There has been much debate about the impact of minimum wages on employment and unemployment. While most of the focus has been on the employment-to-population ratio of teenagers, you decide to check if aggregate state unemployment rates have been affected. Your idea is to see if state unemployment rates for the 48 contiguous U.S. states in 1985 can predict the unemployment rate for the same states in 1995, and if this prediction can be improved upon by entering a binary variable for "high impact" minimum wage states. One labor economist labeled states as high impact if a large fraction of teenagers was affected by the 1990 and 1991 federal minimum wage increases. Your first regression results in the following output:

\begin{aligned}\widehat { U r _ { i } ^ { 95 } } = & 3.19 + 0.27 \times U r _ { i } ^ { 85 } , R ^ { 2 } = 0.21 , \mathrm { SER } = 1.031 \\& ( 0.56 ) ( 0.07 )\end{aligned}

(a)Sketch the regression line and add a 45⁰ line to the graph. Interpret the regression results. What would the interpretation be if the fitted line coincided with the 45⁰ line?
(b)Adding the binary variable DhiImpact by allowing the slope and intercept to differ, results in the following fitted line:

\begin{array} { l } \widetilde { U r _ { i } ^ { 95 } } = 4.02 + 0.16 \times U r _ { i } ^ { 85 } - 3.25 \times \text { Dhilmpact } + 0.38 \times \left( \text { DhiImpact } \times U r _ { i } ^ { 85 } \right) \text {, } \\\quad\quad\quad\text { (0.66) (0.09) }\quad\quad\quad ( 0.89 )\quad\quad\quad\quad\quad\quad\quad\quad\quad(0.11) \\R ^ { 2 } = 0.31 , S E R = 0.987 \\\end{array}

The F-statistic for the null hypothesis that both parameters involving the high impact minimum wage variable are zero, is 42.16. Can you reject the null hypothesis that both coefficients are zero? Sketch the two regression lines together with the 450 line and interpret the results again.
(c)To check the robustness of these results, you repeat the exercise using a new binary variable for the so-called mining state (Dmining), i.e., the eleven states that have at least three percent of their total state earnings derived from oil, gas extraction, and coal mining, in the 1980s. This results in the following output:

U r_{i}^{95}=4.04+0.15 \times U r_{i}^{85}-2.92 \times \text { Dmining }+0.37 \times\left(\text { Dmining } \times U r_{i}^{85}\right) \text {, }

\quad

\quad

\quad

\quad

(0.65) (0.09)

\quad

\quad

\quad

\quad

\quad

(0.90)

\quad

\quad

\quad

\quad

\quad

\quad

(0.10)

R ^ { 2 } = 0.31 , S E R = 0.997

How confident are you that the previously found effect is due to minimum wages?

An Example of the Interaction Term Between Two Independent, Continuous

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