Question

Discuss the implications of a higher degree of uncertainty about the effects of monetary policy on output. What would happen if the range of model predictions increased?

Answer 1

Monetary policy shocks account for probably less than 25% of the variance for the 1-year or more ahead forecast revision of real output, and may easily account for less than 2% at any given horizon. 2. The GDP price deflator falls only slowly following a contractionary monetary policy shock.

The larger the uncertainty, the higher the probability that a more aggressive monetary policy response to shocks may move inflation and output away from the target (due to the interaction between the slope parameter and the output gap) and so the larger the welfare cost

The Regression Approach for Predictions

Using regression to make predictions doesn’t necessarily involve predicting the future. Instead, you predict the mean of the dependent variable given specific values of the dependent variable(s). For our example, we’ll use one independent variable to predict the dependent variable. I measured both of these variables at the same point in time.

The general procedure for using regression to make good predictions is the following:

1. Research the subject-area so you can build on the work of others. This research helps with the subsequent steps.
2. Collect data for the relevant variables.
3. Specify and assess your regression model.
4. If you have a model that adequately fits the data, use it to make predictions.

While this process involves more work than the psychic approach, it provides valuable benefits. With regression, we can evaluate the bias and precision of our predictions:

1. Bias in a statistical model indicates that the predictions are systematically too high or too low.
2. Precision represents how close the predictions are to the observed values.

Example Scenario for Regression Predictions

We’ll use a regression model to predict body fat percentage based on body mass index (BMI). I collected these data for a study with 92 middle school girls. The variables we measured include height, weight, and body fat measured by a Hologic DXA whole-body system. I’ve calculated the BMI using height and weight measurements. DXA measurements of body fat percentage are considered to be among the best

Finding a Good Regression Model for Predictions

We have the data. Now, we need to determine whether there is a statistically significant relationship between the variables. Relationships, or correlations between variables, are crucial if we want to use the value of one variable to predict the value of another. We also need to evaluate the suitability of the regression model for making predictions.

We have only one independent variable (BMI), so we can use a fitted line plot to display its relationship with body fat percentage. The relationship between the variables is curvilinear. I’ll use a polynomial term to fit the curvature. In this case, I’ll include a quadratic (squared) term. The fitted line plot below suggests that this model fits the data.

Make Predictions Only Within the Range of the Data

Regression predictions are valid only for the range of data used to estimate the model. The relationship between the independent variables and the dependent variable can change outside of that range. In other words, we don’t know whether the shape of the curve changes. If it does, our predictions will be invalid.

The graph shows that the observed BMI values range from 15-35. We should not make predictions outside of this range.

Make Predictions Only for the Population You Sampled

The relationships that a regression model estimates might be valid for only the specific population that you sampled. Our data were collected from middle school girls that are 12-14 years old. The relationship between BMI and body fat percentage might be different for males and different age groups.

Using our Regression Model to Make Predictions

We have a valid regression model that appears to produce unbiased predictions and can predict new observations nearly as well as it predicts the data used to fit the model. Let’s go ahead and use our model to make a prediction and assess the precision.

It is possible to use the regression equation and calculate the predicted values ourselves. However, I’ll use statistical software to do this for us. Not only is this approach easier and more accurate, but I’ll also have it calculate the prediction intervals so we can assess the precision.