# There are six parts ( a through1 to this question . I We are interested analyzing the length of time unemployed workers are unemployed i. the length…

This is a qustion from my Econometrics class. pls help me !!!!!!

There are six parts ( a through1 to this question . I We are interested analyzing the length oftime unemployed workers are unemployed i.e . . the length of time it takes for them to find anew job . This is referred to as individual’s unemployment duration . Let I denote an individte annal’s unemploy ment duration . measured in months . Assume that each month the unemployedindividual has a constant probability O of finding a job , ending their spell of unemployment .funempBased on this information one can show that the probability of having an unemployment spellof exactly I months is given byPr ( I = 1 ) = ( 1 – 9 0( 6)It also can be shown that E ( I ) = 1 /0 and var ( I ) = ( 1 – @ ) / 0 ? We would like to estimate theprobability of finding a job in any given month i.e . . to estimate the parameter , BE @ = ( O . 1 )To do this . we use an independently and identically distributed ( in . d ) sample of the unemploy -ment durations of N unemployed individuals . ( T( a ) Write down the likelihood function of the data (T .( 6 ) Derive the maximum likelihood estimator ( ME ) of( C ) Will this ME of A be a consistent estimator of of Briefly explain your answer( 1 ) Derive the asymptotic distribution of the maximum likelihood estimator ( ME ) of A frompart ( 6 )Hint : I would suggest that you break up your answer into parts : First . characterize thelimiting distribution of the sample mean of the It’s next characterize the limiting distribution of your MI E estimator of A then use the latter to characterize the asymptotic distribution of this MIE estimator( e ) Show that the ME estimator of A is biased( f ) Is your ME estimator of @ biased upward or downward ?Hint : You may want to use Jensen’s Inequality See Slide S – 19 in Lecture S for a definitionof Jensen’s Inequality

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