You Have Read About the So-Called Catch-Up Theory by Economic $X_{1}$

question 55

Essay

You have read about the so-called catch-up theory by economic historians, whereby nations
that are further behind in per capita income grow faster subsequently.If this is true
systematically, then eventually laggards will reach the leader.To put the theory to the test,
you collect data on relative (to the United States)per capita income for two years, 1960 and
1990, for 24 OECD countries.You think of these countries as a population you want to
describe, rather than a sample from which you want to infer behavior of a larger population.
The relevant data for this question is as follows:
where $X_{1}$ and $X_{2}$ are per capita income relative to the United States in 1960 and 1990 respectively, and $Y$ is the average annual growth rate in $X$ over the $1960-1990$ period. Numbers in the last row represent sums of the columns above.

(a) Calculate the variance and standard deviation of $X_{1}$ and $X_{2}$ . For a catch-up effect to be present, what relationship must the two standard deviations show? Is this the case here?

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Definitions:

Reinforcement Theory

A theory in psychology that suggests behavior is motivated by its consequences, with reinforcement used to increase or decrease specific behaviors.

Behavior

The actions or reactions of an individual or system in response to external or internal stimuli.

Variable Ratio Schedules

In behavioral psychology, a reinforcement schedule where a response is rewarded after an unpredictable number of responses, enhancing motivation to respond.

Extinction

The process of eliminating a behavior by stopping the reinforcement that previously followed that behavior, often used in behavioral psychology and organizational management.