**2. Barometric Methods**

Just as a barometer indicates changes in atmospheric pressures, certain indicators can be identified which can show the direction in which business winds are blowing. This method was first developed and used in the 192-s by the Harvard Economic Service. This technique is based on the notion that the future can be predicted from certain happenings in the present. It is based on the observation that certain statistical indicators, when used in conjunction with one another, serve as a barometer of economic changes. For example, index of share prices is many times used to predict economic changes. Certain indices like the index of share-prices, or the index of food grains prices or that of cloth prices do indicate business trends and can be taken to suggest a general economic recovery or good prospects or, alternatively, recession or bad prospects. What a firm needs to do is to establish a relation between general economic conditions and the demand for its own product.

The basic approach of barometric techniques is to construct an index of relevant economic indicators and to forecast trends on the basis of movements in the index of economic indicators.

The two kinds of indicators that are used under barometric method of demand forecasting are:

**(a) Lead-Lag Indicators**

The basic approach of lead-lag indicators technique is to construct an index of relevant ecowomzc indicators and to forecast future trends on the basis of movements in the index of economic indicators. The indicators used in this method are classified as:

(i) leading indicators,

(ii) coincidental indicators, and

(iii) lagging indicators.

A time-series of various indicators is prepared to read the future economic trend. The leading series consists of indicators which move up or down ahead of some other series. Some examples of the leading series are: (i) index of net business or capital formation; (ii) new orders for durable goods; (iii) new building permits; (iv) change in the value of inventories; (v) index of the prices of the materials; (vi) corporate profits after tax.

The coincidental series, on the other hand, are the ones that move up or down simultaneously with the level of economic activity. Some examples of the coincidental series are: (i) number of employees in the non-agricultural sector; (ii) rate of unemployment; (iii) gross national product at constant prices; (iv) sales recorded by the manufacturing, trading and the retail sectors.

The lagging series, consists of those indicators which follow a change after some time-lag. Some of the indices that have been identified as lagging series by the NBER are: (i) labour cost per unit of manufactured output, (ii) outstanding loans, and (iii) lending rate for short-term loans.

Let us say, by way of example, that retail prices of cloth or demand for cement or per capita income are some of the indicators. Any one of them which we deem to be the best can be chosen. Let us take that indicator and call it X. Let us suppose the demand for our product is Y. We can now observe: If we observe that the demand for our product, i.e. Y. increases after a gap of three months or six weeks or a fortnight following an increase in the indicator X, then X becomes a leading indicator. If both X and Y rise and fall together, X becomes a coincident indicator. If Y increases first and X increases after wards (may be after a fortnight or three months etc.), X becomes a lagging indicator. Obviously, only leading indicators are useful to us because with their help, we can predict changes in demand for our product on the basis of changes in the leading indicator, in advance.

The time series data on various kinds of indicators are selected on the basis of the following criteria:

(i) Economic significance of the indicator: the greater the significance, the greater the score of the indicator.

(ii) Statistical adequacy of time-series indicators: a higher score is given to an indicator provided with adequate statistics.

(iii) Conformity with overall movement in economic activities.

(iv) Consistency of series to the turning points in overall economic activity,

(v) Immediate availability of the series, and

(vi) Smoothness of the series.

The relative positions of leading, coincident and lagging indicators in the business cycle are shown graphically in the following figure:

**(b) Diffusion indices**

Diffusion indices are used as an alternative to lead-lag indicator when there is problem is the choice of appropriate lead-lag indicators. The problem of choice arises because some of the indicators appear in more than one class of indicators. Furthermore, it is not advisable to rely on just one of the indicators. This leads to the usage of what is referred to as the diffusion index. A diffusion index copes with the problem of differing signals given by the indicators. A diffusion index is the percentage of rising indicators. In calculating a diffusion index, for a group of indicators, scores allotted are 1 to rising series, 11⁄2 to constant series and zero to falling series. The diffusion index is obtained by the ratio of the number of indicators, in a particular class, moving up or down to the total number of indicators in that group. Thus, if three out of six indicators in the lagging series are moving up, the index shall be 50 per cent. It may be noted that the most important is the diffusion index of the leading series. However, there are problems of identifying the leading indicator for the variable under study. Also, lead time is not of an invariable nature.

