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About 833 results. 1294 free access solutions
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| m78079 | Suppose that average worker productivity at manufacturing firms (avgprod) depends on two factors, average hours of training (avgtrain) and average worker ability (avgabil):
avgprod = (0 + (1 avgtrain + (2 avgabil + u.
Assume that this equation satisfies the Gauss-Markov assumptions. If grants have been given to firms whose workers have less than average ability, so that avgtrain and avgabil of avgprod on avgtrain? |
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| m78091 | Suppose that, for a given state in the United States, you wish to use annual time series data to estimate the effect of the state-level minimum wage on the employment of those 18 to 25 years old (EMP). A simple model is
where MINt is the minimum wage, in real dollars, POPt is the population from 18 to 25 years old, GSP, is gross state product, and GDPt is U.S. gross domestic product. The g prefix indicates the growth rate from year t - 1 to year r, which would typically be approximated by the difference in the logs.
(i) If we are worried that the state chooses its minimum wage partly based on unobserved (to us) factors that affect youth employment, what is the problem with OLS estimation?
(ii) Let USMIN, be the U.S. minimum wage, which is also measured in real terms. Do you think gUSMINt is uncorrelated with up
(iii) By law, any state s minimum wage must be at least as large as the U.S. minimum. Explain why this makes gUSMlNt a potential IV candidate for gMINt, |
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| m78092 | Suppose that, for one semester, you can collect the following data on a random sample of college juniors and seniors for each class taken: a standardized final exam score, percentage of lectures attended, a dummy variable indicating whether the class is within the student s major, cumulative grade point average prior to the start of the semester, and SAT score.
(i) Why would you classify this data set as a cluster sample? Roughly, how many observations would you expect for the typical student?
(ii) Write a model, similar to equation (14.12), that explains final exam performance in terms of attendance and the other characteristics. Use s to subscript student and c to subscript class. Which variables do not change within a student?
(iii) If you pool all of the data and use OLS, what are you assuming about unobserved student characteristics that affect performance and attendance rate? What roles do SAT score and prior GPA play in this regard?
(iv) If you think SAT score and prior GPA do not adequately capture student ability, how would you estimate the effect of attendance on final exam performance? |
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| m78134 | Suppose that the equation
yt = a + (t + (1xt1 + ...+(kxtk + u,
satisfies the sequential exogeneity assumption in equation (11.40).
(i) Suppose you difference the equation to obtain
(yt = ( + (1 (xt1 + ... + (k (xtk + (ut.
How come applying OLS on the differenced equation does not generally result in consistent estimators of the (j?
(ii) What assumption on the explanatory variables in the original equation would ensure that OLS on the differences consistently estimates the (j?
(iii) Let zt1,...., ztk be a set of explanatory variables dated contemporaneously with yt. If we specify the static regression model yt = (0 + (1zt1 + ... + (kztk + ut, describe what we need to assume for xt = z, to be sequentially exogenous. Do you think the assumptions are likely to hold in economic applications? |
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| m78139 | Suppose that the idiosyncratic errors in (14.4), {uit: t = 1, 2,....,T}, are serially uncorrelated with constant variance,σit2. Show that the correlation between adjacent differences, Δuit and ΔuI,t+1, is -.5. Therefore, under the ideal FE assumptions, first differencing induces negative serial correlation of a known value. |
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| m78141 | Suppose that the model
pctstck = (0 + (1 funds + (2 risktol + u |
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| m78146 | Suppose that the population model determining y is
y = (0 + (1x1 + (2x2 + (3x3 + u, |
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| m78167 | Suppose that we want to estimate the effect of several variables on annual saving and that we have a panel data set on individuals collected on January 31, 1990, and January 31, 1992. If we include a year dummy for 1992 and use first differencing, can we also include age in the original model? Explain. |
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| m78169 | Suppose that you are asked to conduct a study to determine whether smaller class sizes lead to improved student performance of fourth graders.
(i) If you could conduct any experiment you want, what would you do? Be specific.
(ii) More realistically, suppose you can collect observational data on several thousand fourth graders in a given state. You can obtain the size of their fourth-grade class and a standardized test score taken at the end of fourth grade. Why might you expect a negative correlation between class size and test score?
(iii) Would a negative correlation necessarily show that smaller class sizes cause better performance? Explain. |
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| m78171 | Suppose that you are interested in estimating the ceteris paribus relationship between y and xi. For this purpose, you can collect data on two control variables, x2 and x3 (For concreteness, you might think of y as final exam score, x1 as class attendance, x2 as GPA up through the previous semester, and x3 as SAT or ACT score.) Let / be the simple regression estimate from y on x1 and let be the multiple regression estimate from y on x1, x2, x3.
(i) If is highly correlated with x2 and x3 in the sample, and x2 and x3 have large partial effects on y would you expect and / and to be similar or very different? Explain.
(ii) If x1 is almost uncorrelated with x2 and x3. But x2 and x3 are highly correlated, will / and /tend to be similar or very different? Explain.
(iii) If x1 is highly correlated with x2 and x3, and x2 and x3 have small partial effects on y, would you expect se(/) or se(/) to be smaller? Explain.
(iv) If x1 is almost uncorrelated with x2 and x3, x2 and x3 have large partial effects on y, and x2 and x3 are highly correlated, would you expect se(/) or se(/) to be smaller? Explain. |
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| m78175 | Suppose that you wish to estimate the effect of class attendance on student performance, as in Example 6.3. A basic model is
Stndfnl = β0 + β1 atndrte + β2 priGPA + β3 ACT + u,
where the variables are defined as in Chapter 6.
