Suppose you wish to estimate the marginal effect that income has on consumption.The distributed lag model would be specified as
A) $\text { Consumption } _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Income } _ { i } + \beta _ { 2 } \text { Income } _ { i - 1 } + \varepsilon _ { t } \text {. }$
B) $\text { Consumption } _ { t } = \beta _ { 0 } + \beta _ { 1 } \text { Income } _ { t } + \varepsilon _ { t }$
C) $\text { Consumption } _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Income } _ { i } + \varepsilon _ { i } \text {. }$
D) $\text { Consumption } _ { t } = \beta _ { 0 } + \beta _ { 1 } \text { Income } _ { t } + \beta _ { 2 } \text { Income } _ { t - 1 } + \varepsilon _ { t } \text {. }$

Question

Quizplus · Accepted Answer

The distributed lag model is used to estimate the impact of a variable on another variable over time. In this case, we are interested in estimating the marginal effect of income on consumption. Therefore, we use the lagged income variable (income in the previous period) to capture the dynamic relationship between income and consumption. Option D is the correct specification of a distributed lag model for this purpose.

Suppose You Wish to Estimate the Marginal Effect That Income