would have on their own wealth. As a precaution to this, most would chose to invest their money. This leads to a overall increase in the level of investment and the demand for financial assets subsequently increasing the amount of loanable funds, which in turn would lead to a reduction in real rate of interest1. Fisher (1930) supported that the increase in expected rates of inflation would be larger than the decrease in real interest rates to such a level that, nominal interest rates would rise following a rise in expected rates of inflation.

The one-for-one relationship between the nominal interest rate and expected rates of inflation, with the notion of a constant real rate of interest over time, is what is commonly referred to as the Fisher effect.

As mentioned earlier, there is a vast amount of empirical literature that has tested the extent to which the Fisher effect holds. Significant differences in estimation techniques, econometric methodologies, proxies for inflationary expectation, and countries that have been analysed have led to a variety of results. The next section discusses the variety of studies and focuses on literature that has tested for the fisher effect in developing or emerging economies.

### 2.1 LITERATURE REVIEW

Since the seminal work of Fisher (1930) the Fisher hypothesis has been studied extensively especially in developed countries such as America (US). Mishkin (1992) investigated the relationship between US inflation rates and interest rates and produced evidence supporting the existence of a long-run Fisher effect, but could not validate the existence of a short-run fisher effect. Mishkin (1992) differentiated between the long-run Fisher effect and the short-run Fisher effect. He described the long-run fisher effect as the long run trending of interest rates and inflation rates, in which expected rates of inflation were reflected in long-term interest rates. The short-run Fisher effect was described as changes in expected rates of inflation being reflected in short-term interest rates. He analysed monthly data over 1953-1990 and applied the Engle and Granger (1987) methodology to test for the presence of cointegration between rates of inflation and interest rates. His findings suggested that interest rates and inflation rates moved together and would converge to a long-run equilibrium, subsequently supporting the existence of the long-run Fisher effect. Crowder and Hoffman (1996) also tested for the fisher effect in the US and looked at 3-month US Treasury Bill rates and inflation rates over 1952-1991. They employed Johansen's (1988) maximum likelihood methodology and also found evidence of a long-run cointegrating relationship. Their results showed that changes in expected inflation led to adjustments in the nominal interest rate however, they found that the adjustment was greater than the ‘one-for-one' basis hypothesised by Fisher (1930). Other significant studies of the fisher effect in the US, that apply the Johansen cointegration tests include Fahmy and Kandil (2003), Chu, Pittman & Yu (2003), Yuhn (1996), and Peláez (1995). The majority of literature that analyses the fisher effect in the US, finds sufficient evidence to support the fisher hypothesis, however studies involving other developed countries have produced varying results.

In Yuhn's (1996) analysis of data from the UK, US, Germany, Japan and Canada, satisfactory support for the existence of the fisher effect could not be found for either Canada or the UK. Ghazali and Ramlee (2003) were also unable to determine a long-run relationship between nominal interest rates and rates of inflation in their analysis of the G7 countries between 1974 and 1996. Koustas and Serletis (1999) using Engle and Granger (1987) cointegration examine 11 countries (Germany, France, the Netherlands, the UK, the US, Canada, Belgium, Greece, Ireland, Denmark and Japan) but their results suggest little evidence to support the fisher effect. In contrast, Granville and Mallick (2004) follow a similar methodology in their analysis and find that the linear combination of both UK nominal interest rates and inflation appears to be stationary, supporting the fisher hypothesis.

The majority of empirical studies of the fisher effect in Australia have to a reasonable extent, shown support for the fisher hypothesis. Studies by Mishkin and Simon (1995) find support for the existence of the long-run fisher effect with inflationary expectations, for the period 1962-1993. In addition, Olekalns (1996) and Hawtrey (1997) are able to verify the fisher effect during certain periods following the deregulation of the financial system (1984-1994). However, Inder and Silvapulle (1993) find results that conflict with the fisher hypothesis in their study over the period 1965-1990, rejecting postulated relationship between nominal interest rates and expected rates of inflation.

The majority of the empirical research conducted on the fisher effect has focused on developed countries, with broadly consistent results. In comparison, there are only a few significant studies investigating the fisher effect in developing countries.

