# Macro Econometric Income Consumption Model for India

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Consumer spending is an important factor that can stimulate the economic growth and development through the multiplier process. This study aims to estimate the pattern of consumption expenditure and tries to identify the consumption function for Indian Economy. The study intends to identify the determinants of consumption and to build a econometric model using the annual data from RBI Handbook of Statistics on Indian Economy (2008-2009) for the time period 1970 to 2009. Following are the variables taken into consideration for empirical analysis; Private Final Consumption Expenditure (PFCE), Personal Disposable Income (PDI), Rate of Interest (ROI) and Inflation (INF). We have employed rigorous econometric techniques in analyzing the time series data so as to ensure the credibility and reliable economic relations. The results confirm income (PDI) as the most significant factor. The MPC calculated which ranges between 0.80 to 0.90, which is in affirmation with the theoretical assumptions and is more or less similar to the previous studies. The conclusions from the model suggest that the Keynesian Absolute Income Hypothesis is found to be appropriate to Indian context.

## INTRODUCTION:

The relation between aggregate consumption or aggregate savings and aggregate income, generally termed the consumption function, it has occupied a major role in economic philosophy ever since Keynes made it a keystone of his theoretical structure in The General Theory of Employment, Interest and money. The role of consumption in the multiplier process has increased the scope and dynamics of the topic which led to further developments in this field by developing more realistic and logical consumption (Income) hypothesizes. Consumption which was considered only as a function of income was later refined and redefined.

The purpose of the study is to examine and comprehend the issues, trends and rationale behind the consumption pattern in India. In our study an attempt is done so as to understand and estimate the potential factors that had led development. We estimate the consumption model in India using advanced econometric tools. The study is conducted for period from 1970 to 2009 using the annual data from RBI Hand Book of Statistics on Indian Economy.

## THEORETICAL MODELS:

Consumption function indicates a functional relationship between consumption, income and other factors. It shows how consumption expenditure varies as there is change in the income and other factors such as age, social status, interest rates etc. Whereas Consumption refers to amount spent on consumption at a given level of income. On the other hand consumption function refers to actual consumption at various level of income.

Major development in this respect took place when In 1936 Keynes formulated a consumption function which was the basic element in the income expenditure approach to the determination of national income. Consumption function for him was the basic building block of multiplier analysis. According to Keynes marginal propensity to consume is less than average propensity to consume this is well described in the stagnation thesis around 1940. Keynes observed this as behavior of the consumption expenditure in the short run over the long run.

Keynes offered no precise functional formulation of the propensity to consume; his analysis has come to be associated with a simple version of the consumption function that embodies only the more quantitative aspects of his considerations, popularly known as the simple Keynesian consumption function or Absolute Income Hypothesis (AIH). The theory asserts as income rises, the theory asserts, consumption will also raise but not necessarily at the same rate. The basic principle of the absolute income hypothesis is that the individual consumers who determine what fraction of his income will he devote to consumption on the basis of the absolute level of that income. AIH provided a background for the further studies in this field. This resulted in the development of three more theoretical models namely Relative Income Hypothesis (RIH), Permanent Income Hypothesis (PIH), and Life Cycle Hypothesis (LCH).

Relative Income Hypothesis (RIH) developed by Duesenberry in 1949 conceives consumption in relation to the income of other households and past income. It implies that the proportion of income consumed remains constant provided that a household’s position on the income distribution curve holds constant in the long run. This is consistent with long-run evidence. Higher up the income curve, however, there is a lower average propensity to consume. The second part of the hypothesis suggests that households find it easier to adjust to rising incomes than falling incomes. There is, in other words, a “ratchet effect” that holds up consumption when income declines. Duesenberry’s analysis is based on two relative income hypotheses. The first hypothesis is essentially that consumers are not so much concerned about the absolute level of consumption as they are with their consumption relative to that of rest of population. Second hypothesis Duesenberry argues that present levels of consumption is not influenced merely by present levels of absolute or relative income, but also by levels of consumption attained in previous periods.

Absolute income hypothesis when captures the effect of current income on current consumption the theories developed there after focus on the influence on income on consumption in a broad sense. Permanent income hypothesis developed Milton Friedman further divide the income component into two parts. First include the permanent income component and transitory component the second. He states that consumption is determined by the permanent component and normally transitory income is saved.

