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### Indian Statistical Service(ISS) Exam previous year Solved Paper

TOPIC WISE SOLUTION OF PREVIOUS YEARS ISS PAPERS
STATISTICS-III
TOPIC-Economic Statistics

SYLLABUS OF ECONOMIC STATITICS:
Components of time series. Methods of their determination-variate difference method. Yule-Slutsky effect. Correlogram. Autoregressive models of first and second order. Periodogram analysis. Index numbers of prices and quantities and their relative merits. Construction of index numbers of wholesale and consumer prices. Income distribution-Pareto and Engel curves. Concentration curve.Methods of estimating national income. Inter-sectoral flows. Inter-industry table. Role of CSO.
SOLVED PAPER:- >
Q.[ISS-2011] Let  Ut = aζ + €t , where-∞< t <∞ ,where €t's are i.i.d. with E(€t)=0 and Var(€t)=1. Show that the process is stationary with correlation.(8 Marks)
Hints:- We are given E(€t)=E(ζ)=0;
So     E(€i€j)= 0 if i≠j
= 1 if i=j
And Var(€t)=1=Var(ζ) and E(ζ.€t)=0,
Now, Var(Ut) =Var(aζ + €t)= a² +1
Similarly, Var(Ut+k)= a² +1
And Cov(Ut,Ut+k)=E(Ut.Ut+k),since  E(Ut)=0 and the above covariance is equal to a².
So, Autocorrelation of order k is given by
r = Cov(Ut,Ut+k)/{√(Var(Ut)Var(Ut+k)}
= a²/(1+a²), for k=1,2,3,. . . ., which is independent of k.
Hence the process is stationary with correlation.

Q. [ISS-2010] Write a critical note on the methods of estimating national income of India. (10 Marks)
Sol:-  There are three approaches of calculating national income. They are:
<i> Product or Output method
<ii> Income method
<iii> Expenditure method
We know that Gross Domestic Product(GDP) is the measure of economy's total output,total income & total expenditure & also circular flow of income shows the factor income  received by the public is being spent to buy the output of goods & services produced. Hence we have
Income=Expenditure=Output
Therefore, all these three methods are supposed to give same results. Now we shall discuss three methods of estimating national income of India :
<i> Product or Output method:-  In the output method, the measures of GDP are calculated by adding the total value of the output (of goods and services) produced by all activities during any time period,such as a year. The major challenge of this method is the problem of double counting.
The output of many business is the inputs of some other business,e.g. the output of the tyre industry is the input of bike factory. Counting the final output of both industries will result in double counting of the value of tyre. This problem can be avoided by including only the value added at each stage of production or by adding the final value of output produced.
<ii> Income method:- In the income method,the measures of GDP are calculated by adding the income earned by various factors of production which are engaged in the production of output. The various incomes included to compute Gross National Income are: wages & salaries,income of self-employed,profits & dividends of business corporations,interest,rent,surplus of government enterprises,net flow income from abroad.
All of them are known as factor income & they are paid in return for the inputs engaged in some productive process which have resulted in corresponding output. The sum of all these incomes provide us the estimate of national income of India.
<iii> Expenditure method:- In the expenditure method,the measures of GDP are calculated by adding all the expenditures made in the economy. Expenditure method focuses on finding the total output of a nation by finding the total amount of money spent. The essential components of expenditure are:
C : Consumption expenditure
I : Domestic Investment
G : Government expenditure
X : Exports of goods and services
M : Imports of goods and services
NR : Net income receipts from assets abroad.
The sum of all expenditure provides us the measure of national income.
Therefore,  GDP= C+I+G+(X-M).

Q.[ISS-2009] Distinguish between fixed base & chain base methods for the construction of index numbers. Discuss their merits. (8 Marks)
Sol:- The relative merits & demerits of chain-base and fixed-base methods are:
<i> The fixed-base index numbers become more and more inaccurate as the distance between the base period and the current period increases. As the chain-base index numbers are based on a number of link-indices,each of which is expected to to be quite accurate,it is also claimed that the chain-base index numbers are more accurate than fixed-base index numbers.
<ii> A chain-base index fully utilises the information regarding prices and quantities of all the intervening periods between the base period and the current period,where as a fixed base index makes use of data concerning the base period and current period only.
<iii> Some authorities on the other hand, hold that since a chain index is obtained by multiplying a number of link-indices, it may involve a cummulative error,although none has put forward any convincing proof on this respect.
<iii> Fixed base index numbers are generally easier to calculate & are more easy to understand by users of index numbers than chain-base index numbers.

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