In a more recent study, Berument and Jelassi (2002) conduct an across-the-board study of the fisher hypothesis by sampling a mix of 26 developing and developed countries, including India. They focus on finding a positive long-run linear relationship between nominal interest rates and expected rates of inflation (explanatory variable), by analysing the short-run movement of interest rates. The strength of the fisher effect was dependent on the coefficient estimate, a strong form of the fisher effect would be represented by a positive coefficient estimate equal to one, whereas a weak form would have an positive estimate but less than one. The authors find evidence for the strong form of the Fisher effect in 16 out of the 26 countries sampled, and establish that the amount of evidence supporting the Fisher hypothesis in developed countries is greater than that in developing countries. Berument Ceylan & Olgun (2007) extend previous empirical work by testing the strength of the Fisher hypothesis, and similarly try to establish a positive relationship between expected inflation and interest rates, but this time use a sample of 52 countries. They find that out of the 45 developing countries there was not enough evidence to support the fisher hypothesis in 22 of them, on the other hand they were able to find evidence of the fisher effect in all the G7 countries tested. Kasman, Kasman & Turgutlu (2005) use a similar fractional cointegration technique to those applied by Lardic and Mignon (2003) and Ghazali and Ramlee (2003) to validate the Fisher hypothesis in a mixture of 33 developed and developing countries, including India. Their motivation for using a fractional cointegration methodology in order to verify a long-run relationship between nominal interest rates and rates of inflation, is based on the idea that traditional cointegration techniques are not powerful enough to accurately describe the relationship between the two variables. Their findings could not show support for the majority of the countries tested when traditional cointegration tests were employed, but when fractional cointegration tests were employed a large majority of the countries displayed results in support of the Fisher hypothesis.

Gul (2007) observes the Fisher hypothesis in the context of the Turkish Economy. He employs the Johansen cointegration methodology and monthly interest and inflation rate data over the period 1990-2003. Gul (2007) is able to determine a long-run relationship between nominal interest rates and inflation but is unable to substantiate a one-for-one relationship between the two.

With Latin America countries being well known for their high levels of inflation, analysis of the fisher effect in these countries has been very popular. Jorgensen and Terra (2003) apply a VAR model utilizing 4 variables in order to assess the relationship between interest rates and inflation in seven key Latin American counties (Brazil, Chile, Peru, Mexico, Argentina, Colombia and Venezuela). Their results are only able to prove the fisher relation in Mexico and Argentina. Likewise, a Study by Thornton (1996) that explores the fisher hypothesis using 91- day Treasury bill rates, and inflation rates over the period 1978-1974 is also able to verify the fisher effect in Mexico. Phylaktis and Blake (1993) use cointegration techniques and unit root tests in their studies of the long-run fisher effect within Brazil, Mexico, and Argentina. Utilizing data over 1970-1980 they find that a one-for-one long run relationship between nominal interest rates and inflation rates exists in all three countries. A later study conducted by Carneiro, Divino and Rocha (2002) investigating the same three countries could only find support for the fisher effect in Argentina and Brazil. Carneiro, Divino and Rocha (2002) used monthly data over the 1980-1997 periods and carried out Johansen cointegration analysis and weak exogeneity tests to show that the interest rates changed in order to compensate for changes in expected inflation. This was found in the context of Brazil and Argentina but analysis over the period of Mexico showed that inflation rates adjusted to reflect changes in interest rates. A key observation that arises from the Latin American studies above is the relative consistency in results with substantial evidence in favor of the fisher effect. Wafa and Sabah (2007) employ panel unit root tests for 10 East Asian countries3. Key motivation behind this choice of methodology was to achieve greater power in their tests compared to that of traditional unit root tests, by taking advantage of the cross-country differences in estimation of the data4. Using the panel unit root tests, Wafa and Sabah (2007) were able to prove a long-run relation existed between nominal interest rates and inflation for all the East Asian Countries. They find support for the view expressed by Granville and Mallick (2004) of monetary policy being a useful means of influencing long-term interest rates. A more recent test of the Fisher hypothesis for 6 Asian countries5 by Nusair (2008) finds fairly contradictory results. Nusair (2008) analyses quarterly data over the period 1978-2005 and uses the Engle-granger procedure, Gregory-Hansen procedure, and Dynamic OLS tests (DOLS), to identify a long-run linear relationship between nominal interest rates and expected rates of inflation. Support for the Fisher hypothesis is obtained for Korea, Thailand, Malaysia and Singapore. Using the Engle-granger methodology Nusair (2008) finds robust evidence for Thailand, and weak evidence for Korea and Malaysia. The Gregory-Hansen method also used by Nusair (2008) “accounts for an endogenously determined shift in the cointegrating vector” and shows support at the 10% level for Singapore and Malaysia, and at the 5% level for Korea. In summary, robust support for the fisher effect is only found in Korea, Malaysia and Singapore. Peng (2009) finds similar results to that of Berument Ceylan & Olgun (2007) in his analysis of the Fisher effect in China. Peng (2009) uses the Johansen maximum likelihood cointegration technique to study data over the period 1993-2005, and establishes a cointegrating association between nominal interest rates and inflation. Peng (2009) also employs the error correction model to determine long and short-run fisher effects, and find insufficient proof to support a short-run fisher effect.

