Determinants of Nominal Interest Rates in India

Abstract

This paper examines the role of monetary factors in the variation of nominal interest rates in India for the deregulated regime of interest rates and the exchange rates. Empirical analysis involves quarterly time series dataset including interest rates on 91-day, 364-day treasury bills (TBs), call money rate, money supply (both narrow and broad money), income and exchange rate over the period 1996–97:Q1 to 2015–16:Q4. In the short-run and the long-run variations of interest rates on TBs, role of the broad money supply, income and exchange rate are established; where the broad money negatively affects interest rates indicating the Liquidity effect view. Income and depreciation of exchange rate lead to raise interest rates. In the variations of the call money rate income, the narrow money and the broad money have significant role but the role of exchange rate is not established. The paper also finds evidence that interest rates on TBs are related to the relative growth of money supply and anticipated nominal income. Theatrical base of such relation is discussed based on some seminal work of Friedman. Based on these findings the paper concludes that it would be effective to control interest rate through a comprehensive monetary management.

Appendices

Appendix A

How Nominal Interest Rates are Related to the Relative Growth of Money supply and Anticipated Nominal Income?

Theoretical relation that nominal interest rate is related to the relative growth of money supply and anticipated nominal is has been presented in this section. This theoretical exposition is mainly based on some seminal work of Milton Friedman such as Friedman (1969): ‘The Optimum Quantity of Money, and Other Essays’; Friedman (1970): ‘A Theoretical Framework for Monetary Analysis’; Friedman (1971): ‘A Monetary Theory of Nominal Income’; Friedman (1971): ‘The Keynesian Challenge to the Quantity Theory’.

Friedman view that Keynesian interest rate theory is not a complete theory as it fails to explain empirical phenomena concerning movement of interest rate following changes in money supply. Specifically, Keynesian interest rate theory cannot explain situations where interest rate displays positive response to money supply variations. Again, the Fisher equation fails to explain negative sensitivity of interest rate to money supply. He proceeds to reformulate the interest equation which essentially integrates the fundamental mechanism and reality in Keynesian interest rate theory with the macroeconomic exposition of microeconomic decision as manifested through the Fisher equation of interest rate.

To explain this, let us consider a money demand and a money supply functions are $\hbox {M}^{\mathrm {D}}=\hbox {l}\left( \hbox {i} \right) \hbox {Y}\left( {\mathrm{t}} \right)$ and $\hbox {M}^{\mathrm {s}}=\hbox {M}\left( {\mathrm{t}} \right)$ respectively:

$$\begin{aligned} \hbox {At equilibrium}, \hbox {M}^{\mathrm {D}}= & {} \hbox {M}^{\mathrm {s}}\nonumber \\ \hbox {So}, \hbox {l}(\hbox {i})\hbox {Y}({\mathrm{t}} )= & {} \hbox {M}({\mathrm{t}})\nonumber \\ \hbox {or}, \hbox {Y}\left( {\mathrm{t}} \right)= & {} \hbox {M}\left( {\mathrm{t}} \right) \frac{1}{\hbox {l}( \hbox {i})}\nonumber \\ \hbox {or}, \hbox {Y}( {\mathrm{t}} )= & {} \hbox {M}\left( {\mathrm{t}} \right) \hbox {V}( \hbox {i}) \end{aligned}$$

(2)

where $\hbox {Y}\left( {\mathrm{t}} \right)$ is the nominal income at time period ‘t’, $\hbox {l}\left( \hbox {i} \right)$ is the coefficient of cash-balance demand, $\hbox {M}\left( {\mathrm{t}} \right)$ money supply at time ‘t’, $\hbox {V}\left( \hbox {i} \right)$ is the velocity of money, (which is not a constant, its variation is linked to that in interest rate). Therefore, given $\hbox {V}\left( \hbox {i} \right) ,$ and $\hbox {M}\left( {\mathrm{t}} \right)$ in any economy at any period (t), the nominal income is determined.

