Provide answers to all questions please.,,,
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3. Identify a policy that would provide additional liability coverage for your Homeowners, Auto, and Personal Activity Liability Loss Exposures. Estimate the premium for a $1,000,000 limit of this coverage. Identify six major insurance policies businesses use to manage risks. Identify ve career opportunities in risk management and insurance and list three major insurance companies. 5. Suppose Y = Bo + B1X1 + B2X2 + U, where X1, X2, and U are each independent and identically distributed; E[U] = 0; X1 is uncorrelated with U and X2 is uncorrelated with U but corr(X1, X2) # 0. A researcher is interested in estimating B1 with OLS. Define the following notation: . Vi = V(X1) > 0 and V2 = V(X2) > 0 I . o' = V(U) > 0 . T = corr (X1, X2) . n is the sample size The researcher considers two choices: . short regression: Use OLS to estimate Y = Bo + BiXi + U . long regression: Use OLS to estimate Y = Bo + 81X1 + BX2+ U (a) (4 points) Express the asymptotic mean squared error of the OLS estimator of #, if the researcher uses the short regression in terms of 81, 8,, and the notation used above. (b) (4 points) Express the asymptotic mean squared error of the OLS estimator of & if the researcher uses the long regression in terms of 81, 62, and the notation used above. (c) (4 points) Suppose parameters take the following values: . Vi = VI - o' = 81 = =1 . n = 100 If the researcher wants to minimize MSE, for which values of r should the researcher use the short regression, for which the long regression, and for which would they have the same MSE?where 4, NI - N(0. 1) X = Xi + V, where V ~ N(0, 4). U - Uniform(-5,5). and X1: V, and U are independent, Hint I: a N(0, 4) random variable has standard deviation of 8. In State, you can generale a normal random variable with mean 0 and standard deviation of : using the command rnormal (0. 2)./ /Hint #: Uniform(-5,5) indicates a uniform distribution between -5 and 5. In State, you can generate a uniform distribution between Q and I using the command runtform()./ Simulate this model 10,000 times in State. Hint: get your code working with fewer simula- tions, so you can correct errors quickly. Once your code is ready, change it to simulate 10, 900 times./ For each simulation, generate a data set with n = 100 observations, Then, for each sample, estimate . 8,, and , with OLS, calling your estimates , , andh. Create two sets of estimates for cach simulation: one based on the first 5 observations in the data set, and one based on the full 100 observations. (n) (4 points) Define a new variable 7 = 1 x 8. Estimate y using + = $1 x p, within Each simulation, for each set of estimates. Create a table like the following with average estimates of on, 52, and + based on 5 observations or 100 observations: 5 obs 100 obs (b) (4 points) Which of the values in this table are close to the true values of By. py, and y? For each value (whether close or not), based on what we've learned in class, do we have a good remion to expect that the estimate would be close to the truth? If so, what is that reason? (c) (# points) Now, for each regression, test Ho : 81 - 2 against Hi : A # 2 Conduct this test in two ways: first with a small-sample t-test, and second with the asymptotic t-test For each test, how often do we reject the mull at a 5%% significance level? Create tables like the following with the critical values for the tests and the fraction of observations in which we reject the null hypothesis. Critical values 5 obs | 100 obs Small sample Asymptotic Fraction of rejections 5 obs | 100 obs Small sample AsymptoticQuestion 2: Production a. Spiralhefte Ltd is in the college notebook business. With q representing the amount of output (i.e. notebooks) and :r5 and x! the amounts of capital and labour used in the production process, its production function f(.) takes the following form: q = f(xc,xl) = 4:51:53, where parameters a and b are both positive numbers (a>0, b>0). What is the marginal product of inputs xc and x5? Under what condition is the marginal product of capital decreasing as the amount of that factor alone is varied? b. Consider a representative firm that produces output q in a perfectly competitive market using inputs L and K according to the following production function: q = f(K,L)= v'LJiK. The output price is p, and prices of inputs are w (for input L) and r (for input K) respectively. Illustrate that the conditional input demand functions for inputs L and K are downward sloping. [You may assume that second-order conditions are met, and that an internal solution exists. ] c. Consider a representative rm that produces output q in a perfectly competitive market using inputs L and K according to the following production function: q = f(K,L)= L2 . WfK (where '.' signies a multiplication). The output price is p, and prices of inputs are w (for input L) and r (for input K) reapectively. Is this productlon function characterised by increasing, decreasing or constant returns to scale? Would your answer change if the production function was instead given by: q = L2 + 4K? Explain your
