Model Misspecification

Correct Answer: Omitting a relevant explanatory variable from the regression model

Omitting a relevant explanatory variable from the regression model is an example of model misspecification in regression analysis. When a relevant variable that influences the dependent variable is excluded from the model, it can lead to biased and inconsistent estimates of the coefficients. This is known as omitted variable bias. Including all potentially relevant explanatory variables, even if some may be insignificant, is not necessarily a problem. It is better to include a variable that might be relevant than to exclude a relevant variable. Transforming the dependent variable using a logarithmic function is a valid technique to improve the model's fit or to address non-linear relationships. It does not constitute model misspecification by itself.

Correct Answer: Fitting an ARMA model to data with seasonality, resulting in biased parameter estimates and poor forecasting performance.

Fitting an ARMA model to data with seasonality is an example of model misspecification in time-series forecasting. ARMA models are designed to capture the autocorrelation and moving average components of a stationary time series. However, when the data exhibits seasonality, an ARMA model alone is insufficient to capture the seasonal patterns, leading to biased parameter estimates and poor forecasting performance. To properly model time-series data with seasonality, an ARIMA model that incorporates both the trend and seasonal components should be used. This allows the model to capture the underlying patterns and dynamics of the data more accurately, resulting in improved forecasting accuracy. Incorporating relevant exogenous variables can also enhance the explanatory power and forecasting accuracy of a time-series model. However, this alone does not address the issue of model misspecification when dealing with seasonality in the data.

Correct Answer: Omitted variable bias, where a relevant explanatory variable is excluded from the model, leading to biased estimates of the coefficients and potentially incorrect predictions.

The correct answer is omitted variable bias. In this case, the analyst has failed to include a relevant explanatory variable, the unemployment rate, which is known to have a significant impact on stock market performance. By excluding this variable, the model's estimates of the coefficients for the included variables (GDP growth, inflation, and interest rates) may be biased, leading to potentially incorrect predictions. Functional form misspecification refers to assuming an incorrect relationship between the dependent and independent variables, such as using a linear model when the true relationship is non-linear. This is not the issue described in the question. Measurement error occurs when the variables included in the model are not accurately measured or proxied, leading to biased estimates and reduced predictive power. However, the question does not mention any issues with the accuracy of the variables included in the model.