Friedman starts with the Fisher’s interest rate equation which is:

$$\begin{aligned} \hbox {i}_{\mathrm{t}} =\hbox {r}_{\mathrm{t}} +{ \pi }_{\mathrm{t}}^{\mathrm{e}} \end{aligned}$$

(3)

where $\hbox {i}_{\mathrm{t}}$ is the nominal interest rate, $\hbox {r}_{\mathrm{t}}$ is the real interest rate, ${\uppi }_{\mathrm{t}}^{\mathrm{e}}$ is the expected inflation.

He then seeks to explain ${\pi }_{\mathrm{t}}^{\mathrm{e}}$. He holds that

$$\begin{aligned} \hbox {Y}_{\mathrm{t}} =\hbox {X}_{\mathrm{t}} \hbox {P}_{\mathrm{t}} \end{aligned}$$

(4)

where $\hbox {X}_{\mathrm{t}}$ is the real income, $\hbox {Y}_{\mathrm{t}}$ is the nominal income, $\hbox {P}_{\mathrm{t}}$ is the price level

He holds further that the real income ($\hbox {X}_{\mathrm{t}} )$ and price level ($\hbox {P}_{\mathrm{t}} )$ are determined through two independent processes. Consequently, $\hbox {X}_{\mathrm{t}}$ and $\hbox {P}_{\mathrm{t}}$ are independent such that:

$$\begin{aligned} \hbox {E}( {\hbox {Y}_{\mathrm{t}} })= & {} \hbox {E}({\hbox {X}_{\mathrm{t}} \hbox {P}_{\mathrm{t}} })=\hbox {E}\left( {\hbox {X}_{\mathrm{t}} } \right) \hbox {E}\left( {\hbox {P}_{\mathrm{t}} } \right) \\ \hbox {or}, \hbox {Y}_{\mathrm{t}}^{\mathrm{e}}= & {} \hbox {X}_{\mathrm{t}}^{\mathrm{e}} \hbox {P}_{\mathrm{t}}^{\mathrm{e}} \end{aligned}$$

where $\hbox {X}_{\mathrm{t}}^{\mathrm{e}}$ is the expected real income, $\hbox {Y}_{\mathrm{t}}^{\mathrm{e}}$ is the expected nominal income, $\hbox {P}_{\mathrm{t}}^{\mathrm{e}}$ is the expected price level.

Taking log

$$\begin{aligned} \log \left( {\hbox {Y}_{\mathrm{t}}^{\mathrm{e}} } \right) =\log (\hbox {X}_{\mathrm{t}}^{\mathrm{e}} )+\log (\hbox {P}_{\mathrm{t}}^{\mathrm{e}} ) \end{aligned}$$

Differencing with respect to ‘t’ we have,

$$\begin{aligned} \frac{1}{\hbox {Y}_{\mathrm{t}}^{\mathrm{e}} }\frac{\hbox {dY}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}= & {} \frac{1}{\hbox {X}_{\mathrm{t}}^{\mathrm{e}} }\frac{\hbox {dX}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}+\frac{1}{\hbox {P}_{\mathrm{t}}^{\mathrm{e}} }\frac{\hbox {dP}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}\nonumber \\ \hbox {or}, {\dot{\hbox {Y}}}^e_{\mathrm{t}}= & {} {\dot{\hbox {X}}}^{\mathrm{e}}_{\mathrm{t}}+\pi ^{\mathrm{e}}_{\mathrm{t}}\nonumber \\ \hbox {or}, {\uppi }_{\mathrm{t}}^{\mathrm{e}}= & {} \hbox {y}_{\mathrm{t}}^{\mathrm{e}} -\hbox {x}_{\mathrm{t}}^{\mathrm{e}} \end{aligned}$$

(5)

