Question

Using the monthly data in VOLAT, the following model was estimated: $$ \begin{aligned} \widehat{p c i p} &=1.54+.344 p c i p_{-1}+.074 p c i p_{-2}+.073 p c i p_{-3}+.031 p c s p_{-1} \\ &(.56)(.042) \\ n &=554, R^{2}=.174, \overline{R^{2}}=.168 \end{aligned} $$ where \(p c i p\) is the percentage change in monthly industrial production, at an annualized rate, and \(p c s p\) is the percentage change in the Standard \& Poor's 500 Index, also at an annualized rate. i. If the past three months of pcip are zero and \(p c s p_{-1}=0,\) what is the predicted growth in industrial production for this month? Is it statistically different from zero? ii. If the past three months of pcip are zero but \(p c s p_{-1}=10,\) what is the predicted growth in industrial production? iii. What do you conclude about the effects of the stock market on real economic activity?

Short answer

i. 1.54 (statistically significant); ii. 1.85; iii. Stock market changes seem to marginally affect industrial production.

Step-by-step solution

Interpret the Model

The given model is: \( \widehat{pcip} = 1.54 + 0.344 \cdot pcip_{-1} + 0.074 \cdot pcip_{-2} + 0.073 \cdot pcip_{-3} + 0.031 \cdot pcsp_{-1} \). This model predicts the percentage change in industrial production based on its past values and the previous month's change in stock prices.

Set Past Values to Zero

For part (i), it is given that \( pcip_{-1} = pcip_{-2} = pcip_{-3} = 0 \) and \( pcsp_{-1} = 0 \). Substitute these into the model: \( \widehat{pcip} = 1.54 + 0.344 \times 0 + 0.074 \times 0 + 0.073 \times 0 + 0.031 \times 0 = 1.54 \).

Check Statistical Significance

To determine if this is statistically different from zero, observe that the standard error for the intercept is \(0.56\). The t-statistic is \( \frac{1.54}{0.56} \approx 2.75 \), which indicates statistical significance at typical confidence levels.

Modify Stock Price Change

For part (ii), use the same past \( pcip \) values but change \( pcsp_{-1} = 10 \). Substitute into the model: \( \widehat{pcip} = 1.54 + 0.031 \times 10 = 1.54 + 0.31 = 1.85 \).

Analyze Stock Market Effects

The increase of 0.31 in predicted \( pcip \) when \( pcsp_{-1} \) rises by 10 suggests a positive relationship between stock market performance and industrial production, though the effect size is modest.

Key concepts

Time Series Analysis

Time series analysis is a statistical technique that deals with time-dependence in data. It is commonly used in econometrics to analyze data that is collected over time. In this particular exercise, the time series model is utilized to predict how changes in certain variables can impact future values of other variables.

For instance, the model specified in the exercise incorporates previous monthly records of industrial production changes (\( pcip \)) and also the past stock market changes (\( pcsp \)), allowing predictions for the following month.

Understanding such data patterns over time is crucial because it helps in forecasting and decision-making. It addresses the inherent fluctuation in economic variables due to their 'time' component, something other static analyses might miss.

• It identifies trends: upward, downward, or seasonal.
• Helps in evaluating the behavior of data points through time.
• Enables forecasting for future values based on past observations.

Time series can be complex because each data point may be influenced by the previous points, creating a pattern or trend that is essential for understanding economic activities.

Industrial Production

Industrial production refers to the output of the industrial sector, which includes manufacturing, mining, and utilities. It is an important economic indicator because it gives us insights into the overall economic health.

In the exercise, the percentage change in industrial production is evaluated. This provides information on how much production output has increased or decreased over the period analyzed. Understanding fluctuations in industrial production helps policymakers and analysts predict economic growth.

By examining changes in industrial production, individuals and businesses can make informed decisions about investments and resources:

• An increase in production often indicates economic expansion.
• A decrease could signal contraction or economic downturn.
• Analysis can reveal seasonal patterns that affect production, aiding inventory and workforce planning.

Changes in industrial production reflect manufacturing efficacy and can significantly impact stock market performances and economic strategy. It coincides with business cycles and indicates a nation's industrial activity level.

Stock Market Impact

The impact of the stock market on real economic activity is a significant aspect of econometric studies. The stock market is essentially a reflection of investor sentiment and economic outlook. Changes in stock prices can influence economic variables such as consumption, investment, and production.

In the context of the exercise, a change in the stock market (\( pcsp_{-1} \)) is factored into predicting industrial production. When stock prices rise, it usually reflects investor confidence, potentially leading to increased industrial production as companies may expand due to anticipated increased demand.

The model presented in the exercise illustrates this relationship:

• Stock market performance is directly linked to economic activities such as production.
• A higher past stock price change indicates positive industrial production growth.
• This relationship helps in understanding the economic outlook and can guide investment decisions.

Understanding the stock market's impact helps economists and investors to gauge market trends and their possible economic effects, enhancing strategy formulation both at micro and macroeconomic levels.