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    Introduction to Modern Econometrics Using Stata

    Assignment 3

     

     

     

    Example 17.1 In book woold

    An Introduction to Modern Econometrics Using Stata.pdf Page 250

    A Handbook of Statistical Analyses Using Stata, Second Edition: Chapter-6

    Microeconometrics Using Stata.pdf:Chapter-14

    Stata Primer: Chapter-8

    Your task is to examine the determinants of voluntary contributions to public radio using survey data on approximately listeners and contributors. The data for this case study is contained in the file npr1.txt. Your Assignment should include five sections: (1) conceptual framework, (2) specification of the econometric model, (3) description of the data, (4) discussion of estimation results (5) Marketing plan for NPR based on your results.

     

     

     

    1. Conceptual Framework and Specification of the Econometric Model

     

    Our main task is to construct a model that help us in predicting whether an individual is going to contribute to public radio. For this we observe that amongst the variables listed in dataset the following variables seem to be mostly related to the decision of donation:

    1. age of listener in years
    2. station listening time in quarter hours per week
    • Listener income in dollars
    1. Whether individual has a master’s degree or higher
    2. Whether individual has a bachelor’s but not a Masters.
    3. Whether individual has some college but no degree
    • Whether individual has a high school degree
    • Whether individual is female
    1. Whether individual is white
    2. Whether individual is retired

     

     

    This is because Contributions of others, Estimated number of public radio listeners in market, Total population / land area of MSA (Metropolitan Statistical Area) and the city have no relation with individuals decision to donate.

     

    city          City where station is located

    Age           age of listener in years

    Listen       station listening time in quarter hours per week

    gother       Contributions of others (total contributions from all sources other than the contribution made by individual i) in dollars.

    Tlisten       Estimated number of public radio listeners in market

    Popdens   Total population / land area of MSA (Metropolitan Statistical Area) Donate   Dummy equal to one if individual made donation

    Income      Listener income in dollars

    Pgrad             Dummy =1 if individual has a masters degree or higher Cgrad           Dummy =1 if individual has a bachelor’s but not a Masters. Scol                        Dummy =1 if individual has some college but no degree Hsgrad                   Dummy =1 if individual has a high school degree

    Female       Dummy =1 if individual is female White           Dummy =1 if individual is white Retired                   Dummy =1 if individual is retired

     

    We will use the three models to predict the possibility of donation by an individual:

    1. Linear Probability model where we have the following mathematical model:

    Donate=β0 + β1 age + β2 listen+ β3 income+ β4 Pgrade+ β5 Cgrade+ β6 Scol+ β7 Hsgrad+ β8 Female+ β9 white + β10 retired,

    Here the slope βj ,j=1,2…10 is the predicted change in the probability of donation when the corresponding predictor increases by one unit, β0 is the predicted probability of donation when all preceptors have zero value while y is the predicted probability of success.

    The linear probability model has the drawback that for certain values of the predictors we may have values of predicted probability less than zero or greater than unity which is absurd as probability always lies between 0 and 1. Also non-normality of error terms, heteroscedastic variances of eroor are some other problems. There is one problem that probability cannot linearly related to any predictor as otherwise it may take the value of predicted probability greater than unity. There is one remedy to these problems that we should retain those values of predictors for which probability does not crosses the bound but this may result into loss of some useful information from predictors.

    1. Logit (logistic regression) model where we have the following mathematical model:

    P(Y=1/x)=

    G(β0 + β1 age + β2 listen+ β3 income+ β4 Pgrade+ β5 Cgrade+ β6 Scol+ β7 Hsgrad+ β8 Female+ β9 white + β10 retired),

    =G(β0 + )

    Here G(.) is the cumulative distribution function of standard logistic random variable defined by G(z)=exp(z)/[1+exp(z)], x in bold is the set of all predictors and

    = β0 + β1 age + β2 listen+ β3 income+ β4 Pgrade+ β5 Cgrade+ β6 Scol+ β7 Hsgrad+ β8 Female+ β9 white + β10 retired

    This model ensures the probability to take values in between 0 and 1 including them but not beyond these limits

     

    • Probit model where we have the following mathematical model:

    P(Y=1/x)=

    G(β0 + β1 age + β2 listen+ β3 income+ β4 Pgrade+ β5 Cgrade+ β6 Scol+ β7 Hsgrad+ β8 Female+ β9 white + β10 retired),

    =G(β0 + )

    Here G(.) is the cumulative distribution function of the standard normal variable defined by G(z)= , and x in bold is the set of all predictors and

    = β0 + β1 age + β2 listen+ β3 income+ β4 Pgrade+ β5 Cgrade+ β6 Scol+ β7 Hsgrad+ β8 Female+ β9 white + β10 retired

    This model ensures the probability to take values in between 0 and 1 including them but not beyond these limits

    There is not much difference in the shape and limits of the predicted probabilities given by the logit and probit model except the difference in the cumulative distribution function used in both the models. However, the results are similar but parameters are not directly comparable in both models.

    1. Description of the Data

    Create a table of summary statistics. Provide a brief description of the variables used in your study and discuss the summary statistics.

     

    The table of summary statistics is as follows from where we observe that 33.91% of the individuals in the sample are contributing to public radio by making donations, 38.97% hold masters’ degree or higher, 24.07% hold bachelor’s degree but not masters, 22.49% hold some college degree but nor degree, 11.71% has a high school degree, 47.49% are females (others male), 93.99% are white and 14.42% are retired persons.

    Also, mean age of the individuals in the sample is 45.66 years with minimum age 18 years and maximum 93 years. The average income of the individuals in our sample is $46086.11 with minimum income $2500 and maximum income $184488.4.

