Empirical Relationships

1. Empirical Relationships Lecture 1

2. Today’s Plan • Syllabus & housekeeping issues • Course overview • What is econometrics? • Two econometric examples

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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?

9. 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

10. 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

11. 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

12. 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.

13. 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.

14. 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!

15. 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?

16. 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