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The labor supply of married women has been a subject of a great deal of economic research

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1. The labor supply of married women has been a subject of a great deal of economic research.  Given the data on women who worked in the previous year and those who have not, several models have been estimated.  The variable indicating whether a woman  worked  is  LFP=Labor  Force  Participation,  which  takes  the  value  1  if  a woman worked and 0 if she did not.

 

(a)  Consider the following supply equation specification:

 

 

HOURS = β₁+β₂ln(wage)+β₂educ+β₄age+β₅kidsl6+β₆kids618+β₇nwifeinc+µ

 

 

What sign do you expect each of the coefficients to have, and why?              (b)  The variable nwifeinc=non-wife income is defined as

 nwifeinc = faminc − wage

 hours

 

 

 

The summary statistics for the variables:  wife’s age, number of children less than

6 years old in the household, and the family income for the women who worked (LFP=1) and those who did not work (LFP=0) are provided in the table.  Comment on any differences you observe.

 

 

	MEAN              Standard Deviation
Variable	LFP=1     LFP=0	LFP=1        LFP=0 age
41.97	43.28        7.72	8.47 kidsl6               0.14
0.37	0.39                 0.6 4	faminc           24130
21698	11671             12728

 

 

1. 3. NWIFEINC  and  ln(WAGE)  variables  in  part  (a)  are  endogenous.   Can  the HOURS equation be estimated satisfactory using the

 

 

 

1. 4. Table 1 provides the results of the least squares regression on only the women who worked (LFP=1).  Did things come out as expected?  If not, why?

 

TABLE 1  Dependent variable:  HOURS Included observations:  428
	Coef.	Std.Err.	z       P > |z|
Intercept	2114.69	340.13	6.22	0.000
lnwage	-17.41	54.22	-0.32	0.75
educ	-14.44	17.96	-0.80	0.42
age	-7.73	5.53	-1.40	0.16
kidsl6	-342.51	100.01	-3.43	0.000
kids618	-115.02	30.83	-3.73	0.000
nwifeinc	-0.01	0.01	-1.16	0.25

  

1. 5. The  results  of  the  following  wage  equation  for  the  women  who  worked are provided in Table 2.  What is the effect on wage of an additional year of education?

  ln(wage) = α₁  + α₂educ + α₃age + α₄kidsl6 + α₆kids618 + α₇nwifeinc +  

 

 

 

TABLE 2  Dependent variable:  LNWAGE Included observations:  428
	Coef.	Std.Err.	z        P > |z|
Intercept	-0.357	0.31	-1.13	0.26
educ	0.099	0.015	6.615	0.00
age	-0.001	0.005	-0.650	0.52
kidsl6	-0.056	0.088	-0.631	0.53
kids618	-0.0176	0.027	-0.633	0.53
nwifeinc	-5.69E-06	3.32E-06	1.715	0.08
exper	0.0407	0.013	3.044	0.00
exper2	0.001	0.011	-1.860	0.06

 

 

1. 6. Is the supply equation in part (a) identified?  Name the instrumental variable if any.

 

1. 7. Two-stage least squares estimation of the supply equation is provided in Table

3.  Discuss the sign and significance of the estimated parameters.

 

TABLE 3  Dependent variable:  HOURS Included observations:  428
	Coef.	Std.Err.	z         P > |z|
Intercept	2432.198	594.17	4.093	0.000
lnwage	1544.818	480.7387	3.213	0.004
educ	-177.449	58.142	-3.0519	0.002
age	-10.784	9.577	-1.126	0.260
kidsl6	-210.834	176.934	-1.192	0.234
kids618	-47.557	53.917	-0.835	0.404
nwifeinc	-0.001	0.006	-1.427	0.154

 

 

2. It is common for companies to spend money and time on employee training pro- grams to improve productivity in the workplace.  A company is interested in an- alyzing the effect of a training program on employees’ productivity.  Data from a random sample of 10,000 workers ages 18 and older were collected and a regression

 

 

P RODUCT IV IT Y  = Xβ + αT RAINING + µ

 

 

was  estimated,  where  X  is  a  matrix  of  socio-demographic  characteristics,  and TRAINING  is  a  dummy  variable  that  is  equal  to  1  if  the  person  participated in the  training  program  and is equal  to zero  otherwise.  TRAINING  can depend on  many  factors  and  one  of  them  could  be  whether  a  company  received  a  job training grant to help subsidize the cost of the training, therefore

 

 

T RANING = Zγ + θGRANT +  .

 

 

Here Z is a matrix of firm related factors and GRANT=1 if company received a training grant and =0 otherwise.

 

1. 1. In  estimating  the  PRODUCTIVITY  equation  the  variable  TRAINING  can potentially be endogenous.  Why using OLS can fail in estimating this regres- sion model?  Explain.

