Ordered Probit Model Quiz

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Questions and Answers

What do ordered models indicate regarding the order of options?

The order should always be randomized

The order is irrelevant

The order only matters for visual representation

The order is informative about outcomes (correct)

In the ordered probit model, the marginal effects are dependent on alternative-specific variables.

False

What is the effect of relabelling options in an ordered model?

It breaks up the natural ordering of the outcomes.

In a survey data example, rating very poor would be represented as _____ in an ordered model.

1 Signup and view all the answers

Match the following elements with their correct descriptions:

Yi* = Latent variable representing satisfaction Φ(·) = Cumulative distribution function of the standard normal distribution β = Coefficient indicating the effect of variables on outcomes αk = Cut-off parameter defining thresholds in ordered models Signup and view all the answers

Which of the following is definitive in determining the choice probabilities in an ordered probit model?

Cut-off parameters Signup and view all the answers

The conditional logit model allows β to vary with alternatives.

False Signup and view all the answers

The choice probabilities for an ordered probit model are calculated using the standard normal cumulative distribution function, denoted as _____ .

Φ Signup and view all the answers

Which of the following is NOT a requirement for Instrumental Variables (IV) to work?

The instrument must influence the outcome directly Signup and view all the answers

The Local Average Treatment Effect (LATE) applies to individuals who do not change treatment status regardless of the instrument.

False Signup and view all the answers

What is the sharp RDD?

It is a type of Regression Discontinuity Design where treatment switches cleanly at a cutoff. Signup and view all the answers

The treatment variable for KIPP attendance is represented as ______.

Di Signup and view all the answers

Match the following terms with their definitions:

Instrument Zi = Dummy variable for being offered a seat at KIPP Outcome Yi = Fifth-grade math scores Treatment Di = Dummy variable for attending KIPP Running variable a = Variable determining treatment according to threshold Signup and view all the answers

In which scenario is the concept of Fuzzy RDD typically applied?

When there are variations in treatment assignment around the cutoff Signup and view all the answers

The exclusion restriction assumption can be directly tested with data.

False Signup and view all the answers

What is the significance of the first stage effect in IV analysis?

It indicates that the instrument has a causal effect on the treatment variable. Signup and view all the answers

The average mortality rates at age a is represented as ______ in RDD.

M̄a Signup and view all the answers

Which statement best describes the role of the instrument in the IV setup?

It must only influence the outcome through the treatment variable Signup and view all the answers

In a multinomial logit model, how is the probability of an alternative k calculated?

$\frac{exp(x_i \beta_k)}{1 + \sum_{h=1}^{K} exp(x_i \beta_h)}$ Signup and view all the answers

In the multinomial logit model, the coefficients βk are consistent across all alternatives.

False Signup and view all the answers

What defines the marginal effect of an alternative k regarding covariate j in the multinomial model?

It is given by the formula $\frac{\partial P(Y_i = k|x_i)}{\partial x_{ij}} = P(Y_i = k|x_i) \beta_{jk} - \frac{\sum_{h=1}^{K} exp(x_i \beta_h) \beta_{jh}}{1 + \sum_{h=1}^{K} exp(x_i \beta_h)}$ Signup and view all the answers

In a multinomial logit model, probabilities must ____ to one.

sum Signup and view all the answers

Match the model type with its characteristic:

Multinomial Logit = Coefficients vary with alternatives Conditional Logit = Variables vary across alternatives Binary Logit = Used when there are only two outcomes Ordered Logit = Used for ordered categories Signup and view all the answers

Which of the following statements regarding covariates in a multinomial logit model is true?

Covariates are fixed across alternatives. Signup and view all the answers

In terms of probabilities, a higher value of a coefficient βjk always indicates a higher probability of choosing alternative k.

False Signup and view all the answers

What element of the multinomial logit model normalizes the equation with regard to alternative effects?

The inclusion of $\beta_0 = 0$ ensures that probabilities sum to one. Signup and view all the answers

What does the variable Ti indicate in a fuzzy regression discontinuity design (RDD)?

It represents the treatment assignment based on the GRE cutoff. Signup and view all the answers

In a sharp RDD, treatment is not deterministic based on the running variable.

False Signup and view all the answers

What does the outcome equation Yi = 1 + Di + 1 xi + represent?

It represents the earnings of student i based on their treatment status and GRE score. Signup and view all the answers

In a linear probability model, P(Yi = 1|xi) is expressed as __________.

0 + j xij Signup and view all the answers

What is a key characteristic of fuzzy RDD compared to sharp RDD?

