Economics homework help. **ECO 430– Applied Econometrics**

In the article, “Tattoos, Employment, and Labor Market Earnings: Is There a Link in the Ink?” Michael French and coauthors attempt to empirically verify the notion that individuals with one or more tattoos have lower earnings than those who are tattoo-less. Their empirical model is ln*earnings**i *= *β*0 + *β*1*D**Tattoo,i *+ *β*2*Age**i *+ *β**xx**i *+ *β**ee**i *+ *β**zz**i *+ *β**oo**i *+ *ε**i, *(1) where ln*earnings _{i }*is the logarithm of annual earnings for individual

*i*,

*D*is a dummy variable whose value is 1 for individuals with a tattoo and 0 otherwise,

_{Tattoo,i }*Age*is the age of the individual,

_{i }*x*is a set of demographic variables,

*e*is a set of human capital controls,

*z*is a set of lifestyle controls, and

*o*is a set of occupational variables.

The main estimates for the model in (2) appear in Table 1. Note that the estimate for the intercept is not reported and the standard error for each coefficient estimate appears underneath in parentheses.

Table 1. Estimates of Earnings Determination

x |
Dependent variable: |
lnearnings |
||||

No | Yes | Yes | Yes | Yes | ||

e |
No | No | Yes | Yes | Yes | |

z |
No | No | No | Yes | Yes | |

o |
No | No | No | No | Yes | |

Observations | 3554 | 3554 | 3554 | 3554 | 3554 | |

R¯2 |
0.003 | 0.056 | 0.167 | 0.265 | 0.303 | |

2

Q.*1*. (10) Please interpret the coefficient estimates for *β*_{1 }and *β*_{2 }in column (2) of Table 1.

Q.*2*. (10) Based exclusively on *R*¯^{2 }going from column (2) to (3), is there evidence *e *in the earnings model should belong in the model ? What is the interpretation of *R*¯^{2 }in column (3)?.

Q.*3*. (10) What would the estimate for *β*_{1 }be in column (1) if the base group were to switch from not having a tattoo, to having a tattoo? Interpret this new estimate.

Q.*4*. (10) Assuming that the alternative hypothesis is that tattoos have a detrimental effect on earnings. Write out the appropriate null and alternative hypotheses for this and describe in detail how you would test this null hypothesis for the model estimates appearing in column (1) at the 1% level.

Q.*5*. (5) Now, if instead we use the p-value approach for the test in the previous question, we get a *p*-value of 0.001. What is the conclusion of your test in this setting at the 1% significance level?

Q.*6*. (10) Now, suppose we change the hypothesis to tattoos having an effect on wages. Write out the appropriate null and alternative hypotheses for this and describe in detail how you would test this null hypothesis for the model estimates appearing in column (1) at the 1% level.

Q.*7*. (10) Explain what would happen if I were to include *ln*(*GDP*) and ln(*GDP*^{2}) in the model.

Q.*8*. (5) Explain why it would be useful to include *age*^{2 }in the model .

Q.*9*. (15) If we want to analyse the effect of having a tattoo on being employed or unemployed, a possible model would be:

*employed**i *= *β*0 + *β*1*D**Tattoo,i *+ *β*2*exper**i *+ *β*3*D**Tattoo,i *∗ *exper**i *+ *β*4*other *+ *ε**i, *(2) where *employed _{i }*is a dummy variable which takes the value of 1 if the individual is employed and 0 if the individual is unemployed,

*D*is a dummy variable whose value is 1 for individuals with a tattoo and 0 otherwise,

_{Tattoo,i }*exper*is the number of years

3

of work experience for individual

*i*,

*other*summarizes other variables included in model (2). How would you interpret

*β*

_{1}

*,β*

_{2 }

*and β*

_{3}

*inmodel*(2)

*.*

Q.

*10*. (5) What type of model is model (2) presented in question 9? Give the name of the model and explain when we can use this type of model.

Q.

*11*. (10) Why is it useful to include the interaction term (

*β*

_{3}

*D*∗

_{Tattoo,i}*exper*) in model (2)? What am I trying to capture?

_{i}