Final project - Economics
Build a prediction/fitted model to predict total wealth (tw) in US dollars
● Write up a paper, up to 20 pages (not including the code), 11 size font, and 1.5 spacing ○ Introduction ■ Briefly state the objectives of the study ○ Statistical analyses ■ Describe how you apply the tools you have learned from this course to perform the prediction task ■ You should try different methods and compare their prediction performance and interpretability ○ Conclusions ■ Summarize what you have discovered from this project ■ (Optional) Discuss caveats to the conclusions drawn from your analyses ● Bonus points o We kept 20\% of the sample on which we are going to run your proposed model and method. We will rank the students by accuracy of the prediction on that 20\% of the sample.Contents
1 Basic Commands 2
2 Working with a Data Set 3
3 Basic Linear Regression 4
4 Ridge Regression 4
5 LASSO 5
6 Cross Validation: Ridge vs Lasso 5
7 Forward and backward step wise selection 5
8 Cross Validation: Ridge vs LASSO vs Stepwise 6
9 Polynomials 7
10 Splines 8
11 Natural Cubic Spline 9
12 Generalized Additive Models 9
13 Saving Predictions 9
1
1 Basic Commands
# List of basic commands from the discussion section.
## Clears global enviroment
rm(list = ls(all.names = TRUE))
## Define a vector
my_first_vector <- c(1,2,3)
## Define a vector with repeated elements
my_second_vector <- rep(1, 10)
## Combine the two vectors
my_third_vector <- c(my_second_vector, my_first_vector)
## Square the vector
print(my_third_vector**2)
## [1] 1 1 1 1 1 1 1 1 1 1 1 4 9
## Define a matrix
A <- matrix(c(1:9), nrow = 3, ncol = 3)
B <- matrix(c(1:6), nrow = 3, ncol = 3 )
## Transpose of a matrix
B_t <- t(B)
## Matrix multiplication
A\%*\%B #Note that the we need to use \%*\%
## [,1] [,2] [,3]
## [1,] 30 66 30
## [2,] 36 81 36
## [3,] 42 96 42
A*B #Component wise multiplication: yields different results
## [,1] [,2] [,3]
## [1,] 1 16 7
## [2,] 4 25 16
## [3,] 9 36 27
## Fill a vector with missing values
C <- rep(NA, 10) #Useful for loops. Here you will store the results.
## Fill a matrix with missing values
D <- matrix(NA, nrow = 2, ncol = 2)
## Add columns to a matrix
cbind(A, c(10,11,12))
## [,1] [,2] [,3] [,4]
## [1,] 1 4 7 10
## [2,] 2 5 8 11
## [3,] 3 6 9 12
2
## Add rows to a matrix
rbind(A, c(10,11,12))
## [,1] [,2] [,3]
## [1,] 1 4 7
## [2,] 2 5 8
## [3,] 3 6 9
## [4,] 10 11 12
2 Working with a Data Set
## Working with a data set: once you have downloaded your data set to your computer,
#set the working directory to be the folder where you saved the downloaded data set.
## Set working directoty
setwd(/Users/julianmartineziriarte/OneDrive - UC San Diego/Econ 178/Final Project) #Set
#the working directory. Here R will look for your file
## Open a data set:
data_tr <- read.table(data.txt, header = TRUE, sep = \t, dec = .)[,-1] #Load the data
#set into R
## Add columns to a data set:
data_tr2 <- cbind(data_tr, data_tr$age**2) #Here we added age^2 to our data set.
## Inspect the data set
dim(data_tr) #dimension: number of observations and variables.