**Merits**

i. The only advantage of the barometric method of forecasting is that is helps to overcome the problem of finding the value of an independent variable under regression analysis.

**Limitations**

i. This techniques can be used only if one gets an adequate number of leading indicators and a leading indicator of the variable to be forecast is not always easily available.

ii. This method can be used for short-term forecasts only.

iii. These indicators signal the direction of change, but not the magnitude. Actually how much will be the rise or fall in demand for one’s product is more important.

**(c) Econometric Methods**

The econometric methods combine statistical tools with economic theories to estimate economic variables and to forecast the intended economic variables. The forecasts made through econometric methods are much more reliable than those made through any other method. The econometric methods are, therefore, most widely used to forecast demand for a product, for a group of products and for the economy as a whole.

An econometric model may consist of a single-equation regression model or it may consist of a system of simultaneous equations. These are briefly described under two basic methods.

**i. Regression Methods**

Regression analysis is a statistical device with the help of which we are in a position to estimate (or predict) the unknown values of one variable from known values of another variable. The variable which is used to predict the variable of interest is called the independent variable or explanatory variable and the variable we are trying to predict is called the dependent variable or “explained variable”. The independent variable is denoted by X and the dependent variable by Y.

For example, if we know that advertising and sales are correlated we find out expected amount of sales for a given advertising expenditure or the required amount of expenditure for attaining a given amount of sales. Similarly, if we know that the yield of rice and rainfall are closely related we may find out the amount of rain required to achieve a certain production figure. Regression analysis reveals average relationship between two variables and this makes possible estimation or prediction. Regression relationship may involve one one predicted or dependent and one independent variable- simple regression, or it may involve relationships between the variable to be forecast and several independent variables- multiple regression.

**1. Simple Methods**

In simple regression technique, a single independent variable is used to estimate a statistical value of the ‘dependent variable’, that is, the variable to be forecast. The technique is similar to trend fitting. An important difference between the two is that in trend fitting the independent variable is ‘time’ whereas in a regression equation, the chosen independent variable is the single most important determinant of demand. Besides, the regression method is less mechanical than the trend fitting method of projection.

Suppose we have to forecast demand for sugar for 2008 on the basis of 7-year data given in Table 6.4. When this data is graphed, it will produce a continuously rising trend in demand for sugar with rising population. This shows a linear trend. Now, the demand for sugar in 2008 can be obtained by estimating a regression equation of the form

**Y = a + bX**

where Y is sugar consumed, X is population, and a and b are constants.

For an illustration, consider the hypothetical data on quarterly consumption sugar given in Table given below:

Year |
Population (millions) |
Sugar Consumed (‘000) tonnes |

1995-96 | 10 | 40 |

1996-97 | 12 | 50 |

1997-98 | 15 | 60 |

1998-99 | 20 | 70 |

1999-2000 | 25 | 80 |

2000-2001 | 30 | 90 |

2001-02 | 40 | 100 |

Above equation can be estimated by using the ‘least square’ method. The procedure is the same as shown in Table above. That is, the parameters a and b can be estimated by solving the following two linear equations:

The procedure of calculating the terms in equations (i) and (ii) above is presented in Table below:

Calculations of terms of the Linear Equation

By substituting the values form above table into the equation (i) and (ii) we get

490 = 7a + 152b …….(iii)

12,000 = 152a + 3994b ……..(iv)

By solving equations (iii) and (iv), we get

a = 27.44

and b = 1.96

By substituting values for a and b in following equation, we get the estimated regression equation as:

Y = a + bX

Y = 27.44 + 1.96 X ………………… (v)

Given the regression equation (v), the demand for sugar for 2003-2004 can be easily projected if population for 2003-2004 is known. Supposing population for 2003-04 is projected to be 70 million, the demand for sugar in 2003-04 may be estimated as Y = 27.44 + 1.96(70) = 137 million tonnes.

