Cobb-Douglas production function with expenditures rather than unitsDeriving the translog production functionHow to derive cubic cost function from a problem of constrained optimization?Marshallian demand helpCES production function estimationHow do we estimate production functions?What's the relation between deadweight-loss and alpha in Cobb-Douglas?Consumer preference and price in the Cobb-Douglas functionRegression on derived consumer preferenceNested CES Production FunctionLinking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated?Estimation of a Non-linear production function with Non-linear least squares
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Cobb-Douglas production function with expenditures rather than units
Deriving the translog production functionHow to derive cubic cost function from a problem of constrained optimization?Marshallian demand helpCES production function estimationHow do we estimate production functions?What's the relation between deadweight-loss and alpha in Cobb-Douglas?Consumer preference and price in the Cobb-Douglas functionRegression on derived consumer preferenceNested CES Production FunctionLinking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated?Estimation of a Non-linear production function with Non-linear least squares
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$begingroup$
I want to estimate a standard Cobb-Douglas production function of the form
$ Y=AK^alphaL^beta$. However, I only have data on labour expenditures, not units of labour. I don't have data on the price of labour $w$ either, so I can't back out the units of labour from expenditures. Is it okay to estimate the production function (in a GMM regression framework) using labour expenditures instead of units of labour?
microeconomics econometrics applied-econometrics
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
$endgroup$
add a comment |
$begingroup$
I want to estimate a standard Cobb-Douglas production function of the form
$ Y=AK^alphaL^beta$. However, I only have data on labour expenditures, not units of labour. I don't have data on the price of labour $w$ either, so I can't back out the units of labour from expenditures. Is it okay to estimate the production function (in a GMM regression framework) using labour expenditures instead of units of labour?
microeconomics econometrics applied-econometrics
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
$endgroup$
add a comment |
$begingroup$
I want to estimate a standard Cobb-Douglas production function of the form
$ Y=AK^alphaL^beta$. However, I only have data on labour expenditures, not units of labour. I don't have data on the price of labour $w$ either, so I can't back out the units of labour from expenditures. Is it okay to estimate the production function (in a GMM regression framework) using labour expenditures instead of units of labour?
microeconomics econometrics applied-econometrics
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
$endgroup$
I want to estimate a standard Cobb-Douglas production function of the form
$ Y=AK^alphaL^beta$. However, I only have data on labour expenditures, not units of labour. I don't have data on the price of labour $w$ either, so I can't back out the units of labour from expenditures. Is it okay to estimate the production function (in a GMM regression framework) using labour expenditures instead of units of labour?
microeconomics econometrics applied-econometrics
microeconomics econometrics applied-econometrics
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
asked 9 hours ago
leecarvalloleecarvallo
583 bronze badges
583 bronze badges
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Sure you can, just that your interpretation of your variables in your analysis changes however. In this case you are analyzing how investment in differing factors of production affect output.
I'd recommend that you may want to estimate a more flexible functional form like the Translog Production Function to check if your function is CES instead of just a simple cobb-douglas.
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
$endgroup$
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
1
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
add a comment |
$begingroup$
If prices are constant than quantities are proportional to expenditures. Consider :
$$ Y=AK^alphaL^beta = A(fracE_Kr)^alpha(fracE_Lw)^beta $$
$$ = (fracAr^alpha w^alpha)(E_K)^alpha(E_L)^beta $$
$$ = tildeA(E_K)^alpha(E_L)^beta $$
If prices don't vary too much this may be an acceptable approximation. However, notice that this is a log-additive function:
$$ lnY_t = y_t = a - alpha cdot r_t - beta cdot w_t + alpha cdot ln (E_K,t) + beta cdot ln (E_L,t)$$
If you estimate a regression with time fixed effects, it absorbs the $a - alpha cdot r_t - beta cdot w_t $ term and your expenditures regressions give the same results for $alpha$ and $beta$ as if you knew the quantities. If you want to know $alpha$ or $beta$ this is fine, but you won't identify $a$ this way.
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Sure you can, just that your interpretation of your variables in your analysis changes however. In this case you are analyzing how investment in differing factors of production affect output.
I'd recommend that you may want to estimate a more flexible functional form like the Translog Production Function to check if your function is CES instead of just a simple cobb-douglas.
