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The Mismeasure of Poverty, Happiness & Bias, and RegressionPowerPoint Presentation

The Mismeasure of Poverty, Happiness & Bias, and Regression

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The Mismeasure of Poverty, Happiness & Bias, and Regression

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### The Mismeasure of Poverty, Happiness & Bias, andRegression

In “The Mismeasure of Poverty,” Nicholas Eberstadt notes that the percentage of Americans living under the poverty rate has been stagnant for 30 years, suggesting that antipoverty efforts have failed, and that life has not improved for the nation's poor.

The problem, Eberstadt continues, is that there are anomalies in the official statistics. Why does the poverty rate tend to go up as unemployment falls? Why hasn't it budged while the amounts of money the government spends on the poor have more than doubled in constant dollars?

Eberstadt: The Mismeasure of Poverty anomalies in the official statistics.

- Eberstadt goes back and looks at how the poverty rate is calculated, and finds two realities that are masked by our current statistics, one heartening, one disheartening.
- The first reality is that people living under the poverty line are materially much better off than they were three decades ago.
- They live in much bigger homes.

- Three-quarters own at least one motor vehicle.

- They spend roughly twice as much as they report as income, and not because they are going into debt.

(Networths have not declined.)

In general, poor people today live at about the same standard of living as middle-class people did in the 1960s.

Eberstadt: The Mismeasure of Poverty anomalies in the official statistics.

On the other hand, they live with greater insecurity. In fact, relatively few people live permanently in poverty (power-law distributions).

Butnearly a third of the U.S. population dips into poverty from time to time. Eberstadt paints a picture of greater volatility at the bottom end of the income scale -- a different image from the one portrayed by the immobile statistics, with radically different policy implications (such as?).

Daniel Gilbert: “I’m O.K., You’re Biased” anomalies in the official statistics.

Research shows that decision-makers don’t realize how easily and often their objectivity is compromised. Much of what happens in the brain is not evident to the brain itself.

And yet, if decision-makers are more biased than they realize, they are less biased than the rest of us suspect:

- bathroom scales
- saliva test strips for dangerous enzyme deficiency
- evaluating students’ intelligence by examining info. one piece at a time; when subjects liked the student, they kept turning cards searching for one good piece of info; when they disliked the students, they turned over a few cards, shrugged and quit
- The majority of people claim to be less biased than the majority of people:
84% of medical resident claimed that their colleagues were influenced by gifts from Rx drug companies, but only 16% thought they were similarly influenced.

Daniel Gilbert: “I’m O.K., You’re Biased” anomalies in the official statistics.

Because the brain cannot see itself fooling itself, the only reliable method for avoiding bias is to avoid the situations that produce it.

Doctors should refuse to accept gifts from those who supply drugs to their patients, when justices refuse to hear cases involving those with whom they share familial ties and when chief executives refuse to let their compensation be determined by those beholden to them, then everyone sleeps well.

Professors should grade “blind” as often as possible.

What about college admissions?

Stock Market Volatility & Regression to the Mean anomalies in the official statistics.

Stock Market Volatility & Regression to the Mean anomalies in the official statistics.

Regression anomalies in the official statistics.

Allows you to go beyond correlation and to predict how much, say, a dependent variable Y (e.g., income) changes if independent variable X (e.g., years of education) changes by 1 unit.

Regression anomalies in the official statistics.

Two kinds of regression analysis:

- bivariate(income by years of education)

- multivariate (or multiple regression)

controls for other independent variables

(income by education, age, race, gender, etc)

Bivariate Regression anomalies in the official statistics.

Y = a + bx

Y = dependent variable (what you basically want

to predict/determine)

x = independent variable

a = Y-intercept (the point at which the regression

line intercepts or crosses the Y-axis: anchor)

b = slope of the regression line (the regression

coefficient)

Bivariate Regression anomalies in the official statistics.

Example: Amex Business Service does routine accounting as one of its basic job offerings. Its rate is $20/per hour plus a $25 floppy disk charge.

- The total cost to a customer depends, of course, on the number of hours it takes to complete the job.
- So the total cost, Y, of a job that takes x hours is . . .
- Y = $25 + 20x
- Time & Cost: 5 hours ($125), 7.5 hours ($175),
15 hours ($325), 20 hours ($425), 22.5 hours ($475)

Bivariate Regression anomalies in the official statistics.

Bivariate Regression anomalies in the official statistics.

Y = a + bx + e (error term)

Real-life applications in the natural and social sciences are seldom this straight-forward.

Instead, what we usually have are sets of scores for various independent and dependent variables.