Treatment probability can change at the cutoff. Signup and view all the answers

The linear probability model can produce estimated probabilities greater than 1.

True Signup and view all the answers

What is the first stage equation in a fuzzy RDD?

Di = 2 + Ti + 2 xi + i Signup and view all the answers

In a probit model, the cumulative distribution function used is __________.

(xi ) Signup and view all the answers

Match the following elements with their corresponding roles:

Yi = Earnings of student i xi = GRE score of student i = Effect of treatment on earnings 1 = Effect of GRE score on earnings Signup and view all the answers

Why is maximum likelihood estimation used in binary discrete choice models?

It can handle probabilities constrained between 0 and 1. Signup and view all the answers

Fuzzy RDD requires scaling of estimates based on the treatment probability at the cutoff.

True Signup and view all the answers

What is the main limitation of the Linear Probability Model (LPM)?

It can produce predicted probabilities that are negative or greater than 100%. Signup and view all the answers

In the logit model, the function G(xi ) is expressed as __________.

(xi ) = exp(xi ) / (1 + exp(xi )) Signup and view all the answers

Study Notes

Microeconometrics Weeks 6-10 Revision

This revision covers topics from weeks 6-10 of EC338 - Microeconometrics.

Instrumental Variables (IV)

IV Setup:
- Instrument (Zᵢ): A dummy variable equal to 1 if a student was offered a seat at KIPP, and 0 otherwise.
- Treatment (Dᵢ): A dummy variable equal to 1 if a student attends KIPP, and 0 otherwise.
- Outcome (Yᵢ): Fifth-grade math scores for student i.
- Causal chain reaction: Zᵢ (instrument) → Dᵢ (treatment) → Yᵢ (outcome).
- IV uses first-stage and reduced-form effects to find the effect of interest.
IV Assumptions:
- First Stage: The instrument (Zᵢ) must have a causal effect on the treatment (Dᵢ). This is equivalent to the instrument's effect on the treatment being non-zero; this can be checked using data.
- Random Assignment: The instrument (Zᵢ) should be as good as randomly assigned. This assumption is untestable, but balance checks can offer supporting evidence.
- Exclusion Restriction: The instrument (Zᵢ) should only affect the outcome (Yᵢ) through its effect on treatment (Dᵢ). This assumption is also untestable, especially with only one instrument.
Local Average Treatment Effect (LATE):
- Applies to cases with heterogeneous treatment effects.
- The effect of interest is the LATE.
- Measures the treatment effect for the compliers.
- Compliers are individuals who change treatment status because of the instrument.
- The subsample of compliers depends on the instrument and setting.
- LATE for binary instrument and treatment: λ = E[Yᵢ|Zᵢ = 1] – E[Yᵢ|Zᵢ = 0] / E[Dᵢ|Zᵢ = 1] – E[Dᵢ|Zᵢ = 0]

Regression Discontinuity Designs (RDD)

RDD Setup:
- Running variable (a): A variable determining treatment according to a threshold (e.g., age).
- Treatment variable (Dₐ): A dummy variable, equal to 1 if eligible for treatment (above the threshold), 0 otherwise.
- Outcome variable (Mₐ): E.g., average mortality rates at age a.
- Key feature: sharp switch on treatment at a cutoff point.
Fuzzy RDD:
- Exploits discontinuities in the probability of treatment at a cutoff point.
- Treatment probability (or intensity) changes at the cutoff.
  - Useful when treatment isn't fully deterministic.
- The treatment doesn't switch from 0 to 1, but its probability changes due to some condition.
Difference between Sharp and Fuzzy RDD:
- Sharp RDD: Treatment is a deterministic function; everyone above the threshold gets the treatment; everyone below does not.
- Fuzzy RDD: Treatment is not deterministic; some individuals below the threshold might receive the treatment, and some above the threshold might not.
Fuzzy RDD as IV:
- Intuitively, treatment becomes more likely to the right of the cutoff.
- Fuzzy RDD provides a way to estimate that effect; it scales the estimates by the fraction of individuals who get treated due to crossing the cutoff.
- Outcome equation: Yᵢ = α₁ + xDᵢ + γ₁xᵢ + εᵢ
- First stage equation: Dᵢ = α₂ + φTᵢ + γ₂xᵢ + ξᵢ
- 2SLS second stage: Yᵢ= α₁ + λ₂Dᵢ + γ₁xᵢ + εᵢ

