Your Textbook Gives a Graphical Example Of $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$

question 41

Essay

Your textbook gives a graphical example of $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ , where outcome is plotted on the vertical axis, and time period appears on the horizontal axis. There are two time periods entered: "t = 1"
and "t = 2." The former corresponds to the "before" time period, while the latter represents the "after" period. The assumption is that the policy occurred sometime between the time periods (call this "t = p"). Keeping in mind the graphical example of $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ , carefully read what a reviewer of the Card and Krueger (CK)study of the minimum wage effect on employment in the New Jersey-Pennsylvania study had to say:
"Two assumptions are implicit throughout the evaluation of the 'natural experiment:' (1)[ $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ ] would be zero if the treatment had not occurred, so a nonzero [ $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ ] indicates the effect of the treatment (that is, nothing else could have caused the difference in the outcomes to change), and (2)… the intervention occurs after we measure the initial outcomes in the two groups. … Three conditions are particularly relevant in interpreting CK's work: (1)[t = 1] must be sufficiently before [t = p] that [the treatment group] did not adjust to the treatment before [t=1] - otherwise [ $\bar { Y } \text { treatment,before }$ - $\bar { Y } \text { control,before }$ ] will reflect the effect of the treatment; (2)[t = 2] must be sufficiently after [t = p] to allow the treatment's effect to be fully felt; and (3)we must be sure that the same difference [ $\bar { Y } \text { treatment,before }$ - $\bar { Y } \text { control,before }$ ] would have been observed at [t = 2] if the treatment had not been imposed, that is, [the control group must be good enough] that there is no need to adjust the differences for factors other than the treatment that might have caused them to change."
Use a figure similar to the textbook to explain what this reviewer meant.

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Definitions:

Sensorimotor Substage

A stage in Jean Piaget's theory of cognitive development, occurring from birth to approximately age 2, where infants learn through interacting with their environment using their senses and motor actions.

Secondary Circular Reactions

A substage in Piaget's sensorimotor stage characterized by the repetition of actions that produce interesting consequences.

Primary Circular Reactions

Early repetitive behaviors of infants, focused on the infant’s own body, that serve as the building blocks of sensory and motor development.

Tertiary Circular Reactions

The stage in Piaget's theory of cognitive development where infants aged 12 to 18 months demonstrate trial and error experimentation, showing a more sophisticated understanding of cause and effect.