## [1] 9915 44
names(data_tr) #names of variables: this is useful to call the variables
## [1] ira a401 hval hmort hequity nifa net_nifa
## [8] tfa net_tfa tfa_he tw age inc fsize
## [15] educ db marr male twoearn dum91 e401
## [22] p401 pira nohs hs smcol col icat
## [29] ecat zhat net_n401 hown i1 i2 i3
## [36] i4 i5 i6 i7 a1 a2 a3
## [43] a4 a5
summary (data_tr$tw) #note that to work with a particular variable we
#call it data_tr$ + name of variable.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -502302 3292 25100 63817 81488 2029910
pairs(data_tr[,c(1,2,3)]) #depend“” “ira” “e401” “nifa” “inc” “hmort” “hval” “hequity” “educ” “male” “twoearn”
“nohs” “hs” “smcol” “col” “age” “fsize” “marr” “1” 5700 0 800 5766 0 0 0 14 1 0
0 0 1 0 50 1 0 “2” 0 0 217 9612 0 0 0 17 0 0 0 0 0 1 27 1 0 “3” 0 0 1400 32208 0
0 0 13 0 1 0 0 1 0 35 2 1 “4” 0 0 20 9744 0 0 0 12 0 0 0 1 0 0 53 1 1 “5” 0 0 3613
16290 0 0 0 12 0 0 0 1 0 0 56 1 0 “6” 0 0 0 11340 0 0 0 12 1 0 0 1 0 0 31 1 0 “7”
0 0 629 26175 0 0 0 13 1 1 0 0 1 0 31 5 1 “8” 14000 0 12000 71340 42000 140000
98000 14 1 1 0 0 1 0 35 2 1 “9” 0 0 2647 45351 0 0 0 12 0 1 0 1 0 0 28 2 1 “10” 0
0 100 22095 0 0 0 16 0 0 0 0 0 1 39 1 0 “11” 0 0 4030 38151 97919 135000 37081
12 1 0 0 1 0 0 31 2 0 “12” 3000 0 0 37794 0 0 0 13 0 1 0 0 1 0 60 2 1 “13” 0 0
0 16122 32500 47500 15000 13 0 1 0 0 1 0 34 3 1 “14” 0 0 34568 12675 34900
40000 5100 12 0 0 0 1 0 0 49 3 0 “15” 5800 0 30300 56913 60000 105000 45000
16 1 1 0 0 0 1 39 3 1 “16” 0 0 37100 14400 25000 50000 25000 16 0 0 0 0 0 1 37
2 0 “17” 0 0 0 18156 0 0 0 12 0 1 0 1 0 0 27 4 1 “18” 0 0 100 12501 0 0 0 12 0
0 0 1 0 0 33 2 0 “19” 0 0 3300 44460 0 0 0 14 0 1 0 0 1 0 32 4 1 “20” 0 0 2199
42738 39000 70000 31000 15 0 1 0 0 1 0 26 3 1 “21” 0 0 0 11364 0 0 0 12 0 0 0 1
0 0 31 4 1 “22” 0 0 0 7440 0 0 0 12 0 0 0 1 0 0 53 1 0 “23” 0 0 6500 54852 27000
215000 188000 12 0 1 0 1 0 0 41 5 1 “24” 0 0 1924 37062 18000 58000 40000 18 0
1 0 0 0 1 40 6 1 “25” 0 0 2000 11100 0 0 0 18 0 0 0 0 0 1 26 1 0 “26” 0 0 1520
29529 0 0 0 12 0 0 0 1 0 0 56 4 1 “27” 0 0 0 16029 33000 65000 32000 8 0 0 1 0 0
0 62 5 1 “28” 0 0 199 23850 30000 45000 15000 9 0 1 1 0 0 0 38 4 1 “29” 22071 0
11498 32205 150000 250000 100000 16 0 1 0 0 0 1 44 5 1 “30” 0 0 4999 43020
112000 150000 38000 12 0 1 0 1 0 0 38 5 1 “31” 0 0 0 8160 0 30000 30000 6 0 0 1
0 0 0 38 4 1 “32” 0 0 402 16902 0 0 0 1 0 0 1 0 0 0 29 7 1 “33” 0 0 0 12954 12000
20000 8000 12 0 0 0 1 0 0 27 5 1 “34” 0 0 250 39312 0 58000 58000 16 0 0 0 0 0 1
57 1 0 “35” 0 0 31799 39336 35000 47000 12000 16 0 0 0 0 0 1 28 3 1 “36” 0 0
18796 51981 37000 135000 98000 15 0 0 0 0 1 0 58 5 1 “37” 0 0 300 9642 0 0 0
10 1 0 1 0 0 0 64 1 0 “38” 0 0 4250 43560 79000 85000 6000 13 0 0 0 0 1 0 32 4 1
“39” 0 0 2000 26514 0 0 0 15 0 0 0 0 1 0 29 2 1 “40” 0 0 400 11877 0 0 0 12 0 0
0 1 0 0 63 3 0 “41” 7000 0 3200 35409 34000 200000 166000 6 0 1 1 0 0 0 52 2
1 “42” 0 0 5510 32940 0 0 0 12 0 0 0 1 0 0 50 3 1 “43” 0 0 0 4686 15000 50000
35000 11 0 0 1 0 0 0 54 3 0 “44” 8200 0 44000 22464 0 110000 110000 12 0 1 0 1
0 0 56 2 1 “45” 0 0 5 10338 20000 25000 5000 12 0 0 0 1 0 0 48 3 1 “46” 0 0 1200
29700 0 75000 75000 12 0 0 0 1 0 0 32 3 0 “47” 785 0 40115 70755 30000 80000
50000 17 1 1 0 0 0 1 45 2 1 “48” 0 0 395 34803 21000 32000 11000 11 0 1 1 0 0 0
37 5 1 “49” 1000 0 250 19455 0 0 0 12 0 0 0 1 0 0 37 1 0 “50” 0 0 1125 13215 0
0 0 13 0 0 0 0 1 0 27 1 0 “51” 0 0 340 29298 58000 80000 22000 15 0 1 0 0 1 0
42 4 1 “52” 2250 0 75 19440 31000 65000 34000 12 1 0 0 1 0 0 37 1 0 “53” 0 0
270 15603 15300 35000 19700 7 1 0 1 0 0 0 44 2 1 “54” 0 0 1650 24060 6ECON 178 WI21:
Final Project Guidelines
Instructor: Ying Zhu
TAs: Davide Viviano, Connor Goldstick
©Ying Zhu 2020
Overview of the data
The data is from the 1991 Survey of Income and Program Participation
(SIPP). You are provided with 7933 observations.
