04 Jun Question ECON-UA 380 Topics in Econometrics Section: 011 Spring 2015
Question
ECON-UA 380 Topics in Econometrics
Section: 011 Spring 2015
Problem set 6,
Note: some of the questions below are based on the questions in the textbook, but may have been slightly
altered. Please answer the questions as they appear on this problem set.
1. Consider the following Cobb-Douglas production function
log Yi = 1 + 2 log L1i + 3 log L2i + 4 log Ki + ui
(1)
where Yi = output of rm i, L1i = production labor of rm i, L2i = non-production labor of rm i,
and Ki = capital stock of rm i. Suppose you instead use OLS to estimate
log Yi =
1
+
2 log L1i
+
3 log Ki
+ ui
(2)
using cross-section data on many rms.
(a) Will E[ 1 ] = 1 and E[ 2 ] = 2 ? Explain.
(b) You think that the error term may be heteroscedastic so you use White standard errors for 1 ,
2 , and 3 . Would they be correct? Explain.
(c) How will your answers to (a) and (b) change if it is known that L2 is an irrelevant input in the
production function? Explain.
2. Consider the setup from Question 1 and suppose that L2 is an irrelevant input in the production
function.
(a) Suppose you estimate model (1) by OLS using cross-sectional data on many rms. Will E[ 1 ] =
1 and E[ 2 ] = 2 ? Explain.
(b) You think that the error term may be heteroscedastic so you use White standard errors for 1 ,
2 , 3 , and 4 . Will the standard errors be correct? Explain.
(c) Suppose you estimate models (1) and (2) by OLS using cross-sectional data on many rms. You
test H0 : 2 = 1 against H1 : 2 6= 1 using the t-statistics
t=
and
t=
2 1
s.e.( 2 )
2
1
2 )
s.e.(
and the decision rule reject H0 if |t| > 1.96 (since 1.96 is the 5% critical value). Suppose H0
is true. Are you more likely, less likely, or equally likely to reject H0 using the rst t statistic
(involving 2 ) than using the second t statistic (involving 2 )?
(d) Consider the setup from part (c), but suppose that H0 is false. Are you more likely, less likely,
or equally likely to reject H0 using the rst t statistic (involving 2 ) than using the second t
statistic (involving 2 )?
(e) How will your answers to (a)(d) change if it is known that L2 is uncorrelated with L1 and K?
Explain.
1
3. Download the le incomedatafull.wf1 (or import incomedatafull.xlsx into your statistical software of choice). You will need to estimate the regression models
LOGIN Ci =
1
+
+
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