Applied Quantitative Methods IIHomework Assignment # 2Use a software of your choice to answer the questions. Be sure to upload your final codeand your typed answers on Carmen.1. Estimation of...

Applied Quantitative Methods. / Econometrics


Applied Quantitative Methods II Homework Assignment # 2 Use a software of your choice to answer the questions. Be sure to upload your final code and your typed answers on Carmen. 1. Estimation of the probability of mortgage default. The probability of default is an important input in the calculation of expected losses in credit risk modeling: Expected Loss= (Probability of Default)*(Loss Given Default)*(Exposure at Default) The data for this assignment comes from the Consumer Finance Monthly dataset collected by OSU’s center for Human Resources Research. The dataset was collected from a nation- ally representative sample in five waves from February 2005 to December 2007. For the purpose of this assignment we focus on the performance of mortgage loans. Consider the following mortgage default model: defaulti = { 1 if Xiβ + �i > 0 0 otherwise (1) where X is the matrix of variables listed in the table below (excluding default) plus the intercept and β is a conformable parameter vector. Estimate the mortgage default model by the linear probability model (LPM), Probit, and Logit and present the coefficients in one table along with their standard errors. Present the marginal effects (or average partial effects) and their standard errors in a different table. Discuss/interpret the results. 2. Checking parameter stability. A common practice in the financial industry is to check the robustness/stability of pa- rameter estimates as new data is collected. This is generally done by re-estimating a model by dropping older data and adding new data and examining the robustness of the results to the change in the data. Redo question 1 by considering four waves at a time instead of the full dataset. Specifically, estimate the default model (1) by Logit using data from waves 1-4 and waves 2-5, respec- tively (wave indicator is available in the dataset). Report the marginal effects (or average partial effects) and their standard errors in one table. 1 marshall.624 Cross-Out 3.) ROC/AUC and model backtesting. Randomly allocate 70% of the data to a training dataset and the remaining to a validation (backtest) dataset. Use the training dataset to estimate the predicted probabilities of de- fault by Logit only. Report the Logit parameter estimates, their standard errors, the ROC curve and corresponding AUC. Use the estimated parameters from the training dataset to score the validation data; report the ROC curve and ACU for the validation dataset. 4.) Compute and report the result of the test that the model is uninformative, i.e pre- dictions from the Logit model are as good as random. 5.) Discuss/interpret the overall results (questions 1-5). Table 1: List of dependent and explanatory variables default =1 if household is delinquent for more than 90 days or filed for bankruptcy (dependent variable) num misspay number of missed payment on all debt pay to inc back-end monthly payments (all debt sources) as a percentage of household income ltv mortgage loan as a percentage of assessed value of the home unem rate state unemployment rate children number of children (younger than 18) in the family age age of household head age2 square of age of household head 2 cfm_default_data childrenwaveageunem_ratenum_misspaydefaultpay_to_incltv 01436.60121.739130485.7142857 21423.90020.335051665.3333333 01405.50021.704180155.7692308 11465.50027.692307721.4285714 01305.50014.364705979.1666667 01524.80012.616822450 01444.83072.530 01534.80025.39651071.5 01574.8001216.6666667 01524.80017.153628729.3333333 01694.80024.256336732.4324324 01613.91071.133333392.3076923 01493.90021.544401583.3333333 01553.90116.872998984.2105263 21775.40134.748409535.2 01615.4004.600997521.9230769 01505.41117.980703657.6923077 21375.40026.927072585 01455.40036.547619182.010582 01465.4117.92947582.3529412 014050014.241245166.6666667 014051120.3239465100 01405009.164383657.1428571 015250019.816723947.2222222 3135500150 01485.8009.625348746.6666667 01475.80023.881347463.6363636 01635.80060.843699323.0769231 01614.21028.331226358 21334.21020.482705256.6666667 11354.20017.43286587.5 11314.20019.480195126.4 31285.40025.961538563.3333333 11445.43021.827040242 01487.80048.659.0909091 11585.21069.428571476 31445.20162.412514.2857143 01473.90025.866666747.5 21506.9002141 21376.90046.458333367.6923077 01516.90094.90563986 31333.90013.893362474.8201439 11545.30034.043538784.8648649 01435.5004.918269260.7142857 11475.40016.147058838.8888889 11353.9001466.6666667 01553.90022.054054150 11293.90018.588.5714286 01305.40028.373819290.1554404 01645.40026.694915344.5714286 01445.40013.06134638.5 01544.8009.756440924 01534.8106.244392666 21376.91015.254237330.6 01556000.45571935.9259259 013760026.666666775.9259259 01565.4008.763888930 11325.43034.726027485.7142857 01424.10020.429829150 01574.1008.622754538 21424.10016.143790933.3333333 21414005.050921358.974359 01335.1004.857.1428571 21485.10015.782788480 01525.10019.011013267.4193548 01335.1001278.0487805 01485.10040.723014350 01725.10010.510 213550011.333333392.9411765 015356031.547911660 013753055.864626839.2 01633.90018.857142993.75 21475.40016.68900832.7272727 11456.9010.936037452.2222222 01525.40016.346153955.5555556 21405.40120.570291848.1818182 313750026.904761927.2 01415.1205.607476634 21455.11120.989143690 01725.40047.825701983.8709677 01625.40073.920073976.9230769 21425.40093.62549.3333333 01496.70153.3049041100 21564.30048.510048584.2105263 21494.20021.659883236 01515.90019.764705948.1818182 31385.90025.522252560.8695652 01555.90023.496862563.2 01383.9008.333333366.6666667 01303.90030.821917814 01456.70024.244186190.5263158 21376.7009.602473585.7142857 01226.74062.19512266.6666667 11383.90012.213017871.1111111 01553.90033.269230866.6666667 31393.9007.62584.9090909 01353.90117.167436743 11455.50028.353537661.1428571 01445.50017.721142821.6666667 11495.50019.591836750 01575.50023.6301373.7037037 51475.50020.357142965.8333333 01315.50026.822157455.5555556 11515.50017.090497732 01525.10011.944615444.4444444 01483.9009.516709535 01583.910047.441860572 21473.9009.770114920 01593.90013.333333323 01553.9014.014471854.1666667 01573.90127.161602219.4285714 31384.50018.481751871.4285714 01553.9006.592105340 31343.90036.568228129.2083333 01563.90023.372307758.3333333 11385.40010.151506266.6666667 01575.40010.047846910 01505.42119.12240194 01595.40034.478260958 01525.40143.844178191.4285714 21384.10128.332337156.5714286 01314.1008.842105366.6666667 21364.10018.256410366.6666667 31374.10014.450 01684.80120.692307763.3333333 01665.40015.769230841.6666667 21335.40014.017605176.4705882 01615.40017.356898911.1111111 21345.90139.525691778.3333333 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