To be more specific, The Permanent Income Hypothesis decomposes measured total disposable income, Y, into a permanent component (YP), and a transitory component, (YT). The permanent income component is deemed systematic but unobservable, reflecting factors that determine the household’s wealth, while the transitory component reflects “chance” income fluctuations. Similarly, measured consumption, c, is decomposed into a permanent component, CP, and a transitory component, cT. In giving the hypothesis empirical substance, Friedman assumes the transitory components to be uncorrelated across consumption and income, and with their respective permanent components.

A little different from these above mentioned hypotheses the Life-Cycle Hypothesis presents a well-defined linkage between the consumption plans of an individual income and income expectations as passes from childhood, through the work participating years, into retirement and eventual decease. The main building block of life-cycle models is the saving and consumption decision, i.e., the division of income between consumption and saving. The saving decision is driven by preferences between present and future consumption (and the utility derived from consumption). Given the income stream the household receives over time, the sequence of optimal consumption and saving decisions over the entire life can be computed. It should be noted that the standard life-cycle model as presented here is firmly grounded in expected utility theory and assumes rational behavior.

## THE ECONOMETRIC MODEL AND THE SPECIFICATIONS

## Data Used For the Study:

We have used annual long-run time series data on Private Final Consumption Expenditure, Personal Disposable Income, Gross Domestic Savings, Rate of Interest and Inflation from The Handbook of Statistics on Indian Economy 2008-2009 published by Reserve Bank of India (2008-2009). They are represented as the following: Private Final Consumption Expenditure (PFCE), Personal Disposable Income (PDI), Rate of Interest (ROI) and Inflation (INF). Where in PFCE is the dependent variable. Econometric Methodology:

One of the major and crucial problems that can be faced while dealing with time series data is, many a times data may be non – stationary. So avoid spurious regression it is necessary to check the time series data for stationarity using unit root tests. Keeping this in mind the unit root test has been carried out for each series using the Augmented Dickey-Fuller test for the period 1970 – 2008. All the variables are non stationary at the levels and in order to make them stationary we employed the technique of differencing. All variables other than rate of interest is differenced twice, where (D) stands for differencing once and D (D) for differencing twice.

## Table: 1 Unit root tests with Trend and Intercept: 1970 – 2008

Variable

Level

Inference

1st difference

Inference

(LnPFCE)

-1.51

Non -stationary

-5.23

Stationary

(LnPDI)

-1.38

Non -stationary

-5.26

Stationary

(LnSAV)

-2.04

Non -stationary

-5.94

Stationary

(LnROI)

-2.56

Non -stationary

-8.26

Stationary

(LnINF)

-4.49

Stationary

1% critical value = -3.50, 5% critical value = -2.89, 10% critical value = -2.58

The analysis also takes into account the lag structure that plays a vital role in the consumption analysis. To study the role of previous peak incomes and the role of habits the functional form that we can use is as follows:

Ct = Î± + Î²0Yt + Î²1 Yt-1+ Îµt

Using the given functional model where Ct is consumption at time period (t), Yt represent income at time period (t), Yt-1 representing one year lagged value of income where in we can study the long run effects of income on consumption. But the above equation (distributed lag model), since takes the lag of independent variable there is all possibility of encountering the problem of multicolinearity. Thus we need to transform this model into some other model which takes care of the problems. When we have distributed lag models where lag structure follow the geometric form we can transform them using the Koyack transformation.

The transformed model AR (1) can be re written as follows:

Ct = Î± + Î²0Yt + Î´Ct-1+ ut

This model is called a Auto regressive model where lagged value of dependent variable itself will be a independent variable. In the above model Î²0 measure the short run effect or the short run MPC and Î´ measure the long run effects, in our model it is the long run MPC.

## Estimated Equations:

## Equation: 1

For the above consumption equation the independent variables are income, rate of interest, inflation and a year lagged value of the dependent variable. According to the theoretical setup the coefficient of income demands a positive relationship. This is for the reason that when income increases consumption also increases and more over the coefficient of income indicate the MPC which is supposes to be a positive value less than one. Both our equations satisfy this condition. In both the equation the coefficient of savings and rate of interest shows a negative relationship. It is obvious that when savings increases consumption decreases because savings is considered as an alternative for consumption and savings increases when rate of interest is high thus when rate of interest is high savings increases and the consumption expenditure decreases. Inflation is included as an independent variable to evaluate the effect of prices, when prices increases the expenditure on consumption is bound to increase so we expect a positive relation. The AR coefficient showing a positive relation is having a number of theoretical implications for example for permanent income hypothesis to hold good the AR coefficient should be negative. The theoretical implications of the positive AR coefficient are explained in the following discussions.