     

    Summary statistics
    VariableObsMeanStd. Dev.MinMax
    donate37310.3390510.47345101
    age373145.6585414.996181893
    listen373133.8520540.977191346
    income373146086.1136773.262500184488.4
    pgrad37310.3897080.48774901
    cgrad37310.2406860.42755701
    scol37310.2248730.41755401
    hsgrad37310.1171270.32161401
    female37310.474940.49943901
    white37310.9399630.23758801
    retired37310.1441970.35133701

     

     

     

     

     

     

     

     

     

    1. Results

    Table with three sets of results: (1) Linear Probability Model, (2) Logit Model, and (3) Probit Model is as follows from where we observe that all the three models have same sign of coefficients for all the predictors of donation. Also Percentage Correctly Predicted is almost same for all the three models and R-squared too does not vary much for all the models.

    Now looking at the sign of the coefficients we observe that all the variables have positive impact on probability of donation. Only listen, income, pgrad, cgrad, female and white have significant impact on donation. As listening time increases it is obvious that individual has more tendencies to make donation. Also, if the income increases we expect the individual to make some contribution by donation. Similar is the case that when a person is more educated either masters(Pgrade) or college(Cgrade ) then he is more knowledgeable to know th ebenefit of donation and make some contribution. Donations made by females pertain to human behaviour and females are more concerned about public life. White persons are also having greater chance of making donation due to prosperity.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Coefficients with Standard errors in Parenthesis, *p<.05, **p<.01, ***p<.001
    Dependent Variable: donate
    Independent

    Variables

    LPM

    (OLS)

    Logit

    (MLE)

    Probit

    (MLE)

    age0.0006475

    (.0006152)

    0.003941

    (0.0033092)

    0.0023397

    (0.0019769)

    listen.0027042***

    (.0001954)

    0.012884***

    (0.00096)

    0.0076851***

    (0.0005473)

    income0.00000222***

    (0.00000023)

    0.00001030***

    (0.00000105)

    0.000006260***

    (0.000000623)

    pgrad.2194713*** (.0372072)1.358775***

    (0.3174161)

    0.7745163***

    (0.1702777)

    cgrad.1412591***   (.0378002)0.996871**

    (0.3210875)

    0.5539602**

    (0.1725862)

    scol.0643043   (.0369369)0.575906

    (0.3213468)

    0.3077896

    (0.1721771)

    hsgrad.0447288   (.0380576)0.450842

    (0.3308597)

    0.2290902

    (0.1777501)

    female.061558***   (.0146819)0.309075***

    (0.0756224)

    0.1856696***

    (0.0451472)

    white.0976322***   (.0266236)0.598563**

    (0.1834121)

    0.3479993**

    (0.1042219)

    retired.049004   (.026371)0.228809

    (0.1375911)

    0.1478797

    (0.0819513)

    Constant-.1518637**   (.0482515)-3.52899***

    (0.3828398)

    -2.080306***

    (0.2093689)

    Percentage Correctly Predicted

     

    69.6369.6669.77
    Log-Likelihood Value

     

    ___-2137.9406-2137.4369
    Pseudo R-squared0.1310.10520.1054

     

    For LPM we have following:

     donate_predict 
    donate01Total
    02,2462202,466
    19133521,265
    Total3,1595723,731

     

    So Percentage Correctly Predicted=(2246+352)*100/3731=69.63%

    Table of marginal effects for logit and probit models is as follows from where we observe that

    For logit model:

    1. corresponding to a unit increase in station listening time in quarter hours per week the individual has 0.28% higher probability of making donation.
    2. corresponding to a unit increase in income the individual has 0. 000225% higher probability of making donation.
    • individual having masters degree or higher has 30.26% higher probability of making donation.
    1. individual has a bachelor’s but not a Masters has 23.11% higher probability of making donation.
    2. Females has 6.76% higher probability of making donation.
    3. Whites have 11.69% higher probability of making donation.

     

    For Probit model:

    1. corresponding to a unit increase in station listening time in quarter hours per week the individual has 0.27% higher probability of making donation.
    2. corresponding to a unit increase in income the individual has 0. 000225% higher probability of making donation.
    • individual having masters degree or higher has 28.22% higher probability of making donation.
    1. individual has a bachelor’s but not a Masters has 20.80% higher probability of making donation.
    2. Females has 6.68% higher probability of making donation.
    3. Whites have 11.49% higher probability of making donation.

     

    Marginal Effects with SE in parenthesis, *p<.05, **p<.01, ***p<.001
    Independent

    Variables

    Logit

    (MLE)

    Probit

    (MLE)

    age0.0006804

    (0.00072)

    0.0008409

    (0.00071)

    listen0.0028129***

    (0.00021)

    0.002762***

    (0.0002)

    income0.00000225***

    (<.000001)

    0.00000225***

    (<.000001)

    pgrad0.302615***

    (0.0692)

    0.2822845***

    (0.0.06119)

    cgrad0.2311024**

    (0.07608)

    0.2080118**

    (0.0661)

    scol0.131605

    (0.07582)

    0.1141814

    (0.0654)

    hsgrad0.1036414

    (0.07912)

    0.0852101

    (0.06798)

    female0.0675822***

    (0.01652)

    0.0667931***

    (0.01623)

    white0.1169545**

    (0.03126)

    0.1148938**

    (0.03098)

    retired0.0513111

    (0.03161)

    0.0543233

    (0.0307)

     

     

     

     

     

     

    1. Marketing Implications and Conclusions

    We conclude that only individual having masters degree or, individual has a bachelor’s but not a Masters, Females and Whites have higher probability of making donation.

    Hence NPR should focus on these strata of individuals for donations.