ECON 306 Homework 6 Creighton Mitchell Don t lose points read these instructions carefully Carefully answer each of the questions below You need to show your work not just the final answer Please make sure your work is legible each problem and step are properly numbered lettered in order You can write or type your answers for the questions Please put your name and PSU ID number at the top of the 1st page You may use as many sheets of paper as you need If you did parts by hand o Scan your entire document including the parts you typed and the parts done by hand o Save the file on your computer PDF is the only acceptable format o Merge the separate PDFs into one file using a service such as PDFMerge Failure to submit a single file will result in points being deducted o Upload it to the CANVAS dropbox for this homework assignment If you typed everything o Save the file on your computer PDF is the only acceptable format and then upload it to the CANVAS dropbox for this homework assignment o Be sure your assignment is all on one file Failure to submit a single file will result in points being deducted Pages must be scanned in proper order There are three problems in this homework Be aware that this assignment is relatively long It is also gets a higher weight in the course grade but you have 50 more time to do it than the other HWs Problems 1 and 2 should be submited in the standard format we ve used many times The first pages should contain your answers to all the questions along with showing any key algebraic equations or explanations you need to use along the way After that include a printout of the output from the regressions you executed in support of your answers Highlight any numbers in this output that you used in the first section You are encouraged to save paper here you may print this section with a small font double sided and or with 2 up format Last include a copy of the DO file that contains the commands you asked STATA to execute Be sure you organize these in a way that will be clear to the reader Problem 3 will be presented in a slightly different more polished style Please refer to that specific problem for details Problem 1 50 points total The file Divorce dta contains a four period panel data set including various socioeconomic factors for all 50 US states plus the District of Columbia The panels were taken in 1965 1975 1985 1995 The variables are divorce number of divorces and annulments per state per one thousand population birth number of live births per state per one thousand population marriage number of marriages per state per one thousand population unemploy total unemployment rate as a percentage of the total work force crime total of criminal offenses known to police per one hundred thousand population AFDC average monthly AFDC payments per family AFDC is commonly known as Welfare an income support payment by the government to certain low income groups particularly unmarried women with children a Tell STATA this is a panel data set with panels defined by entities state across periods time The Part 1 command for this is xtset state time a FINISHED b Divorce will be our dependent variable throughout Hypothesize the sign of the coefficients or zero that each of the independent variables in the dataset will have on divorce rates Briefly provide an explanation of your thinking Birth Marriage Unemployment Crime Negative I think that people who increasingly divorce would then have less births Positive Given more people are marrying that would give the propensity to divorce a higher probable incidence Positive As people become more employed they are then around each other more which as we can know is a major issue in marital dynamics Positive an increase in crime would great an overall friction in a community otherwise AFDC causing unhappiness Negative If somebody is accepting welfare it isn t necessarily a choice they want to make or say yes to in aggregate of course c Run a regression of divorce on birth marriage unemployment crime afdc using the entire pooled dataset I ll call this the na ve regression Report the coefficients and their p values Which if any of the variables have a sign different from what you hypothesized Birth Coeff 0 06586 P Value 0 095 Marriage Coeff 0 08420 P Value 0 000 Unemployment Coeff 0 21153 P Value 0 001 Crime AFDC Coeff 0 02067 P Value 0 000 Coeff 0 0008961 P Value 0 702 It seems that my hypotheses worked well given my regression coefficients which I am pleased with I find it interesting the differing strengths of the coefficients and what that may tell me or us about divorce rates Part 2 a Run a fixed effects regression using dummy variables for each state Use the same variables as part 1c The command for this is regress variables i state Report your coefficients and p values for all variables EXCEPT the state dummies Are there any substantial changes in the fixed effect regression vs the na ve pooled regression Birth Coeff 256131 P Value 0 000 Marriage Coeff 0 064883 P Value 0 079 Unemployment Coeff 0 006233 P Value 0 880 Coeff 0 025173 P Value 0 000 Coeff 0 000713 P Value 0 001 Crime AFDC In my regression I noticed that all of my variables increased in the direction that they originally were headed Negative variables got more negative where positive variables got more positive I noticed a substantial change in the P values regression over regression There was a change in the variables that are statistically significant I am not sure quite yet what this may mean but given a fixed effect regression and what that means I assume that over time the impact changes for a few of the variables b All else equal what is the difference in the divorce rate for Mississipi vs Oregon You ll have to open the data to see how these two states are distinguished a Mississippi State label 34 Oregon State label 48 i 1 396179 468246 0 927933 c If AFDC payments increase by 200 what is the predicted increase in the divorce rate a Given from the regression AFDC coefficient 002364 i 0 002364 200 0 4728 Part 3 a Use the built in fixed effects regression command xtreg variables fe robust Note that the coefficients resulting from this are identical to part 2a Don t forget the fe part or you won t get a fixed effects regression b Add to the regression of 3a a series of dummy variables to account for the time period That is estimate xtreg variables i time fe robust This essentially adds fixed effects terms for time in addition to the state specific fixed effects