Binary Outcomes

Linear Probability Model (LPM):
- In an LPM, P(Yᵢ = 1|xᵢ) = E(Yᵢ|xᵢ) = β₀ + Σβⱼxᵢⱼ
- Leads to a linear regression model: Yᵢ = β₀ + Σβⱼxᵢⱼ + εᵢ
- Fitted values estimate the probability, but probabilities can be < 0 or > 1.
Probit and Logit Models:
- Non-linear functions: G(xᵢβ) ∈ [0, 1] ⇒ P(Yᵢ = 1|xᵢ) ∈ [0, 1].
- Probit: Uses the cumulative distribution function (CDF) of the standard normal distribution.
- Logit: Uses the CDF of the logistic distribution.
- Used to get probabilities bounded within [0,1].
Marginal Effects:
- With non-linear models, marginal effects are not equal to the coefficients.
- Marginal effects depend on xᵢ.
Maximum Likelihood Estimation:
- The likelihood function and its log are used to find the best parameter estimates that match observed data.
- Econometric statistical packages do this calculation for us in practice.

Multinomial and Ordered Models

Multinomial Logit:
- Used for models with multiple unordered categories.
- P(Yᵢ = k|xᵢ) = exp(xᵢβₖ) / [1 + Σₖ₋₁exp(xᵢβₙ)].
- Marginal effects now depend on multiple covariates (compared to just single X variable).
Ordered Models:
- Outcome is categorical but ordered.
- Latent (unobserved) variable model is assumed (e.g., measure of satisfaction).
- Choice probabilities are based on a latent variable and cutoff values to determine observed values.
- Marginal effects of ordered models are calculated similarly to other models, based on specific conditions of the model.

Studying That Suits You

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Description

Test your knowledge on ordered probit models and their characteristics. This quiz covers topics like choice probabilities, marginal effects, and the implications of relabelling options. Dive into the specific details of how these models function within survey data and treatment variables.

Ordered Probit Model Quiz

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Podcast

Questions and Answers

What do ordered models indicate regarding the order of options?

In the ordered probit model, the marginal effects are dependent on alternative-specific variables.

What is the effect of relabelling options in an ordered model?

In a survey data example, rating very poor would be represented as _____ in an ordered model.

Match the following elements with their correct descriptions:

Which of the following is definitive in determining the choice probabilities in an ordered probit model?

The conditional logit model allows β to vary with alternatives.

The choice probabilities for an ordered probit model are calculated using the standard normal cumulative distribution function, denoted as _____ .

Which of the following is NOT a requirement for Instrumental Variables (IV) to work?

The Local Average Treatment Effect (LATE) applies to individuals who do not change treatment status regardless of the instrument.

What is the sharp RDD?

The treatment variable for KIPP attendance is represented as ______.

Match the following terms with their definitions:

In which scenario is the concept of Fuzzy RDD typically applied?

The exclusion restriction assumption can be directly tested with data.

What is the significance of the first stage effect in IV analysis?

The average mortality rates at age a is represented as ______ in RDD.

Which statement best describes the role of the instrument in the IV setup?

In a multinomial logit model, how is the probability of an alternative k calculated?

In the multinomial logit model, the coefficients βk are consistent across all alternatives.

What defines the marginal effect of an alternative k regarding covariate j in the multinomial model?

In a multinomial logit model, probabilities must ____ to one.

Match the model type with its characteristic:

Which of the following statements regarding covariates in a multinomial logit model is true?

In terms of probabilities, a higher value of a coefficient βjk always indicates a higher probability of choosing alternative k.

What element of the multinomial logit model normalizes the equation with regard to alternative effects?

What does the variable Ti indicate in a fuzzy regression discontinuity design (RDD)?

In a sharp RDD, treatment is not deterministic based on the running variable.

What does the outcome equation Yi = 1 + Di + 1 xi + represent?

In a linear probability model, P(Yi = 1|xi) is expressed as __________.

What is a key characteristic of fuzzy RDD compared to sharp RDD?

The linear probability model can produce estimated probabilities greater than 1.

What is the first stage equation in a fuzzy RDD?

In a probit model, the cumulative distribution function used is __________.

Match the following elements with their corresponding roles:

Why is maximum likelihood estimation used in binary discrete choice models?

Fuzzy RDD requires scaling of estimates based on the treatment probability at the cutoff.

What is the main limitation of the Linear Probability Model (LPM)?

In the logit model, the function G(xi ) is expressed as __________.

Study Notes

Microeconometrics Weeks 6-10 Revision

Instrumental Variables (IV)

Regression Discontinuity Designs (RDD)

Binary Outcomes

Multinomial and Ordered Models

Studying That Suits You

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