 

1. 2. Propose an estimation method that will help resolve this endogeneity problem.    Describe the estimation method in detail.
   3. Is the  PRODUCTIVITY  equation  identified?  If so  why?  Is it  exact,  under or over -identified?
   4. Now suppose that you only observe the positive level of productivity for those employees who did the training and zero for those who did not do the training. Discuss  and  name  the  model  you  will  use  in  estimating  PRODUCTIVITY equation. What  will  happen  if  you  use  OLS  to  estimate  this  model?    Is endogeneity of TRANING is still a problem?  If so, how can it be fixed?

 

1. 5. What will happen if you only select positive levels of productivity and esti- mate the model?  Explain.

 

3. In general, the two-stage least squares estimation (2SLS) procedure can be used to estimate the parameters of any identified equation within a simultaneous equation system.   In  a  system  of  M  simultaneous  equations  let  y₁, y₂, y₃, ..., y_n   be  the  en- dogenous variables.  Let k be the number of exogenous variables:  x₁, x₂, x₃, ..., x_k. Suppose the first equation is:

 

 y1  = α2y2  + α3y3  + β1x1  + β2x2  + µ1

 

 

1. 1. Describe the steps of 2SLS estimation method in detail, so a researcher who is reading your answer can easily follow the steps you described and estimate the model.

 

1. 2. What is an Instrumental Variable(IV)? Be specific.

 

4. Write  the  following  models  in  terms  of  a  latent  variable,  comment  on  how  to interpret the results of each model and give examples.

 

1. 1. Probit
   2. Multinomial Logit
   3. Conditional Logit
   4. Ordered Probit
   5. Tobit

 

5. The first-order autoregressive model is given by

 

 yt  = α0  + α1yt−1  +  t

 

 

lets assume that the value of y₀  is known.  Then we can write y₁  as

 

 

y1  = α0  + α1y0  +  1.

1. 1. Using the above information write y₂  as a function of y₁  and then as a function of  y₀  by replacing y₁  with above given expression.
   2. Continue the process and write y₃  as a function of y₀.  Simplify your answer by  combining like terms.
   3. Since y_t  = α₀ + α₁y_t−1 +  _t, write the expression for y_t  using y₅  knowing that the value of y_t−1  is obtained from y_t−2  and the value of y_t−2  is obtained from y_t−3  and so on.  Identify the expressions for intercept, slope, and error terms.

 

6. Suppose that your company was hired by the Mayor of one of the America’s large cities  to  help  address  traffic  congestion  problems  during  rush  hour.   You  were given a data on the mode of transportation chosen by commuters, distance trav- eled from home to work/subway,  etc.,  and all the individual  and household level characteristics that are needed for the analysis.

 

1. 1. After careful analysis of the data, you found that you can group the modes of transportation into four general categories ’subway’, ’bus’, ’car’, and ’human- powered’  (walk,  bicycle).   Specify  an  econometric  model  that  fits  the  data best, i.e.  write down the model you will be estimating and label your variables carefully.  Is your model linear or non-linear?  How are you going to interpret your results?

 

1. 2. List all the factors (independent variables) that you as a research think might affect the choice of transportation.

 

7. The RESET test (Regression Specification Error Test) is designed to detect omit- ted variables and incorrect functional form.  It proceeds as follows.  Suppose that we have specified and estimated the regression model

  

yi  = β1  + β2xi2  + β3xi3  + µi.

 

Let (βˆ₁, βˆ₂, βˆ₃) be the least squares estimates and let

 

yˆi     =   β1  + β2xi2  + β3xi3  + γ1^yˆ2  +_i  µi                                                          (1) yˆi     =   β1  + β2xi2  + β3xi3  + γ1^yˆ2  +_i                  γ2^yˆ3  +_i  µi                                        ⁽²⁾

 

 

In  (1)  a  test  for  misspecification  is  a  test  of  H₀   :  γ₁   =  0  against  the  alternative

H₁  : γ₁  = 0. In (2),  testing H₀  : γ₁  = γ₂  = 0 against the alternative H₁  : γ₁  = 0 and/or γ₂  = 0 is a test for misspecification.  In the first case a t- or an F-test can be  used.  An  F-test  is  required  for  the  second  equation.  Rejection  of  H₀   implies the original model is inadequate and can be improved.  A failure to reject H₀  says

 

 

 

the test has not been able to detect any misspecification. The following table contains output for the two models

yi     =   β1  + β2xi  + β3wi  + µi                                                            (3) yi     =   β1  + β2xi  +  i                                                                                (4)

 

 

obtained using n=35 observations.  RESET test applied to the second model yields

 

Variable	Coef.    Std.Error    t-Statistic	Coef.    Std.Error    t-Statistic
C	3.6356           2.763            1.316	-5.8382           2.000           -2.919
X	-0.99845           1.235         -0.8085	4.1072         0.3383            12.14
W	0.49785         0.1174            4.240

 

F-values of 17.98 (for yˆ2i                                          ) and 8.72 (for yˆ2i                   and yˆi3 ).  Answer the following questions using the results provided in the table:

 

1. Should  w_i   be  included  in  the  model?    What  can  you  say  about  omitted-  variable bias?
2. You have discovered that the correlation between x and w is r_xw=0.975.  What can you say about the existence of collinearity and its possible effects?

