8.(a) Explain the method of collection of agriculture data. Describe the (i) official publications for data collection and (ii)…

(a) Collection of agricultural data, official publications and agencies

Methods of collection: Complete enumeration: village land records kept by the revenue agency (patwari or lekhpal) give area under each crop and land use through a full field-to-field crop inspection (girdawari); the Agriculture Census, held every five years (the 11th for 2021-22), covers operational holdings, their size, tenure, irrigation and inputs. Sample surveys: the General Crop Estimation Surveys use crop-cutting experiments to estimate yield per hectare; the Improvement of Crop Statistics scheme checks area data; NSO rounds (for example the Situation Assessment Survey of agricultural households) give income, indebtedness and input use; the Cost of Cultivation Scheme gives costs and returns. Administrative records and other sources: market arrival and price reports (Agmarknet), cooperative and bank credit returns, and satellite remote sensing for crop area and drought assessment. (i) Official publications: Agricultural Statistics at a Glance (area, production and yield of crops), Land Use Statistics, Agriculture Census reports, the Economic Survey, the Statistical Abstract of India, the RBI Handbook of Statistics on the Indian Economy and Report on Currency and Finance, and state statistical abstracts. (ii) Agencies and what they provide: Directorate of Economics and Statistics, Ministry of Agriculture and Farmers Welfare: area, production, yield, prices and the advance estimates of crops. National Statistics Office, Ministry of Statistics and Programme Implementation: agriculture's share in GDP and gross value added, and the NSO household surveys. Office of the Economic Adviser, Department for Promotion of Industry and Internal Trade: wholesale price indices of agricultural commodities. Reserve Bank of India and NABARD: agricultural credit and rural financial data. State Departments of Agriculture and state statistical bureaus: district and block level crop and land data.

(b) GFR and TFR, TFR = 3·29, merits and demerits, and GRR

Difference between GFR and TFR: General Fertility Rate: births in a year per 1,000 women aged 15 to 49 years. It is a single figure that does not allow for the age distribution of women within that range. Total Fertility Rate: the sum of age-specific fertility rates over the reproductive span; for five-year age groups TFR = 5 × ΣASFR when ASFR is per woman per year (or 5 × ΣASFR/1000 when per 1,000 women). It is not affected by the age structure of women. Meaning of TFR = 3·29: if a woman lived through her reproductive years experiencing the current age-specific fertility rates, she would bear on average 3·29 children. This is above the replacement level of about 2·1, so the population would keep growing, ignoring mortality and migration. Merits of TFR: it is independent of age composition, it makes populations comparable, it is easy to interpret, and it measures against the replacement level. Demerits of TFR: it is a period measure that can be distorted by changes in the timing of births, it needs reliable age-specific data, and it ignores mortality of women before the end of the reproductive period and assumes present rates persist. Relation between GRR and TFR: GRR counts only daughters, so GRR = TFR × (female births/total births). If the sex ratio at birth is r males per 100 females, female births form 100/(100 + r) of all births, so GRR = TFR × 100/(100 + r). Interpretation: GRR > 1: each generation of girls is more than replaced by its daughters, so the population grows. GRR < 1: daughters do not replace mothers and the population eventually declines. GRR = 1: each mother is exactly replaced by one daughter and the population is stationary, mortality ignored.

(c) Order and rank conditions and identification of the Keynesian model

Notation: M = 4 endogenous variables (C, I, T, Y) and K = 2 predetermined variables (G, Yₜ₋₁). For an equation with m endogenous and k predetermined variables, M − 1 = 3. Order condition (necessary): K − k ≥ m − 1; that is, the number of variables excluded from the equation must be at least M − 1. Equality means exactly identified, and strict inequality means overidentified. Rank condition (necessary and sufficient): the matrix formed from the coefficients of the variables excluded from that equation, taken from the other equations, must have rank M − 1 = 3. Step 1: Consumption function (C, Y, T in; m = 3, k = 0): K − k = 2 = m − 1, so it is exactly identified by the order condition. Step 2: Investment function (I and Yₜ₋₁ in; m = 1, k = 1): K − k = 1 > m − 1 = 0, so it is overidentified by the order condition. Step 3: Tax function (T and Y in; m = 2, k = 0): K − k = 2 > 1, so it is overidentified by the order condition. Step 4: The income identity has no unknown parameters, so identification is not examined for it. Rank check for the consumption function: the excluded variables are I, G, Yₜ₋₁. From the other equations the matrix with rows (1, 0, −α₁) [investment], (0, 0, 0) [tax] and (1, 1, 0) [identity] has rank 2, which is less than 3. So the order condition is met but the rank condition fails. Rank check for the investment function: excluded variables C, T, Y, G give a matrix of rank 3, so it is identified. Rank check for the tax function: excluded variables C, I, G, Yₜ₋₁ give rank 3, so it is identified. Conclusion: by the order condition alone the consumption function is exactly identified and the investment and tax functions are overidentified, so every stochastic equation passes. The rank condition shows that the consumption function is not identified, since the tax equation links T to Y and a mixture of the two equations has the same form as the consumption function. The system as a whole is therefore not identified.