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We are in the same world as Question 26: w is randomized conditionally on a continuous 11 and the treatment effect is constant: In addition, Ely(0)x1] = a + Y181 + ...

Question

We are in the same world as Question 26: w is randomized conditionally on a continuous 11 and the treatment effect is constant: In addition, Ely(0)x1] = a + Y181 + Y2w2 However; you ran a regression y = & + TW + Y1*1 + & instead ofy = a + Tw + 3181 + Y2x2 + u . Show that MLR4 does not hold when you run a regression ofy on a constant; W, and 11 _

We are in the same world as Question 26: w is randomized conditionally on a continuous 11 and the treatment effect is constant: In addition, Ely(0)x1] = a + Y181 + Y2w2 However; you ran a regression y = & + TW + Y1*1 + & instead ofy = a + Tw + 3181 + Y2x2 + u . Show that MLR4 does not hold when you run a regression ofy on a constant; W, and 11 _



Answers

In the simple linear regression model $y=\beta_{0}+\beta_{1} x+u,$ suppose that $\mathrm{E}(u) \neq 0 .$ Letting $\alpha_{0}=\mathrm{E}(u),$ show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.

Hi, everyone. Uh, just question six from computer. Next isis. Use the data set in wages, too, for his problem. Okay, so the 1st 1 is run a simple congressional bike. You on education to obtain slope? Politicians say Delta one killed. So I just want to find Delta one pill there, and we're gonna run a simple little ration. Oh, I cute on education. And when we do that, So this era of national like education, so they're quite efficient on education. You said Delta. 1/2 that one. Tilda is 3.50 tree. Find some. Just you Question. Okay, so this is deep pool to 3.50 three. The, uh okay. Tech a question. It's a simple progression of large wage on education to obtain slope coefficient Base one. Tilda, Let's do that. So the regression off log wage on education on, we find that equal efficient on education. Just beta. One pill done over estimates. And your point, you 59. This is NATO until the all right. Let's put that used to Well, points. 05 Let's go to more 98. Okay, So the question is from the multiple aggression log wage on education and I to and of things took coefficient, spate, own hats and later to respectably. So when we do that and if the congressional log wage on education and I to coefficient on education, which called beta one had is points 03 91 on the coefficient on ulterior one double Oh Oh 58 Bigger too point or 3 91 25 86. Okay, so Jones put that here they tell one haps is point or 3 91 and data to hat. It's 0.0 phile age. And the last out of the question is asking us to verify they tell one Hilda Easy, cool two A tone hat state, too, and torn Hilda, and could just do that by plugging in limousine. And you will see that this actually holds, all right, overcome potential watching

Part one. The regression of U. T. Had on U T minus one had and the change in unemployment rate gives a coefficient on U T minus one hat of 0.73 with a T statistic of 0.42 Okay, therefore, there is little evidence, a first order serial correlation. Like part two. We have a simple regression. We regret UT head square on the change in unemployment rate and the regression gives a slow coefficient. The beta head of the change in unemployment rate yeah of 2.452 and the teeth statistic of 2.7. So at the 5% significance level, we find the evidence for hetero Scott elasticity and because the beta head of the change in unemployment is positive. So the variance of the error appears to be larger when the change in unemployment is larger. Part three, the hetero scholastic city robbers standard error is 30.2 to 3 and the usual old L s standard error is 0.182 So the hetero scholastic city robots standard error is more than 20% Okay, larger then the usual l as one. And of course, a larger standard. Errol leads to you a wider confidence interval for beta one

Part one. The regression of the residuals on its first leg with 35 observations, produces a row let of minus point 089 and it's standard error is 890.178 This result tells us there is no evidence of a are one cereal correlation. In Part two, we regret consumption growth On its first leg, we get the residual U T hat, then we regress. UT heads square on the first leg of consumption growth and consumption growth. First leg squared using 35 observations. The F statistic with to 32 degrees of freedom yeah, is 1.8 and the P value is about 0.352 So there is little evidence of hetero scad elasticity in the er one model for consumption growth. This means we need not modify our test of the permanent income hypothesis by correcting somehow for hetero ski elasticity.


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