Mid2wsol2 (1)

Mid2wsol2 (1) - 139-Spring 09 Midterm 2 Name DO NOT TURN...

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139-Spring 09 Midterm 2 Name .................................................................. DO NOT TURN OVER UNTIL TOLD TO DO SO Notes: 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 of production functions , a common activity of applied economists. A production function measures how a °rm transforms inputs (such as labor and physical capital) into output. The simplest production function is a Cobb-Douglas, where Y i = " i K ° 1 i L ° 2 i where Y is some measure of value-added in sales by °rm i (the value of output less the cost of material inputs), K i is a \$ measure of the °rm±s physical capital (e.g., machines) and L i is its \$ labor input. " i re²ects the productivity of the °rm (those with higher " i s produce more for given inputs). For estimation it is standard to take logs and add a constant. This gives log Y i = ° 0 + ° 1 log K i + ° 2 log L i + " i A °rm with a higher " i is said to have "higher productivity" or to be "more productive". We can then add other controls to the speci°cation to pick up additional e/ects which may matter. The data in the questions comes from French °rms surveyed in 1973, 1978, 1983 and 1988. 1

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1. 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 standard errors 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. Var log(sales) log(sales) log(sales) log(sales) log(capital) 0.505 0.506 0.417 0.422 (0.026) (0.027) (0.021) (0.022) log(labor) 0.467 0.472 0.509 0.505 (0.035) (0.037) (0.028) (0.030) log(R&D) - -0.006 0.053 0.061 (0.019) (0.013) (0.014) Computer - - -1.959 -1.970 (0.051) (0.054) Government - - - -0.028 (0.010) Constant 2.776 2.785 3.040 3.074 (0.081) (0.082) (0.062) (0.076) Obs. 890 890 890 890 R 2 0.91 0.91 0.96 0.96 Std. errors in parentheses are robust to heteroskedasticty In the °rst speci°cation (column (1)) you only include log(labor), log(capital) and a constant as regressors, with log(sales) as the dependent variable. Questions (a)-(c)(ii) all refer to the results in this column. (a) [3 points] Does the coe¢ cient on the constant have an interpretation in this regression? If you±re not sure, explain on what additional information your answer would depend. SOLUTION: Yes/maybe. It would re²ect 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 to know if there are °rms in this range of the data. As it happens both of these amounts are well within in the range of the data so the constant coe¢ cient does have some meaning here.
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