 

8. (a)  Why is perfect multicollinearity a problem?
   2. Give an example of two (or more) perfectly collinear variables?
   3. Suppose that X₁  and X₂  are highly collinear  and we estimate the following model  Y_i   =  β₁  + β₂1X_1i  + β₃X_2i  + e_i.   Can  we  use  OLS  to  find  unbiased estimates of the coefficients.  Why are these coefficients difficult to estimate precisely (give intuition).

 

9. (a)  Suppose  you  are  interested  in  the  effect  of  high  school  GPA  (gpa_i)  on  ad- mission to Texas University (admit_i), where admit_i  is a binary variable with  admit_i   =  1  indicating  admission  and  admit_i   =  0  indicating  rejection. You estimate the following regression using OLS, admit_i  = β₁  + β₂gpa_i  + e_i and find addmit_i  = 1.2 for some units.  Why is this a questionable predicted value?  How could you model this to avoid this problem?

 

10. (a)  Suppose  you  are  interested  in  the  effect  of  years  of  education  on  income. Why would a regression of income on education give a biased estimate of this effect?  Could this biased estimate be used for forecasting?

 

 

11. Suppose  you  are  interested  in  modeling  U.S.  GDP  data  using  an  autoregression model.  Describe two approaches to choosing the lag-length.  What are the advan- tages and disadvantages of each?

 

12. High humidity levels can cause drivers to be drowsy and increase traffic accidents. We  would  like  to  estimate  the  effect  of  humidity  on  traffic  accidents.   We  have a  cross  sectional  data  set  of  per-capita  traffic  accident  (accident_i)  and  average humidity (humidity_i) data for all states i in 2005.  We also have a panel data set of percapita traffic accident (accident_it) and average humidity (humidity_it) data for all states i from 2005-2010.

 

1. 1. Suppose  I  can  only  use  one  data  set,  which  would  be  the  best  data  set  for finding an unbiased estimate of the impact of humidity on traffic accidents? Why?

 

1. 2. What would be the best model to estimate this effect.  Carefully explain why.

 

13. (a)  Specify the Pooled Model and state when it can be used?
    2. What are the consequences of estimating Pooled Model using panel data?
    3. Specify Fixed and Random Effects models.  Write down the regression models and state the differences between the two.

 

14. In developing an econometric model, you might exclude one or more relevant re- gressors or include one or more irrelevant regressors.

 

1. 1. What are the consequences of including 1 too many regressors? (b)  What are the consequences of excluding 1 too few regressors?

 

15. When using non-experimental data in estimating the regression model it is common to have high correlation among some of the regressors which can lead to Exact and Near Multicollinearity.

 

1. 1. What is Exact Multicollinearity?  How to detect Exact Multicollinearity and what are the remedies?

 

1. 2. What  is  Near  Multicollinearity?   How  to  detect  Near  Multicollinearity  and what are the remedies?

 

16. Suppose you are interested in estimating the elasticity of demand for wheat using:

                    

ln(Qi          wheat) = β1  + β2ln(Pi           wheat) + ei

 

 

1. 1. Is  the  independent  variable  (ln(P ^wheat_i ))  positively  or  negatively  correlated with the error term?
   2. If we estimated this equation with OLS, would you expect βˆ₂  to be larger or smaller than β₂?

 

17. In estimating the regression model y = β₁ +β₂x a researcher had options of scaling either  both  or  one  of  the  variables.  Without  scaling  any  of  the  variables  he/she obtained

  

yˆ   =   83.42 + 0.1021x (se)          (43.41)

       (0.0209)

 

 

 

 

where

y=weekly food expenditure by household, in dollars

x=weekly household income * indicates significance at 10% *** indicates significance at 1%.

 

1. 1. Interpret the above estimated regression model.
   2. Re-write  the  estimated  regression  model  if  x  was  divided  by  100,  i.e.    ^x ₁₀₀ .  Interpret the result.
   3. Re-write  the  estimated  regression  model  if  y  was  divided  by  100,  i.e.    ^y ₁₀₀ .  Interpret the result.
   4. Re-write the estimated regression model if both x and y were scaled, i.e.   ^x  ₁₀₀ and   ₁₀₀^y  .   Interpret the result.