CEA - Certified Economic Analyst Quantitative Analysis and Econometrics Questions and Answers — Questions and Answers
Question 1: An econometrician is analyzing the impact of years of education and years of experience on an individual's wage. They suspect that the error terms in their regression model have a non-constant variance, where the variance of the error term is larger for individuals with higher levels of education. Which of the following econometric problems is most likely present in this model?
- Autocorrelation
- Multicollinearity
- Heteroskedasticity (Correct answer)
- Omitted variable bias
Correct answer: Heteroskedasticity
Heteroskedasticity occurs when the variance of the error terms in a regression model is not constant across all observations. In this scenario, the variance of the error term is dependent on the level of education, which is an independent variable. This violates the classical linear model assumption of homoskedasticity.
Question 2: A researcher is building a multiple linear regression model to predict house prices. The model includes square footage, number of bedrooms, and number of bathrooms as independent variables. The researcher notices a very high correlation (r > 0.9) between the number of bedrooms and the number of bathrooms. What is the primary concern associated with this finding?
- The model will have a low R-squared value.
- The estimated coefficients for the correlated variables may be unreliable. (Correct answer)
- The intercept of the model will be biased.
- The error terms will be serially correlated.
Correct answer: The estimated coefficients for the correlated variables may be unreliable.
The primary concern with high correlation between independent variables is multicollinearity. Multicollinearity inflates the standard errors of the affected coefficient estimates, making them unstable and difficult to interpret. It does not necessarily bias the coefficients, but it increases their variance, reducing their statistical significance.
Question 3: In time-series analysis, which of the following models is most appropriate for a stationary series where the current value is dependent on a finite number of its own previous values and a current error term?
- Moving Average (MA) model
- Autoregressive (AR) model (Correct answer)
- Random Walk model
- Exponential Smoothing model
Correct answer: Autoregressive (AR) model
An Autoregressive (AR) model describes a time series where the current value is a linear combination of its own past values plus an error term. This directly matches the description of a stationary series depending on a finite number of its own previous values.
Question 4: An analyst is studying the effect of a new fertilizer on crop yield. They regress crop yield on the amount of fertilizer used. However, they believe the amount of fertilizer used is correlated with the error term because farmers with better quality soil (an unobserved variable) tend to use more fertilizer. To address this issue, the analyst needs to find a variable that is correlated with fertilizer usage but does not directly affect crop yield, except through its effect on fertilizer usage. What is this type of variable called?
- A dummy variable
- A lagged variable
- A confounding variable
- An instrumental variable (Correct answer)
Correct answer: An instrumental variable
An instrumental variable (IV) is used to address endogeneity problems, such as when an explanatory variable is correlated with the error term. The IV must be correlated with the endogenous explanatory variable (relevance) but uncorrelated with the error term (exogeneity). This allows for a consistent estimation of the true causal effect.
Question 5: Which of the following is a potential consequence of omitting a relevant independent variable from a regression model?
- The R-squared of the model will be artificially inflated.
- The standard errors of the included variables' coefficients will be smaller.
- The coefficients of the included independent variables may be biased. (Correct answer)
- The model will suffer from perfect multicollinearity.
Correct answer: The coefficients of the included independent variables may be biased.
Omitting a relevant variable that is correlated with any of the included independent variables will lead to omitted variable bias. The estimated coefficients of the included variables will capture some of the effect of the omitted variable, leading to biased and inconsistent estimates.
Question 6: An economic analyst is tasked with forecasting quarterly sales for a retail company. The analyst observes that the sales data exhibits a clear upward trend over the years and a recurring pattern of peaks during the holiday season. Which of the following forecasting techniques is best suited to handle both trend and seasonality in the data?
- Simple Linear Regression
- Simple Exponential Smoothing
- Holt-Winters' method (Correct answer)
- Autoregressive Integrated Moving Average (ARIMA)
Correct answer: Holt-Winters' method
The Holt-Winters' method, also known as triple exponential smoothing, is specifically designed for time series data that has both a trend and a seasonal component. It uses three smoothing equations to account for the level, the trend, and the seasonal variation in the data, making it suitable for this scenario.
CEA - Certified Economic Analyst Quantitative Analysis and Econometrics Questions and Answers
An econometrician is analyzing the impact of years of education and years of experience on an individual's wage.
They suspect that the error terms in their regression model have a non-constant variance, where the variance of the error term is larger for individuals with higher levels of education.
Which of the following econometric problems is most likely present in this model?