The sample contains households data in which the reference persons
aged 25-64 years old. At least one person is employed, and no one is
self-employed. The observation units correspond to the household
reference persons.
The data set contains a number of feature variables that you can
choose to predict total wealth. The outcome variable (total wealth) and
feature variables are described in the next slide.
Dataframe with the following variables
Variable to predict (outcome variable):
• tw: total wealth (in US $).
• Total wealth equals net financial assets, including
Individual Retirement Account (IRA) and 401(k) assets,
plus housing equity plus the value of business,
property, and motor vehicles.
Variables related to retirement (features):
• ira: individual retirement account (IRA) (in US $).
• e401: 1 if eligible for 401(k), 0 otherwise
Financial variables (features):
• nifa: non-401k financial assets (in US $).
• inc: income (in US $).
Variables related to home ownership (features):
• hmort: home mortgage (in US $).
• hval: home value (in US $).
• hequity: home value minus home mortgage.
Other covariates (features):
• educ: education (in years).
• male: 1 if male, 0 otherwise.
• twoearn: 1 if two earners in the household, 0 otherwise.
• nohs, hs, smcol, col: dummies for education: no high-
school, high-school, some college, college.
• age: age.
• fsize: family size.
• marr: 1 if married, 0 otherwise.
What is 401k and IRA?
• Both 401k and IRA are tax deferred savings options which aims to increase
individual saving for retirement
• The 401(k) plan:
• a company-sponsored retirement account where employees can contribute
• employers can match a certain \% of an employee’s contribution
• 401(k) plans are offered by employers -- only employees in companies
offering such plans can participate
• The feature variable e401 contains information on the eligibility
• IRA accounts:
• Individuals can participate
• No employer matching
• The feature variable ira contains IRA account (in US $)
Reference: https://www.investopedia.com/ask/answers/12/401k.asp
Your tasks
● Build a prediction/fitted model to predict total wealth (tw) in US dollars
● Write up a paper, up to 20 pages (not including the code), 11 size font, and 1.5 spacing
○ Introduction
■ Briefly state the objectives of the study
○ Statistical analyses
■ Describe how you apply the tools you have learned from this course to perform the prediction task
■ You should try different methods and compare their prediction performance and interpretability
○ Conclusions
■ Summarize what you have discovered from this project
■ (Optional) Discuss caveats to the conclusions drawn from you“” “tw” “ira” “e401” “nifa” “inc” “hmort” “hval” “hequity” “educ” “male”
“twoearn” “nohs” “hs” “smcol” “col” “age” “fsize” “marr” “1” 53550 0 0 100
28146 60150 69000 8850 12 0 0 0 1 0 0 31 5 1 “2” 124635 0 0 61010 32634 20000
