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If the error terms in a regression model are independent $N\left(0, \sigma^{2}\right),$ what can be said about the error terms after transformation $X^{\prime}=1 / X$ is used? Is the situation the same after transformation $Y^{\prime}=1 / Y$ is used?

If the error terms in a regression model are independent $N\left(0, \sigma^{2}\right),$ what can be said about the error terms after transformation $X^{\prime}=1 / X$ is used? Is the situation the same after transformation $Y^{\prime}=1 / Y$ is used?

Applied Linear Statistical Models

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.

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.

A Modern Approach

Questions asked

ANSWERED

Aishwarya Krishnakumar verified

Numerade educator

3. The government is considering building a waste-to-energy plant near Brighton at a cost of £50 million. The plant has a life-time of 20 years. In every year, it saves £2 mln in landfill costs and yields energy worth £3 mln. At a discount rate of 5%, is this a good investment? The government plans to use its hard-won Brexit freedoms and lower emission standards for waste-to-energy plants. Incinerating waste leads to dioxin emissions of 1 g TEQ per year. Dioxins have a life-time of 15 years. One gram of dioxin means that there is a 1% chance that someone will die of cancer. If the value of statistical life is £10 mln, is this a good investment? Show your workings.

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INSTANT ANSWER

\[ f(x)=\theta^{-2} x e^{-\frac{x}{\theta}} \text {, for } x>0, \] and \( f(x)=0 \) otherwise.

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INSTANT ANSWER

\begin{tabular}{lcccc} & Nr of shares & Price & Expected return & standard deviation \\ \hline A & 100 & 4 & 8 & 10 \\ B & 300 & 6 & 12 & 14 \\ C & 100 & 5 & 10 & 12 \\ \hline \end{tabular}

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ANSWERED

Supreeta N verified

Numerade educator

2. The following earnings data represent random samples drawn from male and female company executives in the United Kingdom. Use a significance level of 0.05 with a non-parametric test to undertake the hypothesis that, on average, a male chief executive earns significantly more than a female chief executive. Table 1: Bonus payments (thousands of pounds) egin{tabular}{cc} Male earnings & Female earnings \ hline 50,100 & 41,200 \ 47,800 & 36,600 \ 45,000 & 44,500 \ 51,500 & 47,800 \ 55,000 & 42,500 \ 53,850 & 47,500 \ 51,500 & 40,500 \ 63,900 & 28,900 \ 57,800 & 48,000 \ 61,100 & 42,300 \ 51,000 & 40,000 \ & 31,400 \ hline end{tabular}

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ANSWERED

Meri Siavoshi verified

Numerade educator

1. Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units of X and 20 units of Y in the economy. The preferences of the consumers are represented by the following utility functions: UA(XA, YA) = XA + YA UB (XB, YB) = (XB)^2YB b) Sketch the indifference curves and the initial allocation on an appropriate diagram. In your diagram identify the area where there is scope for a Pareto improvement and explain why this is the case.

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AWAITING AN EDUCATOR

C) Suppose the economy is operating at the zero lower bound for the nominal policy rate; the initial equilibrium is at the positive target rate of inflation and the economy is resting at potential output but there is a large government deficit in period t. A newly elected government vows to cut spending and permanently reduces the deficit by cutting G in period t + 1 and subsequent periods. Explain how the zero lower bound on nominal interest rates makes a fiscal consolidation more difficult. In doing so, illustrate the short-run and medium-run impacts using the IS-LM-PC model. Analyze how this policy lead to a deflation spiral. (40 Marks)

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ANSWERED

Manasvee Singh verified

Numerade educator

B) The rising international integration of economies has led to increasing competitive pressure. Suppose that, as a result, firms can more easily move some of their operations abroad, making them stronger when bargaining with their workers. As we saw in Chapter 7, weaker bargaining power on the part of workers is likely to have implications for the natural rate of unemployment. Explain and illustrate the short-run and medium-run impacts of this development using the IS-LM-PC model. In so doing, ex- plain globalisation’s impact on the Phillips Curve by tracing its effect back to the associated changes in Blanchard’s model of the labour market. (40 Marks)

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ANSWERED

Sanchit Jain verified

Numerade educator

what are the three different concepts of pareto efficiency?

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ANSWERED

Emily Anderson verified

Numerade educator

what are the concepts of pareto efficiency and competitive general equilibrium?

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