Time Series Analysis: Method and Substance Introductory Workshop on Time Series Analysis

Total Multiplier

• Consider the following ADL model (DeBoef & Keele 2008)
• Yt = α0 + α1Yt-1 + β0Xt + β1Xt-1 +εt
• The long run effect of Xt on Yt is calculated as:
• k1 = (β0 + β1)/(1- α1)
• DeBoef & Keele show that many time series models place restrictions on this basic type of ADL model: partial adjustment, static, finite DL, differences, dead start, common factor. They can also be treated as restrictions on a general error correction model (ECM).

Advanced Topics: Cointegration

• As noted earlier, sometimes two or more time series move together in an equilibrium relationship.
• For example, some scholars have argued that presidential approval is in equilibrium with economic conditions (Ostrom and Smith 1992).
• If the economy is doing well and approval is too low, it will increase; if the economy is doing poorly, and the president has high approval, it will fall back to the equilibrium level.

Advanced Topics: Cointegration

• Granger (1983) showed that if two variables are cointegrated, then they have an error correction representation (ECM):
• In Ostrom and Smith’s (1992) model:
• At = Xt + (At-1 - Xt-1) + t
• where At = approval
• Xt = quality of life outcome