ICAR AICE-JRF/SRF (PhD admission and fellowship) · India · National Testing Agency for ICAR
Original practice questions written to the published syllabus · not past papersEstimating economic relationships from data and knowing when the estimates can be trusted: OLS and its assumptions, their violations, simultaneous equations, time series and binary-choice models.
In the exams: agricultural economics PhD entrance and fellowship examinations, quantitative methods (heavy); agribusiness management PhD entrance and fellowship examinations (present)
ICAR AICE-JRF/SRF (PhD) Agricultural Economics, Unit 9 (Research Methodology and Econometrics)
CLRM assumptions and which one each violation breaks; BLUE and the Gauss-Markov theorem; consequences, detection and remedies for multicollinearity, heteroscedasticity and autocorrelation; Durbin-Watson decision rules and Durbin's h; dummy trap; Koyck, adaptive expectations and Nerlovian partial adjustment; order and rank conditions; ILS and 2SLS; DF/ADF, cointegration and ECM; LPM, logit and probit. Short numericals: slope from sums, R-squared, adjusted R-squared, F from R-squared, t, DW, VIF, elasticities from log models, long-run elasticities.
ICAR AICE-JRF/SRF (PhD) Agri-Business Management, Research Methods unit
Regression interpretation for business data: dummy variables, logistic regression for choice and adoption, multicollinearity among marketing variables, reading regression output (coefficients, t, p-values, R-squared, F).
How our questions for ICAR AICE-JRF/SRF spread across the units of Econometrics. Difficulty: 29 easy, 65 medium, 31 hard.
| Linear probability, logit and probit models | 12 | |
| Simultaneous equations and identification | 11 | |
| Classical linear regression model and OLS | 9 | |
| Hypothesis testing in regression | 9 | |
| Stationarity and unit roots | 9 | |
| Cointegration and error-correction models | 9 | |
| ARIMA models | 9 | |
| Multicollinearity | 8 | |
| Autocorrelation | 8 | |
| Specification error | 8 | |
| BLUE properties and the Gauss-Markov theorem | 7 | |
| Heteroscedasticity | 7 | |
| Distributed lag models | 7 | |
| Maximum likelihood | 6 | |
| Dummy variables | 6 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A linear yield response Y = 21 + 0.12N (Y in q/ha, N in kg/ha) is estimated. At the sample means N = 100 kg/ha and Y = 33 q/ha, the elasticity of yield with respect to nitrogen is
A. 0.364
In a linear model the elasticity is b x (X-bar/Y-bar) = 0.12 x 100/33 = 0.364. The slope 0.12 is a marginal effect in q per kg, not an elasticity; 0.040 inverts the ratio of means. 3.030 is the ratio of means (100/33) without the slope.
Further reading: Gujarati and Porter, Basic Econometrics
Which assumption is NOT needed for the Gauss-Markov theorem that OLS is BLUE?
C. Normal distribution of the error term
The Gauss-Markov theorem needs linearity in parameters, zero conditional mean, homoscedasticity, no autocorrelation and no perfect multicollinearity. Normality is added only to derive exact t and F distributions for inference in small samples.
Further reading: Gujarati and Porter, Basic Econometrics
Which pattern in regression output most strongly suggests multicollinearity?
A. High R-squared and significant F, but few individually significant t ratios
Collinear regressors jointly explain Y well (high R-squared, significant F), but their separate effects cannot be isolated, so individual standard errors are large. A fan of residuals points to heteroscedasticity; RESET to misspecification.
Further reading: Gujarati and Porter, Basic Econometrics
With the same bounds (dL = 1.284, dU = 1.567), a computed d of 2.90 indicates
D. negative autocorrelation
For negative autocorrelation compare d with 4 - dL = 2.716 and 4 - dU = 2.433. Since 2.90 > 2.716, negative autocorrelation is indicated. Between 2.433 and 2.716 would be inconclusive.
Further reading: Gujarati and Porter, Basic Econometrics
True model: yield = b1 + 0.3 fertiliser + 5.0 soil index + u. Soil index is omitted, and the slope from regressing soil index on fertiliser is 0.02. The expected value of the estimated fertiliser coefficient is
B. 0.40
E(b2) = b2 + b3 x b32 = 0.3 + 5.0 x 0.02 = 0.40. The fertiliser effect is overstated because better soils receive more fertiliser and also yield more. 0.10 is the bias alone. 0.20 subtracts the bias instead of adding it.
Further reading: Gujarati and Porter, Basic Econometrics
A researcher must choose between two non-nested models of farm credit demand, neither a special case of the other. A suitable test is
B. the Davidson-MacKinnon J test
The J test adds the fitted values of the rival model as a regressor and tests their significance, in both directions. It can reject both models or neither. The other tests address structural change, autocorrelation and heteroscedasticity.
Further reading: Gujarati and Porter, Basic Econometrics
In a Koyck distributed lag with impact coefficient b0 = 0.25 and decay rate lambda = 0.6, the long-run multiplier and mean lag are
B. 0.625 and 1.5 periods
Long run = b0/(1 - lambda) = 0.25/0.4 = 0.625. Mean lag = lambda/(1 - lambda) = 0.6/0.4 = 1.5. 1.36 is the median lag (-ln 2/ln lambda), a different measure.
Further reading: Gujarati and Porter, Basic Econometrics
Applying OLS to a structural demand equation in which price is endogenous gives estimates that are
B. biased and inconsistent
Price is determined jointly with quantity and so is correlated with the demand error. That is simultaneity bias, which does not disappear as the sample grows.
Further reading: Gujarati and Porter, Basic Econometrics
In the Dickey-Fuller regression Delta Y_t = delta Y_(t-1) + u_t, the null and alternative hypotheses are
A. H0: delta = 0 (unit root); H1: delta < 0 (stationary)
delta = rho - 1, so delta = 0 means rho = 1, a unit root. The alternative is one-sided stationarity. KPSS reverses the roles, taking stationarity as the null.
Further reading: Gujarati and Porter, Basic Econometrics
A regression of one district's wheat price on another's, both in levels over 25 years, gives R-squared 0.96 and Durbin-Watson 0.31. This should first raise the suspicion of
C. spurious regression between non-stationary series
Granger and Newbold's warning sign is R-squared above d. The series may be cointegrated, but that must be tested (residual ADF with Engle-Granger critical values); a high R-squared alone proves nothing. d near 0 means strong positive, not negative, autocorrelation.
Further reading: Gujarati and Porter, Basic Econometrics
Ten here, 125 in the app. The Laisha app has every practice question we have written to ICAR AICE-JRF/SRF in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
Free for ten days, then one subscription of US$10 a month. We would rather say so here than have you find it later.
An AI operating system for agriculture: free guides, manuals and tools written for every country.