Since the estimates are partial regression coefficients all the coefficients are explained by keeping the assumption, when effect all the other variables are kept constant what is the impact of a variable on consumption. From equation one the value of income co efficient can be read as follows, when there is one percent increase in income there will be 0.83 percent increase in consumption. Thus a value of 0.92 in the second equation for the income coefficient indicates, when there is one percent increase in income consumption will increase by 0.92 percent. Theoretically the coefficient of income is the MPC which give information about the change in consumption when income changes by one unit. The limits of MPC are zero to one and our both equation satisfies this condition. It is also important to note that both the equations income turns out to be the most significant factor, the t values for this coefficient is 19.31 and 23.82 respectively.

The coefficient of savings and the rate of interest show a negative relation which indicate an inverse relation of these variables with respect to the dependent variable consumption, this holds good for both the equations. For both the equations the coefficient is same for savings. When all other variables are kept constant an increase in savings by one unit will decrease consumption by 0.06 percent and for a unit increase in rate of interest will decrease the consumption by 0.0183 percent in the first equation and 0.0244 percent according to the second equation. In both the equations savings is backed by significant t- values but interest rates are relatively in significant in both the equations

In the first equation inflation is one of the very significant variable, it is proved that inflation will have a positive impact on consumption and this was expected, this is because of the reason that in a developing nation like India the maximum is spend on the necessary commodities thus an increase in price will increase the consumption expenditure. It is estimated that one percent increase in inflation will lead to increase in consumption by 0.0115 percent.

Equation (1) is supported by statistically significant t value and high R2 of 0.97 which imply 97%, of the variation in consumption expenditure is explained by the explanatory variables. A DW statistic of 2.01 rules out the problem of series auto correlation. Equation (2) is also supported by statistically significant t values and high R2 of 0.95 which imply 95%, of the variation in consumption expenditure is explained by the explanatory variables. In an AR (1) for identifying the elements of auto correlation we need to look at D.W ‘h’ statistic. The calculated D.W ‘h’ of 0.07 rejects the possibility of auto correlation.

## Calculation of Long Run MPC

For the given AR model (Equation: 2):

Ct = Î± + Î²0Yt + Î´Ct-1+ ut

Î² is the short run MPC and according to theoretical models the Î² (MPC) should be less than one. AR model can be used even to calculate the long run MPC. According to theoretical models long run MPC should be greater than the short run and should be equal to one. The long run MPC can be calculated as follows:

Long run MPC (Î´) = Î² / 1- Î´

= 0.92 / 1-0.07

= 0.989

Thus the AR coefficient of 0.07 can be interpreted as follows, when the increase in the income is sustained, then the increase in the MPC (long run MPC) out of income will be 0.989. In other words when consumers have time to adjust for one unit change in income, they will increase their only for about 0.989 percent.

## Theoretical Implications:

Macro Econometric models must fit into a theoretical framework and should be handy in terms of policy implications. This holds well in the case of Consumption models also. So in this respect it is necessary to validate the model (Equation 1 & 2) by testing and classifying them to the income hypothesis developed.

Some of the previous studies in the Indian context conforms that for a developing economy like India the major source for consumption for any given time period will be the current income source and thus the nature of economy fits itself into Keynesian Hypothesis. Krishnamurthy (1996) supports Keynesian setup with a (0.75) MPC. Pandit (2000) in Macroeconometric Policy Modeling for India: A Review of Some Analytical Issues support the Keynesian setup by stating that in consumption function follows Absolute Income Hypothesis. The results of a study by Ghatak contradict with Friedman results. She by examining the Indian economic scenario for the year (1919-1986) found that, in India the transitory component of the income also consumed. This is because of the reasons in a developing country such as India, temporary increases in income are likely to be consumed wholly; this was deliberately encouraged by government policies to push people above the poverty line. Whereas Permanent income hypothesis argue that permanent income is consumed and savings is determined by transitory component.

Equations (1 & 2) confirm the significant role of current income determining current consumption which supports Keynesian argument of Absolute Income Hypothesis. The MPC value derived from both the equations satisfies the theoretical requirements as proposed by Keynes (0 < MPC < 1).

Equation (2) which is an AR model with a positive value for the AR coefficient and the calculated long run MPC tested equal to one prove the Keynesian argument that the Long run MPC > Short run MPC and the constant behavior of the long run MPC.

Thus the analysis conclude that given the annual time series data for Indian economy form 1970-2008, the consumption pattern follows Keynesian model.

