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RBI Grade B Causal Inference, Panel Data & Efficiency Analysis: practice questions

RBI Grade B (DSIM) - Department of Statistics and Information Management · India · Reserve Bank of India Services Board

Original practice questions written to the published syllabus · not past papers
10worked here, free
77written to this exam in this subject
10syllabus units

What this subject covers

Did the scheme, technology or variety cause the change? Potential outcomes, matching and weighting, difference-in-differences, instrumental variables, regression discontinuity and synthetic control, panel data models, quantile regression, and stochastic frontier and DEA efficiency analysis. Classical econometrics (OLS violations, simultaneous equations) is in the Agribusiness track and is assumed here.

In the exams: Not an explicit unit in AICE-JRF Ag Stat; AICE-JRF Ag Econ research methodology (present); RBI Grade B DSIM (reported); research and evaluation roles (applied)

What RBI Grade B asks from it

RBI Grade B (DSIM) and Indian Statistical Service (reported)

Econometric identification: endogeneity and instrumental variables, panel data fixed and random effects with the Hausman test, and basic programme-evaluation designs.

Where the 77 questions fall

How our questions for RBI Grade B spread across the units of Causal Inference, Panel Data & Efficiency Analysis. Difficulty: 21 easy, 40 medium, 16 hard.

Randomised evaluation in agriculture and its limits9
Propensity score matching and weighting9
Difference-in-differences and event studies8
Instrumental variables and local average treatment effects8
Panel data: fixed and random effects and the Hausman test8
Dynamic panels (introduction to GMM)8
Potential outcomes and the identification problem7
Regression discontinuity designs7
Quantile regression7
Synthetic control6

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Potential outcomes and the identification problem · hard

In a causal graph, both adopting a technology and high yield cause a farm to be selected for a media award. Analysing only award-winning farms will:

  1. Turn the award into a valid instrument
  2. It conditions on a collider
  3. Leave the adoption-yield relation unchanged
  4. Remove all confounding between adoption and yield
Answer and working

B. It conditions on a collider

The award is a common effect (collider) of adoption and yield; conditioning on it induces an association between them even if none exists in the population.

Further reading: Imbens and Rubin, Causal Inference; Angrist and Pischke, Mostly Harmless Econometrics

2 · Propensity score matching and weighting · easy

What is the propensity score?

  1. The share of treated units in the sample
  2. The probability of treatment given covariates
  3. The difference in outcomes between matched pairs
  4. The predicted outcome under treatment
Answer and working

B. The probability of treatment given covariates

e(X) = P(D = 1 | X); Rosenbaum and Rubin showed it balances observed covariates between treated and untreated units.

Further reading: Imbens and Rubin, Causal Inference; Rosenbaum and Rubin (1983)

3 · Propensity score matching and weighting · hard

A matched evaluation of a credit scheme shows excellent balance on all observed covariates. What bias can remain?

  1. No bias at all once balance is achieved
  2. Bias from imbalance in the observed covariates
  3. Bias from unobserved confounding factors
  4. Bias from using the propensity score as a weight
Answer and working

C. Bias from unobserved confounding factors

Matching relies on selection on observables (unobserved confounders such as managerial ability are not handled); unobserved factors affecting both take-up and outcome still bias the estimate. Sensitivity analysis gauges how strong they would need to be.

Further reading: Imbens and Rubin, Causal Inference; Rosenbaum and Rubin (1983)

4 · Propensity score matching and weighting · medium

What does imposing common support do in propensity-score matching?

  1. Removes the need for a caliper
  2. Drops treated units without matches
  3. Adds controls to the sample until sizes match
  4. Forces all propensity scores to equal 0.5
Answer and working

B. Drops treated units without matches

Treated units whose scores exceed the controls' range have no counterparts and are dropped; the estimate then refers to the remaining units, which should be reported.

Further reading: Imbens and Rubin, Causal Inference; Rosenbaum and Rubin (1983)

5 · Difference-in-differences and event studies · medium

In an event study, coefficients for the three years before a scheme are large and significant. What does this suggest?

  1. Pre-trends or anticipation
  2. That the scheme was randomly assigned
  3. That standard errors must be too large
  4. A large and genuine treatment effect
Answer and working

A. Pre-trends or anticipation

Leads should be near zero under parallel trends; significant leads cast doubt on the design.

Further reading: Angrist and Pischke; Cunningham, Causal Inference: The Mixtape

6 · Difference-in-differences and event studies · medium

At what level should standard errors be clustered in a DiD study of a district-level scheme with yearly farm data?

  1. The calendar year only
  2. Standard errors need no clustering
  3. The district
  4. The individual farm-year observation
Answer and working

C. The district

Cluster at the level of treatment assignment to allow for serial and within-district correlation; Bertrand, Duflo and Mullainathan showed unclustered DiD errors are far too small.

Further reading: Angrist and Pischke; Cunningham, Causal Inference: The Mixtape

7 · Instrumental variables and local average treatment effects · medium

A lottery offering subsidised tractors raises mean farm income by 6,000 currency units and tractor ownership by 30 percentage points. What is the Wald IV estimate of the effect of tractor ownership?

  1. 1,800 currency units
  2. 200 currency units
  3. 6,000 currency units
  4. 20,000 currency units
Answer and working

D. 20,000 currency units

Wald = reduced form / first stage = 6,000/0.30 = 20,000. 1,800 multiplies; 6,000 is the reduced form (ITT).

Further reading: Angrist and Pischke; Imbens and Angrist (1994)

8 · Instrumental variables and local average treatment effects · medium

Distance to the nearest input dealer is used as an instrument for fertiliser use. Which threat to exclusion is most plausible?

  1. Distance also shapes prices and access
  2. Distance is too strongly related to fertiliser use
  3. Distance has no variation between farms
  4. Distance can be measured precisely
Answer and working

A. Distance also shapes prices and access

Remote farms may also face lower output prices, less credit and fewer services, which affect income directly, violating exclusion.

Further reading: Angrist and Pischke; Imbens and Angrist (1994)

9 · Synthetic control · medium

A synthetic control tracks the treated state poorly before the policy, with a large pre-treatment RMSPE. What follows?

  1. The gap is not a credible effect
  2. The method is valid if donors are many
  3. The policy had no effect
  4. The effect is larger than the gap
Answer and working

A. The gap is not a credible effect

A credible counterfactual must reproduce the pre-treatment path; with poor fit the gap may reflect mismatch rather than the policy.

Further reading: Abadie (2021), Using synthetic controls

10 · Quantile regression · hard

A treatment's conditional quantile effect at tau = 0.1 is large. Does this mean the farms that were poorest before treatment gained most?

  1. No; ranks need not be preserved
  2. Yes, by definition of quantile effects
  3. Yes, if the sample is large
  4. No, quantile effects are always zero
Answer and working

A. No; ranks need not be preserved

Quantile effects compare distributions, not individuals; without rank invariance, the farms at the 10th percentile after treatment need not be those that were there before.

Further reading: Koenker, Quantile Regression

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Causal Inference, Panel Data & Efficiency AnalysisThe full study manual, free RBI Grade BFormat, sections and how it has changed

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