Consider the following models estimated using regression...

Consider the following models estimated using regression analysis applied to time-series data. What is the long-term effect of a 1-unit increase in $x$ in period $t$ ? a. $y_t=10+2 x_t+0.34 y_{t-1}$ b. $y_t=10+2.5 x_t+0.24 y_{t-1}$ c. $y_t=10+2 x_t+0.64 y_{t-1}$ d. $y_t=10+4.3 x_t+0.34 y_{t-1}$

Consider the following models estimated using regression analysis applied to time-series data. What is the long-term effect of a 1-unit increase in $x$ in period $t$ ?
a. $y_t=10+2 x_t+0.34 y_{t-1}$
b. $y_t=10+2.5 x_t+0.24 y_{t-1}$
c. $y_t=10+2 x_t+0.64 y_{t-1}$
d. $y_t=10+4.3 x_t+0.34 y_{t-1}$

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Key Concepts

Stationarity

Stationarity is a fundamental concept in time-series analysis where the statistical properties of a series, such as mean, variance, and autocorrelation, remain constant over time. This assumption is crucial for the validity of many time-series models and for the proper interpretation of long-run multipliers, as it ensures that the effect of shocks does not vary over time.

Dynamic Regression Models

Dynamic regression models incorporate lagged terms of the dependent variable to account for temporal dependencies and persistence in the data. These models help analyze both the immediate (short-term) impact and the evolving effects (long-term) of changes in explanatory variables, making them particularly useful in time-series analysis.

Long-run Multiplier

In dynamic regression models that include lagged dependent variables, the long-run multiplier captures the cumulative effect of a one-unit change in an explanatory variable on the dependent variable after all the dynamic adjustments have taken place. It is typically computed as the ratio of the immediate effect (the coefficient on the regressor) to one minus the coefficient on the lagged dependent variable, provided that the series is stationary.

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