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Empirical Relationships

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Empirical Relationships

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Empirical Relationships

Lecture 1

Today’s Plan

- Syllabus & housekeeping issues
- Course overview
- What is econometrics?
- Two econometric examples

Teaching Team

Professor: Andrew K. G. Hildreth

515 Evans Hall (510) 643-0715

hildreth@econ.berkeley.edu

Office Hours: Monday 2-3 pm & Wednesday 10-11am

Assistant: Judi Chan, (510) 643-1625 chan@econ.berkeley.edu

GSIs:

Brachet Tanguy: tbrachet@econ.berkeley.edu

Office Hours: location and time to be advised. Sections 105 & 106.

Francisco ‘Paco’ Martorell: martorel@econ.berkeley.edu

Office Hours: location and time to be advised. Sections 101 & 102.

Sally Kwak: skwak@econ.berkeley.edu

Office Hours: Tues & Thurs 12.30-2pm 508-5 Evans. Sections 103 & 104.

Course Website

- emlab.berkeley.edu/users/hildreth/e140_sp02/e140.html
- What you’ll find at the website:
- My picture
- Excel files
- Lecture notes
- Problem Sets (& Solutions)
- Midterms (after the tests) & Solutions
- Supplemental handouts

What is Econometrics?

- Broadly defined: the study of economics using statistical methods
- Founding members of the econometric society described it:
“..as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference.” --Samuelson, P., Koopmans, T. & Stone, R. Report of the Evaluative Committee for Econometrica, Econometrica, 1954, p. 142

Why Econometrics?

- When we read the newspaper or see announcements of economic statistics or predictions, how are the stats and predictions derived?
- Some uses:
- Returns from investing in 1 more year of school
- 2000 Florida election
- Macroeconomic indicators
- Production function estimates

Takeaways

- Econometrics is a doing subject!
- It is an art that must be learned through practice - working out problems algebraically, using economic data, building models using computer software
- No one exact way to present a statistical argument
- Course objective: providing you with knowledge of econometrics in theory and application
- Vocational uses
- consultancy
- business planning
- politics or public policy
- lawyers, circuit court judge, Supreme Court judge

Returns to Education

- Examining relationship between years of education and earnings using Gary S. Becker’s 1964 theory on human capital
- Comparing the cost and future returns of an additional year of schooling
- Future earnings are function of schooling given by:
W=f (s) where s = given # years of schooling

- But there’s a simultaneity problem: do you earn more because you have more schooling or do you pursue more schooling to earn higher wages?

- Future earnings are function of schooling given by:

Returns to Education (2)

- Test the relationship using cross-section data from Current Population Surveys (CPS) for CA males in 1979 and 1995
- You can use the 1995 data to graph gross weekly earnings vs. years of schooling, but it’s impossible to see any relationships between earnings and years of schooling
- The same goes for the 1979 data - it’s a mess!
- To highlight an array in EXCEL, hold CTRL+SHIFT and press the down arrow

Returns to Education (3)

- Use conditional means to get a better approximation of the earnings and education relationship
- Conditional mean: the mean value of a variable Y given the value of another variable X
- General formula:
- In our case:
Wi= gross weekly earnings

S = years of schooling

Returns to Education (4)

- Using conditional means, you can compare the mean gross weekly earnings associated with different years of schooling - the graph is less messy
- There may be problems with our analysis !
- definitions of schooling changed
- boundary set for top coding changed: in 1979, it was $999. In 1995 it was $1923
- Macro and microeconomic factors

Chasing Butterflies

- What happened in Palm Beach, Florida during the 2000 election?
- Can we test the assertion that the butterfly ballot confused voters and caused them to accidentally vote for Buchanan rather than Gore?
- If Palm Beach County hadn’t used the butterfly ballot, can we show that Gore would have won Florida?
- The course website has Excel datasets of voting outcomes in Broward County, Palm Beach County, and Florida.

Chasing Butterflies (2)

- Broward County is similar to Palm Beach in size and demographics, but the butterfly ballot was unique to Palm Beach
- Graphing the number of votes for Buchanan against those for Gore in Broward County, we see that he received less than 10 votes in any of the voting precincts
- Looking at the same graph for Palm Beach, we see that Buchanan received many more votes there than he did in Broward County.

Chasing Butterflies (3)

- We can also look at the number of votes for a party vs. the number of registered voters for that party
- We see a similar upward trend for Democrats and Republicans
- However, for the Reform voters Palm Beach is an extreme outlier - for the other 66 counties, there were less than 1,000 Reform votes cast. Palm Beach County had 3,407 Reform votes cast!

Chasing Butterflies (4)

- You can use a confidence interval to test whether the Palm Beach observation is statistically different from the others
- Regress the number of Reform votes on the number of registered Reform voters by county, not including Palm Beach
- We find the coefficients are highly statistically significant

- 95% confidence interval means that there is a 5% chance that an observation will lay outside that interval by error. Notice that Palm Beach doesn’t lie in that interval.
- What degree of confidence do we need to include Palm Beach in the confidence interval?

Wrap up

- An overview of what’s to come
- An introduction to economic data and the idea of empirical relationships between two measured variables.
- Example: years of education and gross earnings

- Problems inherent in using economic data to test empirical relationships
- Conditional mean function
- Examining differences in data relationships
- Other forms of data: time-series and its relation to cross-section data