Equation (5) indicates that expected inflation rate is the difference between the expected rate of growth of nominal income and the expected rate of growth of real income. Now, putting (5) into (3) we have,

$$\begin{aligned} \hbox {i}_{\mathrm{t}}= & {} \hbox {r}_{\mathrm{t}} +{ \pi }_{\mathrm{t}}^{\mathrm{e}}\nonumber \\ \hbox {or}, \hbox {i}_{\mathrm{t}}= & {} \hbox {r}_{\mathrm{t}} +\hbox {y}_{\mathrm{t}}^{\mathrm{e}} -\hbox {x}_{\mathrm{t}}^{\mathrm{e}} \nonumber \\ \hbox {or}, \hbox {i}_{\mathrm{t}}= & {} \left( {\hbox {r}_{\mathrm{t}} -\hbox {x}_{\mathrm{t}}^{\mathrm{e}} } \right) +\hbox {y}_{\mathrm{t}}^{\mathrm{e}} \end{aligned}$$

(6)

Friedman holds that, because of money illusion, people usually expect real income growth to remain constant, and nominal income growth to undergo changes. Consequently given $\hbox {r}_{\mathrm{t}}$, we have a constant value for $\hbox {x}_{\mathrm{t}}^{\mathrm{e}}$.

Thus, $\hbox {r}_{\mathrm{t}} -\hbox {x}_{\mathrm{t}}^{\mathrm{e}} =\hbox {k}$ (constant)

In such case from Eq. (6) we have,

$$\begin{aligned} \hbox {i}_{\mathrm{t}} =\hbox {k}+\hbox {y}_{\mathrm{t}}^{\mathrm{e}} \end{aligned}$$

(7)

Thus, the nominal interest rate ($\hbox {i}_{\mathrm{t}} )$ is the sum of a constant and a rate of nominal income growth.

Friedman uses the adaptive expectation hypothesis for the determination of $\hbox {y}_{\mathrm{t}}^{\mathrm{e}}$. He holds that the change in the expected rate of growth of nominal income ($\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} )$ in proportion to the deviations of the observed from the anticipated rate of growth. This indicates that expectations are adjusted to the forecast error. A part of forecast error is taken into the reformulation of anticipated value of nominal income growth. Consequently,

$$\begin{aligned}&\hbox {y}_{{\mathrm{t}}+1}^{\mathrm{e}} =\hbox {y}_{\mathrm{t}} +{\beta }\left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right) \nonumber \\&\hbox {or},\, \hbox {y}_{{\mathrm{t}}+1}^{\mathrm{e}} -\hbox {y}_{\mathrm{t}} ={ \beta }\left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right) ; \hbox {where}, \left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right) = \hbox {forecast error}\nonumber \\&\hbox {or},\, \frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}={\upbeta }\left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right) \end{aligned}$$

(8)

Variations in Interest Rates due to Change in Money Growth and Anticipated Income Growth

According to Friedman, the fall or rise of interest rate depends on the rate of growth of money supply and rate of growth of anticipated income. To show this, differentiating Eqs. (7) and (8) with respect to ‘t’ we have,

$$\begin{aligned} \frac{\hbox {di}_{\mathrm{t}} }{\hbox {dt}}= & {} \frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}\end{aligned}$$

(9)

$$\begin{aligned} \hbox {Again}, \frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}= & {} \upbeta \left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right) \end{aligned}$$

(10)

Case 1: When Money Growth is Greater than Expected Income Growth

When $\hbox {m}>\dot{\hbox {y}}^{e}_{t}$ then $\hbox {y}_{\mathrm{t}} >\hbox {y}_{\mathrm{t}}^{\mathrm{e}}$, consequently, $\frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}>0$ [from Eq. (10)]. Therefore, from Eq. (9) we have $\frac{\hbox {di}_{\mathrm{t}} }{\hbox {dt}}>0$ . So, it indicates that interest rate will rise over time when money supply growth rate rises provided that the rate of growth of money supply exceeds the rate of growth of nominal income.

