Show That for the Following Regression Model $$Y _ { t } = e ^ { \beta _ { 0 } + \beta _ { 1 } x d + u }$$

question 4

Essay

Show that for the following regression model $$Y _ { t } = e ^ { \beta _ { 0 } + \beta _ { 1 } x d + u }$$
where $t$ is a time trend, which takes on the values $1,2 , \ldots , T , \beta _ { 1 }$ represents the instantaneous ("continuous compounding") growth rate. Show how this rate is related to the proportionate rate of growth, which is calculated from the relationship
$$Y _ { t } = Y _ { 0 } \times ( 1 + g ) ^ { t }$$
when time is measured in discrete intervals.

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Definitions:

Classical Conditioning

A learning process that occurs when two stimuli are repeatedly paired; a response that is first elicited by the second stimulus is eventually elicited by the first stimulus alone.

Negative Reinforcement

A behavioral principle where the removal of an unfavorable event or outcome after the display of a behavior increases the likelihood of that behavior being repeated in the future.

Fixed-Ratio Schedule

A schedule of reinforcement where a response is rewarded only after a specified number of responses have been made.

Negative Reinforcement

A process in behavioral psychology where the removal of an undesirable or unpleasant stimulus following a desired behavior increases the likelihood of that behavior being repeated.