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Unemployment big concem due t0 people baing Iald 0ff due l0 the Coronavirus pandemic, It Is estlmated that 30% of all householde have been directly affected. Suppos...

Question

Unemployment big concem due t0 people baing Iald 0ff due l0 the Coronavirus pandemic, It Is estlmated that 30% of all householde have been directly affected. Supposa randomly sample 20 households and detarmine tha numbor of households that have been dlrectly affected ,Identity Ihe type of dlstrlbulion that can be used to analyze Ihls data. Make sure t0 Identlly any parameters that would be needed In thls Identlficallon (ex N, P, H; o).What Is the probabillly Ihat more than 6 of these 20 sampled

Unemployment big concem due t0 people baing Iald 0ff due l0 the Coronavirus pandemic, It Is estlmated that 30% of all householde have been directly affected. Supposa randomly sample 20 households and detarmine tha numbor of households that have been dlrectly affected , Identity Ihe type of dlstrlbulion that can be used to analyze Ihls data. Make sure t0 Identlly any parameters that would be needed In thls Identlficallon (ex N, P, H; o). What Is the probabillly Ihat more than 6 of these 20 sampled households has been dlrectly affected? Show work lo get full credlit What Is the probabillty that more (han but no moro than 9 of the sampled household has been direcily affected? Show work t0 get Iull credit:



Answers

In Example $13.8,$ we used the unemployment claims data from Papke $(1994)$ to estimate the effect of enterprise zones on unemployment claims. Papke also uses a model that allows each city to have its
own time trend:
$\log \left(u c l m s_{i t}\right)=a_{i}+c_{i} t+\beta_{1} e z_{i t}+u_{i t}$
where $a_{i}$ and $c_{i}$ are both unobserved effects. This allows for more heterogeneity across cities.
(i) Show that, when the previous equation is first differenced, we obtain
$\Delta \log \left(u c l m s_{i t}\right)=c_{i}+\beta_{1} \Delta e z_{i t}+\Delta u_{i t}, t=2, \ldots, T$
Notice that the differenced equation contains a fixed effect, $c_{i}$
(ii) Estimate the differenced equation by fixed effects. What is the estimate of $\beta_{1} ?$ Is it very
different from the estimate obtained in Example 13.8$?$ Is the effect of enterprise zones still
statistically significant?
(iii) Add a full set of year dummies to the estimation in part (ii). What happens to the estimate
of $\beta_{1} ?$

In this problem, the number of unemployed will cost millions is given. The first question asked is finding being number unemployed a millions to find that first with fine diese some Isha Thanks that this be some off all the number off unemployed broke us the number of unemployed workers they rented noted by eggs. So Summation X is equal to 82.65 The former lover me experienced summation X divided by end. So this is it will do 82.65 Do you read it? But the information given is off 10 years. So what n is then? So these equal to 8.265 and it this a millions 8.265 millions now for that is asked which years had employment unemployment No zest to be mean from dinky one day that we can see that the years doesn't two and 2004 had unemployment no zest to demean the years 2002 Add to 1000 full Now in the next caution. It is for us to find this time that aviation for drink even Decca 25 day. But we've been fined summation X quipped that this some off all the X squared values summation it's good is equal to 7. 32 buying buttons. You go 97 The form level Standard division is another move. Submission X squared minus and multiplying by X Birth square divided by end minus one. So mission excluded 72 point Once you don't 97 minus our anything will do then. So big day. My people like by eggs that we about to be 8.265 We have to take its square that this 8.265 square be ready by end minus one over any Stine so n minus one is none. Therefore, our standard deviation is equal to 2.334 Now, in the next caution This us How many off these years is unemployment? The din. But stand the aviation off the me So on. So that first we will find exact minus s and expect. Plus s. It's very minus s will be eight point no. 65 minus our X is 2.334 So expert minus s is it will do 5.931 Thank you. Expect Plessis is it point 465 Yes, 2.334 So exactness s is equal to 10 point. Find 99 as we can usually see from the give ended up that it off the 10 years the number of unemployed Brokaw's is between 51 91 and 10.599 So in a year's the number off I have probable cause is within one standard deviation off. You mean now? In the next caution, it is asked in harmony off these years is unemployment bidding three standard deviations off the mean one so that we find X behind us three years and expect plus to be Yes, it's about minus two years is it will do but 20.263 and expect last two years is it will do 15.267 because in the given data, that all thank yours for in this range that this between 1.263 and 15.267 So in 10 years, the number of unemployed workers is bidding three standard deviations off the mean

