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1. (32p) The data file income_democracy.dta contains a panel data set for 195 countries for the years 1960, 1965, … 2000.1 The data set contains an index of political freedom/democracy for each country each year, together with each country’s income and various demographic controls. (The income and demographic controls are lagged five years relative to democracy index to allow time for democracy to adjust to changes in these variables)

Variable Name

country year dem_ind log_gdppc log_pop age_1 age_2 age_3 age_4 age_5

educ

age_median code

Description

country name
year
index of democracy
logarithm of real GDP per capita
logarithm of population
fraction of the population age 0-14
fraction of the population age 15-29
fraction of the population age 30-44
fraction of the population age 45-59
fraction of the population age 60 and older average years of education for adults (25 years and older)
median age
country code

Notes: The income and demographic variable are lagged five years. For example, log_gdppc for year = 1965 is the logarithm of GDP per capita in 1960.

  1. (a)  (2p) Start by “telling” Stata that this is panel data. Is this data set a balanced panel? Explain
  2. (b)  (2p) What is the democracy index for United States in 1965? For Uruguay in 1965? For Trinidad and Tobago in 1995? For Venezuela in 1995?
  3. (c)  (3p) What is the average overall democracy index for all years in this data set? What are the minimum and maximum values of dem_ind? What is the standard deviation? What are the 10th, 25th, 50th, 75th, and 90th percentiles of its distribution?
  4. (d)  (3p) Regress democracy index on logarithm of per capita GDP using standard errors that are clustered by country. Report your results.
  5. (e)  (5p) Interpret the coefficient of log of gdp in part (d). Is it significant? Explain.
  6. (f)  (5p) If per capita income in a country increases by 20%, by how much is the democracy index predicted to increase? What is 95% confidence interval for the prediction?

1 The data were supplied by Professor Daron Acemoglu and are a subset of the data used in his paper with Simon Johnson, James Robinson, and Pierre Yared, “Income and Democracy” American Economic Review, 2008, 98:3: 808- 842

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  1. (g)  (6p) Regress democracy index on logarithm of per capita GDP controlling for country fixed effects and using standard errors that are clustered by country
  2. (h)  (6p) Generate year dummies. Regress democracy index on logarithm of per capita GDP and year dummies, controlling for country fixed effects and using standard errors that are clustered by country. Report your results.

2. (36p) The data file Employment_08_09 contains data on 5412 workers who were survey in the April 2008 Current Population Survey and reported that they were employed. The data file contains their employment status in April 2009, one year later, along with some additional variables.

Variable Names

employed unemployed

age female married race

union ne_states so_states ce_states we_states educ_lths educ_hs educ_somecol educ_aa educ_ba educ_adv earnwke private government self

  1. (a)  (6p) What fraction of workers in the sample were employed in April 2009? Use your answer to compute a 95% confidence interval for the probability that a worker was employed in April 2009, conditional on being employed in April 2008.
  2. (b)  (6p) Regress 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 on 𝑎𝑔𝑒 and 𝑎𝑔𝑒2, using a linear probability model.
    1. (i)  Based on this regression was age a statistically significant determinant of employment in April 2009?
    2. (ii)  Compute the predicted probability of employment for a 20-year-old worker, a 40-year- old worker, and a 60-year-old-worker.
    3. (iii)  Is there evidence of nonlinear effect of age on the probability of being employed?
  3. (c)  (8p) Repeat part (b) using probit regression.
  4. (d)  (8p) Repeat part (b) using logit regression.

Description

Variables form the 2009 Survey = 1 if employed in 2009
= 1 if unemployed in 2009 Variables form the 2008 Survey age

=1
=1
=1
= 2
= 3
=1
=1
=1
=1
=1
=1
=1
=1
=1
=1
=1
average weekly earnings
= 1 if employed in a private firm
= 1 if employed by the government = 1 if self-employed

if female
if married
if self-identified race = white (only)
if self-identified race = black (only)
if self-identified race was not white (only) or black (only)
if a member of a union
if from a northeastern state
if from a southern state
if from a central state
if from a western state
if highest level of education is less than a high school graduate if highest level of education is high school graduate
if highest level of education is some college
if highest level of education is AA degree
if highest level of education is BA or BS degree
if highest level of education is advanced degree

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(e) (8p) Generate four educational level related variables such as 𝑒𝑑𝑢𝑐_1 for high school degree or less, 𝑒𝑑𝑢𝑐_2 for some college and AA, 𝑒𝑑𝑢𝑐_3 for college degree and 𝑒𝑑𝑢𝑐_4 for advance degree. Generate two race related variables white for race = 1 and black for race = 2. Run the necessary regressions and fill out the following table

Dependent variable: employed

Regression Model Regressor

𝑎𝑔𝑒 𝑎𝑔𝑒2 𝑓𝑒𝑚𝑎𝑙𝑒 𝑚𝑎𝑟𝑟𝑖𝑒𝑑 𝑒𝑑𝑢𝑐_1 𝑒𝑑𝑢𝑐_2 𝑒𝑑𝑢𝑐_3 𝑟𝑎𝑐𝑒 𝑒𝑎𝑟𝑛𝑤𝑘𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

LPM Logit (1) (2)

Probit Probit (3) (4)

()()()() ()()()() ()()()() ()()()()

() () ()

() () ()()()() ()()()()

3. (32p) What is the effect of children on the labor force participation of mothers? In the data set MROZ.dta, 428 of the 753 women in the sample report being in the labor force at some point during the year. Variables in the data file MROZ.dta are:

inlf

educ exper expersq age kidslt6 kidsge6 nwifeinc

“in the labor force” =1 if women reports working for a wage outside the home at some point during the year, and zero otherwise
Years of education

Past years of labor market experience
Experience squared
Age in years
Number of kids less than 6 years old
Number of kids between 6 and 18 years of age
Other sources of income including husband’s earnings (in $1000s)

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(a) (4p) Estimate a linear probability model by regressing inlf on nwifeinc, educ, exper, expersq, age, kidslt6 and kidsge6.

  1. (b)  (4p) Estimate a probit model using the same control variables in part (a).
  2. (c)  (4p) Estimate a logit model using the same control variables in part (a).
  3. (d)  (4p) Report your results from 3(a), 3(b) and 3(c) on Table 1.
  4. (e)  (4p) Test the hypothesis that the coefficient on kidslt6 is zero in the population version of the regression in 3(a), against the alternative that it is nonzero, at the 5% significance level.
  5. (f)  (4p) Test the hypothesis that the probability of being in the labor force does not depend on the amount of work experience in the regression in 3(a). In words, describe the estimated relationship between working and experience (holding the other regressors constant).
  6. (g)  (4p) Test the hypothesis that the coefficient on kidslt6 is zero in the population version of the regression in 3(b), against the alternative that it is nonzero, at the 5% significance level.
  7. (h)  (4p) Test the hypothesis that the probability of being in the labor force does not depend on the amount of work experience in the regression in 3(b). In words, describe the estimated relationship between

Independent Variables:

nwifeinc educ exper exper2 age kidslt6 kidsge6 constant

Table 2
LPM, Probit and Logit results

Dependent Variable: inlf
LPM Probit

Logit (MLE)

(OLS) (MLE) ()()() ()()() ()()() ()()() ()()() ()()() ()()() ()()()

Percent Correctly Predicted Log-Likelihood Value Pseudo R-Squared

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Following questions will not be graded, they are for you to practice and will be discussed at the recitation:

4. [ungraded] SW Empirical Exercise 10.1 5. [ungraded] SW Empirical Exercise 11.2

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