## Forecasting From the Equations:

To examine the credibility of equations (both [1] & [2]) validation tests are performed. In sample forecasts are obtained in this respect for the period from 1970 to 2008. The accuracy of the model is tested by calculating the Root Mean Squared Error and Theil Inequality Coefficient. The values imply that the forecasted series in model is very close to the actual series and there are no systemic tendencies to over/under estimate the actual data. Forecasts are based on Dynamic simulations.

## Table: 2 Forecasting Performance Measures

Root Mean Square Error

Theil Inequality coefficient

Equation 1

0.021

0.14

Equation 2

0.013

0.0005

The Root Mean Square Error and the Theil Inequality Coefficient for both the equations are satisfactory and ensure the credibility of using the model for forecasting. (See graph 1&2 in appendix)

## Granger Causality Tests:

Granger causality test is a technique for determining whether one time series is useful in forecasting another. Granger causality tests reveal whether one variable reveals whether one variable granger cause other. Pair wise Granger causality results for the respective variables are presented below. Inferences are drawn looking at the probabilities. We reject the null hypothesis where the probability values are lower.

## Table 3 Pair wise Granger Causality Results

## Null Hypothesis:

## Obs

## F-Statistic

## Probability

## LnPFCE does not Granger Cause LnSAV

## 36

## 0.16843

## 0.84576

## LnSAV does not Granger Cause LnPFCE

## 0.84369

## 0.43976

## LnPFCE does not Granger Cause LnINF

## 36

## 0.82960

## 0.44568

## LnINF does not Granger Cause LnPFCE

## 5.03564

## 0.01277

## LnPFCE does not Granger Cause LnPDI

## 36

## 1.22505

## 0.30757

## LnPDI does not Granger Cause LnPFCE

## 4.81197

## 0.01514

## LnROI does not Granger Cause LnPFCE

## 36

## 0.49455

## 0.61457

## LnPFCE does not Granger Cause LnROI

## 0.55794

## 0.57803

From the table above we can infer that savings (LnSAV) granger cause consumption expenditure (LnPFCE), Inflation (LnINF) granger cause consumption expenditure, income (LnPDI) granger cause consumption expenditure (LnPFCE) and consumption (LnPFCE) and (LnROI) show a bi- directional causal relationship . These results are supported by a strong theoretical base. It is theoretically and empirically proved that consumption expenditure is influenced by income, savings, and inflation.

## SUMMARY AND CONCLUSIONS:

The present study attempts to examine some of the issues relating to India’s consumption pattern and to identify the significant determinants that influence Indian consumption function. The study considers the data from 1970-2008. Data sources are RBI Handbook of Statistics on Indian economy (2008-2009). Empirical modeling is taken up by considering the theoretical issues. The economic reforms and the increasing income and population explosion have contributed to increase in the consumption expenditure in Indian resulting in higher standard of living. From our study we infer that almost 85 – 95 percentage increase in consumption is as a result of increasing income levels of individuals in the economy.

Identifying the major determinants of consumption function includes more of econometrical techniques and empirical estimations. The exercise revels that income is the most significant factor that affect the consumption any given period. Other significant determinants turn out to be Savings, Rate of Interest, and Inflation. Identifying the suitable Income hypothesis for India concludes that it is Keynesian theory of Absolute Income Hypothesis that suits Indian economy for the following reasons. Firstly the estimates indicate the significant effect of current income on consumption as suggested by Keynes. Second the MPC value estimated from the (equation 1 & 2) is in tune with the theoretical assumptions made by Keynes where he argues that the MPC should positive integer less than one. The MPC calculated which ranges between 0.80 to 0.90, which is in affirmation with the theoretical assumptions and is more or less similar to the previous studies. The MPC calculated from some of the previous study on Indian economy are as follows:

## Table: 4 MPC calculated from some of the previous study on Indian economy

Author

MPC

YEAR

Narasimham

0.90

1919-1952

Anita Ghatak

0.80

1919-1986

Iyengar & Moorthy

0.71

1948-1955

Moorthy & Thore

0.66

1948-1955

Tinter & Narayanan

0.67

1948-1957

K.Krishnamurthy

0.81

1948-1961

Thirdly Keynesian hypothesis argue that long run MPC should be larger than the short run this is established in the second equation where we obtained a positive value of 0.0727 from the AR (1) coefficient. The Hypothetically tested results prove that the long run MPC is constant and is not significantly different from one.

## APPENDIX

## Figure: 1 Insample Forecasting Estimates From Equation: 1

## Figure: 2 Insample Forecasting Estimates From Equation: 2

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