We display them on a scatterplot and use inferential statistics to determine both: the [1] slope (the regression coefficient) and, then, [2] predictions for other independent variables.

For example, consider the education levels and income of 32 employees ...

Bivariate Regression anomalies in the official statistics.

Bivariate Regression & its Measure of Association anomalies in the official statistics.

- Remember that Lambda (for nominal variables) and Kendall’s tau-b/c (for ordinal variables) are PRE measures, which stands for Proportional Reduction in Error.
- PRE: When predicting a dependent variable, how much error can you reduce by knowing the independent variable?
- Regression has a similar statistic:
R-Square or (R2) or “goodness of fit”

always between 0 and 1

(0=no reduction in error, 1=error eliminated)

2.5 anomalies in the official statistics.

2.0

1.5

Visits to Cardiologists per enrollee

1.0

0.5

R2

= 0.49

0.0

0.0

2.5

5.0

7.5

10.0

12.5

15.0

Number of Cardiologists per 100,000 residents

Association between cardiologists and visits per person to cardiologists among Medicare enrollees: 306 HRRsSource: John Wennberg (2005)

400 anomalies in the official statistics.

Discharges for

all Medical

Conditions

R2 = 0.54

350

300

250

200

Discharge Rate

150

100

Discharges for

Hip Fracture

R2 = 0.06

50

0

1.0

2.0

3.0

4.0

5.0

# of Hospital Beds/per 1,000 Residents

Association between # of hospital beds per 1,000 residents and discharges per 1,000 Medicare enrollees in 306 HRRsSource: John Wennberg (2005)

Bivariate Regression & Measure of Association anomalies in the official statistics.

Bivariate Regression & Measure of Association anomalies in the official statistics.

X = 6 years of education & $8,000 incomeRegression line estimated approx. $9,000 in income for 6 years of education.Yet the mean score ($13,866) would have left you with $5,866 in estimated error.With the regression line (coefficient), you reduced the amount of error by $4,866; you are left with $1,000 in estimated error. In other words, by knowing the independent variable, you have $4,866 of explained variation and $1,000 of unexplained variation.explained ($4,866)2explained ($4,866)2 + unexplained ($1,000)2R-Square = aggregating (summing) this for all of the data points in the scatterplot

Bivariate Regression & Measure of Association anomalies in the official statistics.

.751 x .751 = 0.56r2 = R2

Multivariate or Multiple Regression anomalies in the official statistics.

Y = a + b1x1 + b2x2 + b3x3 + e

Allows you to determine the marginal effect of an independent variable on one dependent variable by simultaneously controlling for several other independent variables.

The regression coefficient b1 estimates the average change in Y (dependent variable) for each unit change in independent variable x1, controlling for the other independent variables: x2 and x3, etc.

Same concepts as bivariate regression, but in a three-dimensional + scatterplot (which can’t be graphically illustrated)

The difference is that you obtain partialslopes and partial regression coefficients, which means the “marginal” effect that each independent variable has on the dependent variable.

Methylphenidate and Amphetamine Distribution (DEA data) anomalies in the official statistics. (average = 4,150 grams/100,000 individuals)

grams/per 100,000 Individuals

0 to 1,600 Low (4.6%)

1,600 to 3,150 Below Average (25.5%)

3,150 to 5,150 Average (43.5%)

5,150 to 6,750 Above Average (19.6%)

6,750 to 8,350 High (4.9%)

8,350 to 11,000 Extremely High (1.8%)

Analysis of the Demand for Psychostimulants: anomalies in the official statistics. Multivariate Regression

Data Sources:

- Dependent variable I: DEA data provides the distribution of methylphenidate and amphetamine in grams down to the 5 digit zip code-level (1998-2001)
- Dependent variable II: Source® Territory Manager by NDC HEALTH provides Rx Sales and Rx Quantity sold by product down to zip/county or HSA level from 1996 onwards;
** Average price to be derived from Total Sales/Total Quantity **

- Independent variables: Area Resource Files (ARF), InterStudy, Census Estimates, County Business Patterns, Dept. of Education’s Common Core of Data
Market Definitions:

- 3,030 U.S. counties

Selected Regression Coefficients for Market Model anomalies in the official statistics. * indicates that the coefficient is significant at the 10% level, ** at the 5% level, *** at the 1% level

Selected Regression Coefficients for Market Model anomalies in the official statistics. * indicates that the coefficient is significant at the 10% level, ** at the 5% level, *** at the 1% level

R2 (Ritalin) = 0.715 R2 (Adderall) = 0.672

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