The simple regression techniques is based on the assumption

(i) That independent variable will continue to grow at its past growth rate, and

(ii) That the relationship between independent and dependent variables will continue to remain the same in the future as in the past.

**2. Multivariate Methods**

The multi-variate regression equation is used where demand for a commodity is deemed to be the function of many variables or in cases in which the number of explanatory variables is greater than one.

The procedure of multiple regression analysis may be briefly described here. The first step in multiple regression analysis is to specify the variables that are supposed to explain the variations in demand for the product under reference. The explanatory variables are generally chosen from the determinants of demand, viz., price of the product, price of its substitute, consumers’ income and their taste and preference. For estimating the demand for durable consumer goods, (e.g., TV sets, refrigerators, houses, etc.), the other explanatory variables which are considered are availability of credit and rate of interest. For estimating demand for capital goods (e.g., machinery and equipment), the relevant variables are additional corporate investment, rate of depreciation, cost of capital goods, cost of other inputs (e.g., labour and raw materials), market rate of interest, etc.

Once the explanatory or independent variable are specified, the second step is to collect time-series data on the independent variables. After necessary data is collected, the next step is to specify the form of equation which can appropriately describe the nature and extent of relationship between the dependent and independent variables. The final step is to estimate the parameters in the chosen equations with the help of statistical techniques. The multi-variate equation cannot be easily estimated manually. They have to be estimated with the help of computer.

**ii. Simultaneous Equations**

The simultaneous equations method is a complete and systematic approach to forecasting. This technique uses sophisticated mathematical and statistical tools .

**Basic features**

The first step in this technique is to develop a complete model and specify the behavioural assumptions regarding the variables included in the model. The variables that are included in the model are called (i) endogenous variables, and (ii) exogenous variables.

**(i) Endogenous variables**

The variables that are determined within the model are called endogenous variables. Endogenous variables are included in the model as dependent variables, i.e., the variables that are to be explained by the model. These are also called ‘controlled’ variables. It is important to note that the number of equations included in the model must equal the number of endogenous variables.

**(ii) Exogenous variables**

Exogenous variables are those that are determined outside the model. Exogenous variables are inputs of the model. Whether a variable is treated as endogenous or exogenous depends on the purpose of the model. Some important examples of exogenous variables are ‘money supply; ‘tax rates’, ‘government spending’, ‘time’, and ‘weather’, etc. The exogenous variables are also known as ‘uncontrolled’ variables.

The second step in this method is to collect the necessary data on both endogenous and exogenous variables. More often than not, data is not available in the required form. Sometimes data is not available at all. In such cases, data has to be adjusted or corrected to suit the model and, in some cases, data has even to be generated from the available primary or secondary sources.

After the model is developed and necessary data are collected the next step is to estimate the model through some appropriate method. Generally, a two-stage least square method is used to predict the values of exogenous variables.

Finally, the model is solved for each endogenous variable in terms of exogenous variables. Then by plugging the values of exogenous variables into the equations, the objective value is calculated and prediction is made.

This method is theoretically superior to the regression method. The main advantage of this method is that it is capable of capturing the influence of interdependence of the variables. But, its limitations are similar to those of the regression method. The use of this method is sometimes hampered by non-availability of adequate data.

**Comparison of simultaneous equation method with regression method**

1. Regression technique of demand forecasting consists of a single equation. In contrast, the simultaneous equations model of forecasting involves estimating several simultaneous equations. These equations are, generally, behavioural equations based on mathematical identities and market-clearing equations.

2. Regression technique assumes one-way causation, i.e., only the independent variables cause variations in the dependent variable, not vice versa. In simple words, regression technique assumes that a dependent variable affects in no way the independent variables. For example, in demand function D = a-bP used in the regression method, it is assumed that price affects demand, but demand does not affect price. This is an unrealistic assumption. On the contrary, forecasting through econometric models of simultaneous equations enables the forecaster to take into account the simultaneous interaction between dependent and independent variables.