Part one. The coefficient on their attempt trend is minus point 0139 and it's standard error is 1390.12 So monthly unemployment claims is a dependent variable and it enters Theis equation in lock. So the change of this kind of variable should be interpreted as percent a percentage change. The size of the Tan Trinh implies that monthly unemployment claims falls 1.4% almost 1.4% per month on average. Yeah, and given the result for the coefficient of the temp, Trine, we can calculate the T statistic. The T strut is with a head divided by its standard error. And we have a very small number of send it Errol here. So we should have a fairly large T statistic. And given the value of the T statistic, you can conclude that the trend is significant. Okay, so that is the trend of unemployment claims about their seasonality. We will look at the estimation results for the monthly dummies. We will evaluate their individual significance and their joint significance. So you will look at the t the individual T statistic. You may find that six out of 11 monthly dummy. Dummy variables have a high T statistic. Yeah. Yeah. Okay. So I can write Six out of 11 dummies are highly significant for joint significance. You in run an F test and find a p value of the F statistic. You may get the P value of the F statistic as mhm going. Oh 01 So these monthly dummies are also jointly highly significant. You can conclude that there is a very strong seasonality in unemployment claims. Okay, in part to doing ad variable Easy to the regression. It's estimated coefficient is minus 0.508 The standard error is 0.146 We can interpret this result as unemployment claims are estimated to fall. Okay, because the Beta head has a minus sign, it is negative. We we need to convert. We we need to calculate very quickly. Thio, find the change in unemployment claims, so you will need to take one minus the exponential of beta hat minus 0.5 08 so e to the power of minus 0.58 and to get their percent change, you would multiply the whole bracket with 100 and what you get is unemployment claims are estimated to fall by almost 40% after Enterprises Zone designation. For part three, we must assume that around the time of enterprise zone designation, there were no other external factors that can cause a shift down in the trend of the lark of unemployment claims. Yeah, so no other factors influence unemployment claims, unemployment claims trend around the time of easy designation. Okay, we already controlled for a time, trend and seasonality, but this may not be enough.

The following video is a solution of number 57, so it's a percentage of homeowners Between the ages of 18 and 34 is 26% percentage of homeowners between 35 and 44 is 50%, and then the percentage of homeowners who are aged 55 and older or greater than 55 I guess is 88%. And it says what um Uh sample size is needed for the 18-34 year old, if the expected number is at least 20 or needs to be at least 20. And I wrote this formula down the expected, this is a binomial situation, So expect the value of X. Is in times P. So we're looking for in in this case and we know the P. Is the 0.26 and we know it needs to be at least 20 because that's what the direction says. It says for the expected value, which is n times P to be at least 20. And this is just simply solving a basic Algebra one inequality, so divided by .26 and you get in is greater than equal to 76.9. That's very important that you always always always round up. Now, even if this had been this should be obvious, it's you know, at least 77. Right? So in this case would be at least 77. That's pretty straightforward. But even if it were 76.1, let's just pretend for a second and is greater than equal to 76.1, you would still round up to 77. All right, So that's it. I know it goes against what we kind of think, but you will always always always round up instead of rounding off and that's basically what we're gonna do for this first part. That's I guess part A And then part B is this part is the same thing, but for 35-44 year olds, So in times 50 needs to be at least 20 this time. And so you just divide by 50 or multiplied by two if you want to guess. So, in is at least 40 on the nose, so you need to have at least 40 35 to 44 year olds In order to get the expected value of 20 and then the last one. So part C In times 8 8 needs to be at least 20, And then you divide by .88, so and is at least 22.7. But again, we're going to round up 2 23 So they need to be at least 23 Adults age 55 rolled. Okay, so that's part a being see pretty straightforward. Now, the next part we're asked to find the standard deviation if these are the sample sizes and the standard deviation for a binomial distribution is the square root of n times p times one minus P. So in this case for the I think we're supposed to do, yeah, we're supposed to get 18, year olds. The end remembers the 77, so we take the square to 77 Times The P. That's the .26 And then 1- people, 1 -1.74. So I didn't show that work, but I'm assuming we know it and then you plug that in the calculator and the square to 77 times 770.26 times 0.74 You should get about 3.849 So that's the standard deviation. If we actually use the sample size of 77 then part E. It's kind of the same thing, we're still using the same formula. Sometimes you'll see one minus P sq just depends on the book, but this time we're using the sample size of the 35 to 44 year olds, and remember that was 40 you can see it up there, it's 40 so 40 times 50 times 50, because that he was slightly different, right? So the percentage there was 50, And then 1 -2 would also be 50. And then you plug that in the calculator, so it's essentially the square to 10, right? So the square to 10 is three 1623. So that's the standard deviation of The 35 44 year olds.

Part one. This is the estimated equation. In first differences, we need to comment on the size sign and significance level of the main coefficient. The estimate on the change in unemployment rate the size of beta one hat is about 0.842 and this is quite large. The estimate is negative, implying that there is a trade off between unemployment and inflation. Okay, regarding statistical significance, we can calculate the T statistic. You intake 0.842 divided by 0.314 you get a T value of minus 2.68 This is quite a large number. So this variable is significant in exact it is statistically different from zero. We can also test whether these variable is whether the coefficient is statistically different from minus one. And for this hypothesis test, we will do another calculation for the T start. I mean, you would take the estimate of beta one hat minus 0.842 minus minus one. That is plus one altogether divided by its standard error, and the T value is 0.5. So we are unable to reject the knob, which means beta one is not statistically different. from minus one and with a beta one of minus one. The trade off between inflation and unemployment is almost a one, for one are to. We will compare this model with estimation Equation 11.19 and the model from part one has higher our square and it just it are square. So this model is better than the 11.19 it is so because this model can explain more variation in the difference of inflation.


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