Paul (1984) is one of the earliest studies that analyses the Fisher effect, in the context of India. His research was aimed at studying the impact of the changing rates inflation rates on nominal rates of interest over the period 1952-1977. Using both short and long-term interest rates, results of his study found that there was a positive relationship between expected rates of inflation and nominal rates of interest, supporting Fisher's hypothesis. In addition, Paul (1984) found that rises in expected rates of inflation were only partially passed on to nominal rates of interest, a finding highlighted by Fama (1975). On the contrary, a study by Payne and Ewing (1997) found no evidence of the Fisher effect in India. Applying the Johansesen cointegration methodology they assess the hypothesis in 9 developing countries (Argentina, Fiji, India, Niger, Thailand, Malaysia, Sri Lanka, Singapore and Pakistan) but could only fully confirm the fisher effect in Sri Lanka, Pakistan and Malaysia. Other, significant studies of the Fisher hypothesis in the context of India include Nachane (1988) and Bhanumurthy and Agarwal (2002). Nachane (1988) finds that the administering of interest rates in India during the time was the reasoning behind not being able to find a one-for-one relationship between monthly interest rates and expected rates of inflation over the period 1970-1985. Bhanumurthy and Agarwal (2002) research the long-run relationship between nominal interest rates and expected inflation and utilize 3 different interest rates (Call money rate, Commercial paper and 364 day- Treasury bill rates) and rates of inflation. In their examination of monthly Indian data over the period 1990-2001 using an autoregressive distributed lag method, they could not find evidence to support the fisher relation. Thenmozhi and Radha (2005) also take into account the administering of interest rates in India and explore the short and long run movements of nominal interest rates and inflation. Employing cointegration techniques and error correction model, their findings reveal a long relationship between yields on 91-day treasury bills and inflation. They use the error correction model to take into account the short run alteration needed for the long run relationship. With evidence of co-movement between nominal interest rates and expected rates of inflation, they accept the Fisher hypothesis. Sathye, Canberra, Sharma and Liu (2008) examine the fisher hypothesis in emerging economies and focus on validating the fisher effect in India based on short-term nominal interest rates and inflation. They carryout Augmented Dickey-Fuller unit root tests, utilize both the Engle-Granger and Johansen-Juselius cointegration techniques, and carry out Granger causality tests with Error correction model to determine the nature of the relationship between the two variables. Using monthly data over the period 1996-2004 they do not reject the existence of the Fisher effect in India, as results from both cointegration tests indicate a cointegrating relationship between short-term interest rates and expected rates of inflation. Sathye, Canberra, Sharma and Liu (2008) also show that “expected inflation is Granger caused by nominal short-term interest rates”, conveying the positive ability of short-term nominal interest rates in predicting future inflation.