(i) Let dist be the distance from the students living quarters to the lecture hall. Do you think dist is uncorrelated with u?
(ii) Assuming that dist and u are uncorrelated, what other assumption must dist satisfy to be a valid IV for atndrte?
(iii) Suppose, as in equation (6.18), we add the interaction term priGPA-atndrte:
stndnl = β0 + β1 atn.drte + β2 priGPA + β3ACT + β4 priGPA∙atndrte + u.
If atndrte is correlated with u, then, in general so is priGPA∙atndrte. What might be a good IV for priGPA∙atndrte? |
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| m78176 | Suppose that {yt} and {zt} are 1(1) series, but yt - βzt is 1(0) for some β ≠ 0. Show that for any δ ≠ β, yt - δzt must be 1(1). |
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| m78177 | Suppose that yt follows the model
yt = α + δ1 zt-1 + ut
u, = put-1 + et
E(et | It-1) = 0,
where It-1 contains y and z dated at t - 1 and earlier.
(i) Show that E(yt+1| It) = (1 - p) α + pyt + δt Zt - p δl Zt-1
(ii) Suppose that you use n observations to estimate α, δ1, and p. Write the equation for forecasting yn+1.
(iii) Explain why the model with one lag of z and AR(1) serial correlation is a special case of the model
yt = α0+ pyt-1 + γ1 zt-1 + γ2 zt-2 + et.
(iv) What does part (iii) suggest about using models with AR(1) serial correlation for forecasting? |
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| m78213 | Suppose the process [(xt, yt): t = 0, 1, 2, ...} satisfies the equations
yt = βxt + ut
and
Δxt = γΔxt-1, + vt,
where E(ut | It-1) = E(vt | It-1) = 0, It-1, contains information on x and y dated at time t - 1 and earlier, β ≠ 0, and |γ| < 1 [so that xt, and therefore yt, is I(1)]. Show that these two equations imply an error correction model of the form
Δyt = γ1 Δxt-1 + δ(yt-1 - βxt-1) + et,
where y, = βγ, δ = - 1, and et = ut + Bvt. |
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| m78238 | Suppose we want to estimate the effects of alcohol consumption (alcohol) on college grade point average (colGPA). In addition to collecting information on grade point averages and alcohol usage, we also obtain attendance information (say, percentage of lectures attended, called attend). A standardized test score (say, SAT) and high school GPA (hsGPA) are also available.
(i) Should we include attend along with alcohol as explanatory variables in a multiple regression model? (Think about how you would interpret (alcohol-)
(ii) Should SAT and hsGPA be included as explanatory variables? Explain. |
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| m78248 | Suppose you are hired by a university to study the factors that determine whether students admitted to the university actually come to the university. You are given a large random sample of students who were admitted the previous year. You have information on whether each student chose to attend, high school performance, family income, financial aid offered, race, and geographic variables. Someone says to you, "Any analysis of that data will lead to biased results because it is not a random sample of all college applicants, but only those who apply to this university." What do you think of this criticism? |
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| m78249 | Suppose you are interested in estimating the effect of hours spent in an SAT preparation course (hours) on total SAT score (sat). The population is all college-bound high school seniors for a particular year.
(i) Suppose you are given a grant to run a controlled experiment. Explain how you would structure the experiment in order to estimate the causal effect of hours on sat.
(ii) Consider the more realistic case where students choose how much time to spend in a preparation course, and you can only randomly sample sat and hours from the population. Write the population model as
sat = (0 + (1 hours = u
where, as usual in a model with an intercept, we can assume E(u) = 0. List at least two factors contained in u. Are these likely to have positive or negative correlation with hours?
(iii) In the equation from part (ii), what should be the sign of (1 if the preparation course is effective?
(iv) In the equation from part (ii), what is the interpretation of (0? |
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| m78255 | Suppose you collect data from a survey on wages, education, experience, and gender. In addition, you ask for information about marijuana usage. The original question is: "On how many separate occasions last month did you smoke marijuana?"
(i) Write an equation that would allow you to estimate the effects of marijuana usage on wage, while controlling for other factors. You should be able to make statements such as, "Smoking marijuana five more times per month is estimated to change wage by x%."
(ii) Write a model that would allow you to test whether drug usage has different effects on wages for men and women. How would you test that there are no differences in the effects of drug usage for men and women?
(iii) Suppose you think it is better to measure marijuana usage by putting people into one of four categories: nonuser, light user (1 to 5 times per month), moderate user (6 to 10 times per month), and heavy user (more than 10 times per month). Now, write a model that allows you to estimate the effects of marijuana usage on wage.
(iv) Using the model in part (iii), explain in detail how to test the null hypothesis that marijuana usage has no effect on wage. Be very specific and include a careful listing of degrees of freedom.
(v) What are some potential problems with drawing causal inference using the survey data that you collected? |
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| m78256 | Suppose you have quarterly data on new housing starts, interest rates, and real per capita income. Specify a model for housing starts that accounts for possible trends and seasonality in the variables? |
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| m78257 | Suppose you have quarterly data on new housing starts, interest rates, and real per capita income. Specify a model for housing starts that accounts for possible trends and seasonality in the variables? |
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