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Unformatted text preview: 139-Spring 09 Midterm 2Name ..................................................................DO NOT TURN OVER UNTIL TOLD TO DO SONotes:1. Use a calculator where necessary.2. Show your work, place your answers in the spaces provided and make use of the cheat sheet.3. If you want to make any additional assumptions to simplify a problem, please state them clearly.5.Keep verbal answers concise(no more than 4 sentences, and bullet points are &ne).5. There are 75 points in total (1 point per minute)Background:The &rst two questions in this exam are motivated by the estimation ofproductionfunctions, a common activity of applied economists.A production function measures how a &rmtransforms inputs (such as labor and physical capital) into output. The simplest production functionis a Cobb-Douglas, whereYi="iK&1iL&2iwhereYis some measure of value-added in sales by &rmi(the value of output less the cost of material inputs),Kiis a $ measure of the &rm¡s physical capital(e.g., machines) andLiis its $ labor input."ire¢ects the productivity of the &rm (those with higher"is produce more for given inputs).For estimation it is standard to take logs and add a constant.This giveslogYi=&+&1logKi+&2logLi+"iA &rm with a higher"iis said to have "higher productivity" or to be "more productive".We canthen add other controls to the speci&cation to pick up additional e/ects which may matter. The datain the questions comes from French &rms surveyed in 1973, 1978, 1983 and 1988.11. You begin by estimating three di/erent speci&cations using only data from a single year (1978).You use OLS and calculate heteroskedasticity robust standard errors. The coe¢ cients and standarderrors are shown in the following table. The sales variable has been converted to a value added form,and prior to take logs the sales, labor and capital variables were all measured in millions of $s.(1)(2)(3)(4)Dep. Varlog(sales)log(sales)log(sales)log(sales)log(capital)0.5050.5060.4170.422(0.026)(0.027)(0.021)(0.022)log(labor)0.4670.4720.5090.505(0.035)(0.037)(0.028)(0.030)log(R¡D)--0.0060.0530.061(0.019)(0.013)(0.014)Computer---1.959-1.970(0.051)(0.054)Government----0.028(0.010)Constant2.7762.7853.0403.074(0.081)(0.082)(0.062)(0.076)Obs.890890890890R20.910.910.960.96Std. errors in parentheses are robust to heteroskedastictyIn the &rst speci&cation (column (1)) you only include log(labor), log(capital) and a constant asregressors, with log(sales) as the dependent variable.Questions (a)-(c)(ii) all refer to the resultsin this column.(a) [3 points] Does the coe¢ cient on the constant have an interpretation in this regression?Ifyou£re not sure, explain on what additional information your answer would depend.SOLUTION: Yes¤maybe. It would re¥ect expected logsales of a &rm having zero logcapital (i.e.,capital = $1M) and zero loglabor (i.e., labor = $1M). So to know whether to interpret it you need toknow if there are &rms in this range of the data. As it happens both of these amounts are well withinin the range of the data so the constant coe¢ cient does have some meaning here.in the range of the data so the constant coe¢ cient does have some meaning here....
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This note was uploaded on 08/03/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.
- Spring '08