Welcome toPMBA0608: Economics/Statistics Foundation Fall 2006 Session 4: September 6
Study • Chapters 1 through 4 of Mankiw • Chapters 1 through 3 of Mendenhall, Beaver and Beaver • Send me your questions • I will do one or all of the following • Answer you privately • Publish the answer to your question on line • Answer your question in our next class
Discuss Assignment 1 • Problem 5, Page 16 of Mankiw • $5 million is sunk cost • MC = $1 million • MB = $3 million • MB>MC should complete the project • As long as MB >MC, the answer is the same
Discuss Assignment 1 2) Problem 8, Page 17 of Mankiw • The new bill will increase the incentive for economic activity. • Efficiency may increase for two reasons • Resources are not wasted as much as before • If tax rates go down current work force will have an incentive to work harder • Equity may decline as • Current workers’ tax rate may go down • Some current welfare recipients may not be able to find jobs the pay a much as welfare.
Discuss Assignment 1 3) The discussion on the connection between the article and the economic principle should be well developed.
Discuss Assignment 1 4) Question 1.2, Page 10 of Mendenhall, Beaver and Beaver • Population of interest is the population of the measurements of the appraisals of the land by all experienced appraisers. • Population is large but it does exist, so it is not conceptual. • Populations are different • Buyers may underestimate. Sellers may over estimate…. • More than one appraisal should be used.
Discuss Assignment 1 5) Question 1.7, Page 10 of Mendenhall, Beaver and Beaver • Population of shopper opinions (in favor or opposed background music) • Not possible to examine the entire population as future shoppers are not known. • No, sample percentages will not be the same as population percentage but it will serve as an estimate as population percentage.
Back to Chapter 2 of Mankiw: Macro/micro economics • Macro = big Picture = Forest • Focuses on the aggregate markets • Micro = small picture = tree • Focuses on individual markets
The effect of tax policy on the price of gas in Ohio. The effect of tax policy on the general price level in Ohio. The effect of agricultural subsides on the income of farmers. The effect of agricultural subsidies on income tax rates in the U.S. Which of the following is a macro/micro topic?
Which of these topics will be covered in a macro/micro economics course? • The impact of the 1987 market crash on consumers’ spending. • How a higher rate of inflation alters the distribution of wealth and income. • The effect of war in Iraq on the price of oil. • The effect of the increase in the price of oil on the overall unemployment rate.
Normative/Positive Statements • Positive Statement • is descriptive • But not necessarily true • can be tested for validity • Example • Normative statement • is an opinion • can not be tested for validity • Example
Note • A normative economic statement that is not backed up by positive statement is worthless.
Chapter 2 of Mendenhall, Beaver & Beaver (Stat) • Which of the following is (are) a Variable? • Interest rates • My name • My weight • Price of gasoline • 1, 3 and 4. • Variable = characteristics that change over time or across different objects.
Which of the following is (are) experimental unit (s)? • Jackie • United States • Unemployment rate • A PMBA student • 1, 2 and 4 • Experimental unit = an individual or object on which a variable is measured.
Which of the following variables is (are) qualitative? • Gender of students in this class • Height of students in this class • Seasons • Cost of production • 1 and 3 • Qualitative variables can be categorized but not measured.
Which of the following variables is continuous? • The number of your children over time. • Your weight over time. • The year • 2 • Continuous variable can assume all of the infinitely many values corresponding to a line interval.
Can a qualitative variable be continuous? • No. • Gender • Male = 1 • Female = 2
Make sure • You know how to create a graph using Excel or any other program. • Highlight your columns that contain data and click on Chart Wizard. • You know what type of graph is more appropriate in different scenarios and why?
Histograms are used to show relative frequencies: Example Relative frequency 75% 25% 0 Number of kids 1 2 3
Do you use a bar graph or a histogram in each of the following situations? • You want to compare heights of 10 individuals in this class. • Bar • You want to compare total revenues of five different companies. • Bar • You want to compare numbers of companies that make from 0 to $10,000; from $10,000 to $20,000; from $20,000 to $30,000 and so on. • Histogram
Check out the following interactive site for creating histograms • http://www.shodor.org/interactivate/activities/histogram/?jv=1.4.1_02&jb=MSIE
The arithmetic mean • Helps us describe the sample (xbar)or the population (μ) • The sample mean, xbar is • xbar = (x1 + x2 + . . . + xn) / n . • Mean member of US households • = total population /number of households • In 2003 =2.57 • Mean household income in the US • = total income/households • In 2003 =$59,067
What is median? • 50% of observations fall below median and 50% of observations fall above median • In 2003 median income of a household in the US was $43,318 • 50% of households received less than $43,318. • 50% of households made over $43,318.
