Lesson 1 Analysis of Economic Data is difficult but intuitive Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-1
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-1 Lesson 1: Analysis of Economic Data is difficult but intuitive
Outline Capture-Recapture experiment Estimator Simulations what is Statistics? Sampling How to estimate unemployment rate? Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-2
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-2 Outline Capture-Recapture experiment Estimator Simulations What is Statistics? Sampling How to estimate unemployment rate?
Capture/Re-capture Goali 1. Illustrate that how to estimate the population size when the cost of counting all individuals is prohibitive 2. Illustrate how intuitive statistics could be. statistics need not be completely deep, murky and mysterious. Our common sense can help us to negotiate our way through the course Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-3
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-3 Capture/Re-capture Goal: 1. Illustrate that how to estimate the population size when the cost of counting all individuals is prohibitive. 2. Illustrate how intuitive statistics could be. Statistics need not be completely deep, murky, and mysterious. Our common sense can help us to negotiate our way through the course
Counting the stones We are interested in knowing the number of black stones in the box a We only need to do to obtain a reasonable estimate of stones in the box-allowing for errors of counting or estimation Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-4
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-4 Counting the stones ◼ We are interested in knowing the number of black stones in the box. ◼ We only need to do to obtain a reasonable estimate of stones in the box – allowing for errors of counting or estimation
Two examples Example #1: The box contains only a small number of stones Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-5
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-5 Two examples ◼ Example #1: The box contains only a small number of stones
Two examples Example #2: The box contains a lot of stones that will take days to count Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-6
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-6 Two examples ◼ Example #2: The box contains a lot of stones that will take days to count
History and examples of capture / recapture method a Capture-recapture methods were originally developed in the wildlife biology to monitor the census of bird, fish, and insect populations(counting all individuals is prohibitive) Recently, these methods have been utilized considerably in the areas of disease and event monitoring ahttp://www.pittedu/yuc2/cr/history.htm Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-7
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-7 History and examples of capture / recapture method ◼ Capture-recapture methods were originally developed in the wildlife biology to monitor the census of bird, fish, and insect populations (counting all individuals is prohibitive). Recently, these methods have been utilized considerably in the areas of disease and event monitoring. ◼ http://www.pitt.edu/~yuc2/cr/history.htm
The fish example Estimating the number n of fish in a lake or pond. 1. C fish is caught, tagged, and returned to the lake. 2. Later on, R fish are caught and checked for tags. Say T of them have tags. 3. The numbers c r and t are used to estimate the fish population. Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-8
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-8 The fish example ◼ Estimating the number (N) of fish in a lake or pond. 1. C fish is caught, tagged, and returned to the lake. 2. Later on, R fish are caught and checked for tags. Say T of them have tags. 3. The numbers C, R, and T are used to estimate the fish population
Stones in a box The objective is to estimate the number n)of fish (represented by black stones)in a pond. Capture one handful of fish(black stones). Count them and call it C. Mark the fish b out replacing the black stones with red stones. them back into the pond a Capture another handful of fish(stones). Count the total number of fish or stones (r)and the number of marked fish or white stones D) Based on this information, How to obtain a reasonable estimate of the number of fish in the pond or stones in the box? Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-9
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-9 Stones in a box ◼ The objective is to estimate the number (N) of fish (represented by black stones) in a pond. ◼ Capture one handful of fish (black stones). Count them and call it C. Mark the fish by replacing the black stones with red stones. Put them back into the pond. ◼ Capture another handful of fish (stones). Count the total number of fish or stones (R) and the number of marked fish or white stones (T). ◼ Based on this information, ◼ How to obtain a reasonable estimate of the number of fish in the pond or stones in the box?
Stones in a box ■ We know that c/NaT/R Hence a simple estimate is N=CR/T C= the number of fish or stones captured in the first round R= the total number of fish or stones captured in the second round T= the number of marked fish or white stones captured in the second round Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-10
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-10 Stones in a box ◼ We know that C/N ≈ T/R ◼ Hence, a simple estimate is N=CR/T ◼ C= the number of fish or stones captured in the first round. ◼ R= the total number of fish or stones captured in the second round. ◼ T= the number of marked fish or white stones captured in the second round