78000 58000 16 0 0 0 0 0 1 52 5 0 “3” 192949 1800 0 7549 52206 15900 200000
184100 11 1 1 1 0 0 0 50 3 1 “4” -513 0 0 2487 45252 0 0 0 15 0 1 0 0 1 0 28 4 1
“5” 212087 0 0 10625 33126 90000 300000 210000 12 0 0 0 1 0 0 42 3 0 “6” 24400
0 0 9000 76860 99600 120000 20400 15 0 1 0 0 1 0 49 6 1 “7” 33299 0 0 1099
57477 63000 89000 26000 17 0 1 0 0 0 1 40 4 1 “8” 2500 0 0 1700 14637 0 0 0 14
0 0 0 0 1 0 58 1 0 “9” 0 0 0 0 6573 0 0 0 12 0 0 0 1 0 0 29 4 0 “10” 52625 8000 0
16900 43239 68000 83000 15000 12 1 0 0 1 0 0 45 1 0 “11” -675 0 0 100 40323
0 0 0 12 1 1 0 1 0 0 25 3 1 “12” 8100 0 0 0 30000 0 0 0 14 0 0 0 0 1 0 30 2 1
“13” 59519 34000 0 1400 85086 235 12000 11765 12 1 1 0 1 0 0 42 4 1 “14” 64800
2300 0 60000 63525 0 0 0 18 0 0 0 0 0 1 35 1 0 “15” 15112 0 0 612 31896 0 0 0
12 0 0 0 1 0 0 41 5 1 “16” 123098 0 0 3098 74589 0 120000 120000 16 0 0 0 0 0 1
62 3 1 “17” 43258 0 0 298 38148 0 0 0 11 1 0 1 0 0 0 45 1 0 “18” 660413 50250 0
310163 71535 0 300000 300000 18 0 0 0 0 0 1 63 2 1 “19” 35999 0 0 499 21678 0
35000 35000 13 0 0 0 0 1 0 56 1 0 “20” 3700 0 0 500 27360 17000 12000 -5000 13
0 0 0 0 1 0 52 4 1 “21” 72300 0 0 1000 29724 35000 100000 65000 12 0 1 0 1 0 0
58 3 1 “22” 346394 0 0 53698 42084 52000 250000 198000 16 1 0 0 0 0 1 42 1 0
“23” 1000 0 0 1300 35100 0 0 0 12 0 0 0 1 0 0 61 5 0 “24” 7420 0 0 670 15051
0 10000 10000 10 0 0 1 0 0 0 62 2 1 “25” 77570 0 0 670 14328 0 80000 80000
12 0 1 0 1 0 0 48 3 1 “26” 116515 2115 0 14100 68214 83000 83000 0 14 0 0 0 0
1 0 28 3 1 “27” 78550 2000 0 17100 30030 57000 110000 53000 12 1 0 0 1 0 0
51 3 0 “28” 74400 0 0 0 9315 0 75000 75000 14 0 0 0 0 1 0 45 2 0 “29” 63399
8000 0 2399 47934 95000 150000 55000 17 0 1 0 0 0 1 42 4 1 “30” 275240 0 0
40 27168 73000 300000 227000 7 0 0 1 0 0 0 43 6 1 “31” 25380 0 0 8311 41610
31000 50000 19000 14 0 1 0 0 1 0 28 4 1 “32” 2125 0 0 799 31848 45000 45000 0
15 0 1 0 0 1 0 39 4 1 “33” 125947 14000 0 7747 38949 0 56000 56000 12 0 0 0 1 0
0 58 2 1 “34” 5249 0 0 5249 31098 0 0 0 16 0 0 0 0 0 1 30 1 0 “35” -1501 0 0
3199 53700 0 0 0 16 1 1 0 0 0 1 32 4 1 “36” 64219 0 0 1069 37317 62000 80000
18000 16 1 0 0 0 0 1 31 2 0 “37” 3253 0 0 1150 23748 0 0 0 16 1 0 0 0 0 1 31 1 0
“38” 19250 250 0 1500 31470 50000 60000 10000 13 0 1 0 0 1 0 31 2 1 “39” 67450
0 0 35300 42750 86000 112000 26000 12 0 1 0 1 0 0 31 2 1 “40” 3199 0 0 1399
32976 0 0 0 18 0 0 0 0 0 1 40 1 0 “41” 17300 0 0 500 40473 74000 95000 21000
12 0 1 0 1 0 0 31 4 1 “42” 500 0 0 0 4590 0 0 0 12 0 0 0 1 0 0 45 1 0 “43” 3000 0
0 3000 34764 0 0 0 10 1 1 1 0 0 0 63 2 1 “44” 0 0 0 0 25200 0 0 0 16 1 0 0 0 0 1
55 1 0 “45” 130000 0 0 57000 58878 130000 195000 65000 1 0 0 1 0 0 0 29 3 1
“46” 3100 0 0 100 14496 28000 35000 7000 15 0 0 0 0 1 0 53 2 0 “47” 4800 0 0 0
17280 0 0 0 12 0 0 0 1 0 0 46 6 0 “48” 1811
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