Mean /medianNote: Area under the curve is 100% • What does this tell you about income equality in the US? Relative frequency 50% of households 50% of households $43,318 = median Income household $59,067 = mean
Which nation has more poor households? • Mean income is the same Relative frequency Relative frequency $60,000 income 60,000 income Nation A Nation B
Need a measure of dispersion in order to describe our data better • Range • Maximum value – minimum value • Makes more sense for small samples
Are these two samples the same? • Weight sample 1 • Four observations: 100, 110, 170, 200 • Mean = 145 • Median = 140 • Range = 100 • Weight sample 2 • Eight observations: 100, 115, 125, 130, 150, 160, 180,200 • Mean = 145 • Median = 140 • Range= 100 • According to mean, median and range, yes.
= mean of absolute values of deviation of each observation from mean Measures of dispersion: (2) Mean Absolute Deviation (MAD) • MAD = (Σ |wi- wbar|)/n) =(45+35+25+55)/4= 40
What is MAD for Sample 2? • Weight sample 2 • 100, 115, 125, 130, 150, 160, 180,200 • Mean = 145 • MAD = 27.5 • MAD in sample 2 < MAD in sample 1 • What does this mean? • The distribution of Sample 2 is tighter
Measures of dispersion:(3) Variance • In population = Σ(wi- wbar)2/n • In sample = Σ(wi- wbar)2/n-1 • Calculate the variance in Sample 1 and Sample 2 • Variance in Sample 1 = 2300 • Variance in Sample 2 =1150 • Standard deviation is the square root of variance.
Empirical Rule • If the sample is very large population • If the relative frequency distribution is bell shaped • Then • 68% of observations fall within one standard deviation from the mean • 95% of observations fall within two standard deviation from the mean
Empirical Rule • Suppose standard deviation is 30 Rela. frequency 68% 95% 175 weight 85 115 145 205
In our example, both samples had the same mean and Sample 1 had a higher standard deviation • So, Sample 1 was more variable. • But what if two samples have different means? • How do we measure which one is more variable? • Coefficient of variation = (standard deviating/mean) * 100 • The higher the mean, the ______ the CV. • The higher the standard deviation, the _____ the CV.
Bivariate data • Sometimes we want to focus on two variables at the same time • Example 1 • Are women earning less than men for doing the same job? • One of my students wanted to answer this question • Collected a sample of area attorneys at different stages of their careers
Bivariate data • The study of earning gap Earnings Male Female Years after graduation
Bivariate data: relationship • There is economic theory suggesting that there is a negative relationship (trade off) between inflation and unemployment • Collect data on both variables
Bivariate data: relationship • Plot your points Unemployment rate 1990 1991 1993 1994 1992 • What type of relationship is there between inflation and unemployment? Inflation
Is there a measure of correlation between two variables (x and y)? • Yes? • Correlation coefficient (r) • Takes a value between -1 to +1 • If r =0 x and y are not correlated • If r = -1 x and y are perfectly and indirectly correlated • If r = +1 x and y are perfectly and directly correlated
How do we calculate r? • Formula on Page 66 of stat book • Excel calculates it automatically • Under fx type =CORREL (A2:A10;B2:B10)
Suppose you are told that your salary is at 70th percentile in the distribution of salaries in your organization. What does this mean? • 70% of other salaries in your organization are lower than your salary and 30% are higher than your salary.
Another measure of relative standing is z-score • Measures the number of standard deviations between an observation an the mean of the set. • Example • If z = 2 • Then your salary is lies 2 standard deviations above the mean • Formula on page 71 of Stat Book
Note: • Sections 2.5 and 2.13 of this Chapter are dropped.
Assignment 2 • Due: On or before September 16 • Problem 3, Page 59 of Mankiw • Problem 6. Page 60 of Mankiw • Application 2.6, Page 24 of Mendenhall, Beaver and Beaver (Use Excel or similar program. Explain why one presentation is more effective.) • Application 2.12, Page 33 of Mendenhall, Beaver and Beaver (Use Excel or similar program.) • Exercise 2.47, Page 67 of Mendenhall, Beaver and Beaver (Use Excel or similar program.) Notes: • Each question has 4 points. • Don’t hesitate to contact me.