Many researchers have endeavored to try and justify, why the Fisher effect may not be present, and why it cannot be proved to the same extent as first hypothesized by Fisher (1930). Sahu, Jha and Meyer (1990), Hsing (1997) and Olekalns (1996) observe that the contradictory nature of empirical tests of the Fisher effect is a result of variation in methodologies and data used. With the Fisher equation containing unobservable parameter estimates such as expected rates of inflation, Sahu, Jha and Meyer (1990) emphasize that the robustness of tests of the fisher effect clearly depend upon the choice of proxy used. Nusair (2009) extends his previous study by investigating reasons why previous studies have failed to show support of the Fisher effect. Nusair (2009) claims that the reasoning behind the failures is due to the assumption that adjustments between nominal interest rates and inflation occur at a constant rate, and represent a linear relationship, when this is not the case in most inflation-targeting economies. Similarly, Christopoulos and Leon-Ledesma (2007) in their analysis of quarterly US nominal interst rates and CPI inflation rate are able to find a non-linear cointegrating relationship between the two. They apply Monte Carlo simulations to the data and results indicate that the nonlinearites are a key factor in obtaining a less than one-for-one relationship in the Fisher relation. Fisher (1930) himself is unable to empirically prove his theorized ‘one-for-one' relationship in his study of US nominal rates of interest and inflation, only managing to attain correlation coefficients of a little less than one, and subsequently only moderately satisfying his hypothesis. One explanation for this, relates to the theory of money illusion. Money illusion can be described as the inability of agents to differentiate between changes in real and nominal variables. In a practical context, changes to the inflationary expectations of agents would not be fully accounted for in their intertemporal decision making, and subsequently not passed on through to nominal interest rates. Another explanation is based on ideas presented by Mundell (1963) and Tobin (1965). Mundell (1963) states that as the rate of inflation rises consumer purchasing power is likely to decrease, and subsequently lead to a fall in real interest rates. Tobin (1965) puts forward the idea that as inflation rates rise, there is a greater opportunity cost for agents who hold cash money, this leads to a fall in the amount of cash balances held and to a rise in the amount of holdings of real capital. The incorporation of these two school of thoughts is more widely known as the Mundell-Tobin effect, and offer an explanation as to why nominal rates of interest rise by a factor smaller than one, in response to changes in inflation.

Studies by Mishkin (1992), Hawtrey (1997), and Monnet and Weber (2001) have cited that the form, strength and efficiency of a country's monetary policy is reflected in the ability of changes to expected inflation to transmit through to nominal interest rates. With the effectiveness of monetary policy being a key motivation behind investigation of the Fisher effect, a significant study by Soderland (2001) shows that when the combination of an inflation-targeting outline, and an active monetary policy exist, the strength of the Fisher effect is reduced.

Darby (1975) and Feldstein (1976) take into account the impact of taxes on the relationship between nominal interest rates and expected rates of inflation. Darby (1975) asserts that a premium should be included to ensure constant real interest rates and emphasizes that nominal interest rates will vary in response to changes in expected inflation by a factor larger than one. Studies by Peek (1992) and Engsted (1996) find substantial support for the ‘Darby-Feldstein' effect. In contrast to the ‘Mundell-Tobin' and ‘Darby-Feldstein' effects the concept of the ‘Inverted Fisher effect' researched by Carmichael and Stebbing (1983) and Barth and Bradley (1988), also provides an alternative explanation as to why the fisher effect cannot be proven in its theoretical form. Carmichael and Stebbing (1983) extend a model where nominal interest rates extracted from financial assets are described as remaining constant, thereby indicating an inverse relationship between real interest rates and inflation. Utilising quarterly data on 3-month US and Australian Tresuary bills over 1953-1978, Carmichael and Stebbing (1983) are able to find support for the Inverted Fisher effect. However, later studies by Barth and Bradley (1988), Moazzami (1991) and Woodward (1992) fail to obtain satisfactory support for the inverted Fisher hypothesis.