Case 2: When Money Growth is Equal to Expected Income Growth

$$\begin{aligned} \hbox {Let}, {\dot{\hbox {m}}}, \hbox {then}\; {\dot{\hbox {y}}}_{\mathrm{t}}= & {} \hbox {y}_{\mathrm{t}}^{\mathrm{e}}\\ \hbox {Here},\; \frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}= & {} { \beta }\left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right) =0\\ \hbox {Thus},\; \frac{\hbox {di}_{\mathrm{t}} }{\hbox {dt}}= & {} \hbox { }\frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}=0 \end{aligned}$$

Here we have found that interest rate remains unchanged following money supply when the rate of growth of money supply is equal to the rate of nominal income.

Case 3: When Money Growth is Less than the Expected Income Growth

$$\begin{aligned}&\hbox {When}\; {{\dot{\hbox {m}}}}<{\dot{\hbox {y}}}^{e}_{t}\, \hbox {then}\; \hbox {y}_{\mathrm{t}}<\hbox {y}_{\mathrm{t}}^{\mathrm{e}} \\&\hbox {Then},\; \frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}={ \beta }\left( {\hbox {y}_{\mathrm{t}} -\hbox {y}_{\mathrm{t}}^{\mathrm{e}} } \right)<0\\&\hbox {Consequently},\; \frac{\hbox {di}_{\mathrm{t}} }{\hbox {dt}}=\hbox { }\frac{\hbox {dy}_{\mathrm{t}}^{\mathrm{e}} }{\hbox {dt}}<0 \end{aligned}$$

It is also proved that interest rate will fall following increase in money supply when the rate of growth of money supply lags behind the rate of growth of anticipated nominal income.

Therefore, a fall or a rise of interest rate depends on the rate of growth of money supply and rate of growth of anticipated income where interest rate rises when money growth rate rises provided that the rate of growth of money supply exceeds the rate of growth of nominal income. Conversely, interest rate falls following increase in money supply when the rate of growth of money supply lags behind the rate of growth of anticipated nominal income and, in fact, interest rate remains unchanged following money supply when the rate of growth of money supply is equal to anticipated nominal income.

Appendix B

See Figs. 5, 6 and 7.

Fig. 5

Source: Author’s presentation

Time plot of interest rates.

Fig. 6

Source: Author’s presentation

Time plot of real money supply.

Fig. 7

Source: author’s presentation

Time plots of nominal GDP and seasonally adjusted nominal GDP.

Fig. 8

Source: Author’s estimation

Time plots of nominal income and anticipated nominal income (log level).

Fig. 9

Source: Author’s estimation

Correlogram of ARIMA residual.

Estimation of Anticipated nominal Income Through ARIMA Forecasting

It is found that seasonally adjusted nominal income series has followed ARIMA [(1, 2), 1, 0) process which is estimated and presented in Eq. (11).

$$\begin{aligned}&\hbox {Estimated ARIMA} [(1, 2), 1, 0]\, \text { Model of Nominal Income}\nonumber \\&\Delta Y_\mathrm{t}= 0.01686 + 0.1791 \Delta Y_{\mathrm{t-1} }- 0.4008 \Delta Y_{\mathrm{t-2}}\nonumber \\&\hbox {(t)}\quad (6.0375)\quad (1.672)\quad (-3.721)\nonumber \\&[\hbox {prob}.]\quad [0.02]\quad [0.09]\quad [0.00] \end{aligned}$$

(11)

DW = 1.958, F-Statistic = 7.685 (prob. 0.00), Log likelihood = 151.12, AIC = −3.847, SC = −3.756

Time plots of the ARIMA forecast (or anticipated nominal income) series of income with the actual series of income has been presented in Fig. 8. Correlogram of the ARIMA residual series is presented in Fig. 9 which indicates that the forecast residuals are white noise.