From our study of the literature it is clear to see that the Fisher hypothesis/effect is a key macroeconomic relationship, and its popularity is highlighted though the substantial investigations of the Fisher effect in developed countries, and to a lesser extent in developing countries. Results from US and UK studies of the Fisher effect are fairly mixed, but overall are in favour of the fisher hypothesis. With research by Mishkin (1992), Crowder and Hoffman (1996), Granville and Mallick (2004) and Ghazali and Ramlee (2003) all showing support for the long-run fisher hypothesis. Similarly, research utilising data from Australia and a mixture of European counties such as the G7, have on the whole been able to verify the existence of the Fisher effect. This is confirmed by studies by Berument and Jelassi (2002) and Berumant Ceylan & Olgan (2007) who examine a comprehensive mixture of both developed and developing countries. Surprisingly, empirical literature analysing Latin American countries with their characteristically high, and volatile levels of inflation finds that the majority of the studies reveal fairly undisputed results in favour of the fisher effect. Investigations of many East Asian countries have yielded mixed results, with many researchers looking to analyse the impact of the Asian Financial crisis on the Fisher effect such as Nusair (2008). Research of the Fisher hypothesis/effect has been relatively scarce in the context of the Indian economy. However, studies by Paul (1984), Thenmozhi and Radha (2005), and more recently by Sathye, Canberra, Sharma and Liu (2008) are all able to justify the existence of the Fisher relation in India. In contrast, the use of Johansen cointegration techniques by Payne and Ewing (1997) and the application of an autoregressive distributed lag methodology by Bhanumurthy and Agarwal (2002) in their studies reject the existence of the Fisher effect in India. The popularity of two key methodologies employed in verifying a long-run relationship between nominal rates of interest and inflation, include the Engle Granger cointegration concept and the Johansen (1988) cointegration test. Many explanations as to why the Fisher effect cannot be found in its explicit theoretical form have been developed. A key and significant finding, suggests that major differentials in methods used to test the hypothesis, and the variation in proxies used for nominal interest and inflation variables have been the cause of such a wide variety of results. Other explanations include the ‘Mundell-Tobin' and ‘Darby-Feldstein' effect, in addition, the concept of the ‘Inverted Fisher effect' and the effectiveness of a country's monetary policy.

### CHAPTER 4 – METHODOLOGY

From the analysis of the literature surrounding the Fisher Hypothesis, this study aims to study the relationship between short-term nominal interest rates and inflation in India. Fisher (1930) claimed that a one-for-one positive relationship existed between expected rates of inflation and nominal interest rates. This dissertation chooses to follow similar econometric methodologies used by Mishkin (1992), Mishkin and Simon (1995) and Sathye, Canberra, Sharma and Liu (2008) to validate the Fisher effect in the context of the Indian economy.

### 4.1 THEORETICAL & EMPIRICAL MODEL

The relationship between nominal interest rates, ‘ex-ante' real interest rates and expected rates of inflation are combined in Fisher's (1930) equation:

= + (1.4)

With:

( ) = the nominal interest rate

( ) = the ‘ex-ante' real interest rate

( ) = expected rates of inflation

The ‘ex-ante' real interest rate can be described as the unobservable, expected rate of real interest, with ‘ex-post' real rates of interests indicating the actual rate. As mentioned previously both expected rates of inflation and ‘ex-ante' real rates of interest must be proxied. The theory of rational expectations signified by Fama (1975) asserts that prospective variations in future prices are created by taking into account all available information the time. Hence, realised rates of inflation can be decomposed into the expected inflation rate ( ) together with a forecast error ( ).

= + (1.5)

This error term can be described as being completely random and can be translated as E ( ) = 0, and for this reason is stationary.

Fisher (1930) postulates that the real rates of interest are constant; subsequently the ‘ex-ante' real rate of interest ( ) can be created from a constant value (a) and a stationary error ( ):

= a + (1.6)

Substituting (1.6) into (1.4) and rearranging:

= a + -

This equation is representative of the relationship hypothesised by Fisher (1930). Many past studies of the Fisher effect have incorporated expected inflation rates as a dependent variable, evaluating the equation below:

= + + (1.7)

Citing the methodology applied in Mishkin (1992) we rewrite the above equation as:

= + + (1.9)

where = + . This equation can be further modified to represent a regression framework:

= + (1.10)

Where, = the inflation rate at time t

= the nominal interest rate at time t

= the sum of the two stationary components at time t

Considerable correlation between nominal interest rates and actual rates of inflation is one of the key conditions that validate the Fisher effect, with a one-for-one relationship describing the hypothesis in its strictest form. The coefficient in the regression equation represents the extent to which the Fisher effect holds. Subsequently, a coefficient of one would represent a unit proportional relationship between nominal interest rates and inflation, and a value of zero would represent the non-existence of the Fisher effect.

### Considering the nonstarionary charistecs of macroeconomic time series variables

However, taking into account the nonstationary nature of macroeconomic time series data such as inflation and nominal rates of interest as proposed by Nelson and Plosser (1982), suggests that the estimation of equation (1.10) would be subject to the problem of spurious regression described by Granger and Newbold (1974). This is attributed to the fact that the t-ratios (on which the evaluation of the significance of the estimated coefficient is based on) could be misleading. Consequently, this could lead to possible invalid conclusions of the statistical relationship between the variables, and could therefore lead to false acceptances of the presence of the Fisher effect within the UK.