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
$endgroup$
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
1
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
add a comment |
$begingroup$
Sure you can, just that your interpretation of your variables in your analysis changes however. In this case you are analyzing how investment in differing factors of production affect output.
I'd recommend that you may want to estimate a more flexible functional form like the Translog Production Function to check if your function is CES instead of just a simple cobb-douglas.
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
$endgroup$
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
1
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
add a comment |
$begingroup$
Sure you can, just that your interpretation of your variables in your analysis changes however. In this case you are analyzing how investment in differing factors of production affect output.
I'd recommend that you may want to estimate a more flexible functional form like the Translog Production Function to check if your function is CES instead of just a simple cobb-douglas.
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
$endgroup$
Sure you can, just that your interpretation of your variables in your analysis changes however. In this case you are analyzing how investment in differing factors of production affect output.
I'd recommend that you may want to estimate a more flexible functional form like the Translog Production Function to check if your function is CES instead of just a simple cobb-douglas.
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
answered 6 hours ago
EconJohn♦EconJohn
3,5432 gold badges11 silver badges41 bronze badges
3,5432 gold badges11 silver badges41 bronze badges
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
1
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
add a comment |
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
1
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
$begingroup$
Ok, thanks! And thanks for the recommendation! The translog production function is distinct from just log transforming a regular Cobb-Douglas production function, right?
$endgroup$
– leecarvallo
6 hours ago
1
1
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
$begingroup$
@leecarvallo yep its different, see this here for more details. economics.stackexchange.com/questions/26144/… be sure to accept and upvote this answer if it answers your question. It helps move the site out of beta.
$endgroup$
– EconJohn♦
6 hours ago
add a comment |
$begingroup$
If prices are constant than quantities are proportional to expenditures. Consider :
$$ Y=AK^alphaL^beta = A(fracE_Kr)^alpha(fracE_Lw)^beta $$
$$ = (fracAr^alpha w^alpha)(E_K)^alpha(E_L)^beta $$
$$ = tildeA(E_K)^alpha(E_L)^beta $$
If prices don't vary too much this may be an acceptable approximation. However, notice that this is a log-additive function:
$$ lnY_t = y_t = a - alpha cdot r_t - beta cdot w_t + alpha cdot ln (E_K,t) + beta cdot ln (E_L,t)$$
If you estimate a regression with time fixed effects, it absorbs the $a - alpha cdot r_t - beta cdot w_t $ term and your expenditures regressions give the same results for $alpha$ and $beta$ as if you knew the quantities. If you want to know $alpha$ or $beta$ this is fine, but you won't identify $a$ this way.
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
$endgroup$
add a comment |
$begingroup$
If prices are constant than quantities are proportional to expenditures. Consider :
$$ Y=AK^alphaL^beta = A(fracE_Kr)^alpha(fracE_Lw)^beta $$
$$ = (fracAr^alpha w^alpha)(E_K)^alpha(E_L)^beta $$
$$ = tildeA(E_K)^alpha(E_L)^beta $$
If prices don't vary too much this may be an acceptable approximation. However, notice that this is a log-additive function:
$$ lnY_t = y_t = a - alpha cdot r_t - beta cdot w_t + alpha cdot ln (E_K,t) + beta cdot ln (E_L,t)$$
If you estimate a regression with time fixed effects, it absorbs the $a - alpha cdot r_t - beta cdot w_t $ term and your expenditures regressions give the same results for $alpha$ and $beta$ as if you knew the quantities. If you want to know $alpha$ or $beta$ this is fine, but you won't identify $a$ this way.
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
$endgroup$
add a comment |
$begingroup$
If prices are constant than quantities are proportional to expenditures. Consider :
$$ Y=AK^alphaL^beta = A(fracE_Kr)^alpha(fracE_Lw)^beta $$
$$ = (fracAr^alpha w^alpha)(E_K)^alpha(E_L)^beta $$
$$ = tildeA(E_K)^alpha(E_L)^beta $$
If prices don't vary too much this may be an acceptable approximation. However, notice that this is a log-additive function:
$$ lnY_t = y_t = a - alpha cdot r_t - beta cdot w_t + alpha cdot ln (E_K,t) + beta cdot ln (E_L,t)$$
If you estimate a regression with time fixed effects, it absorbs the $a - alpha cdot r_t - beta cdot w_t $ term and your expenditures regressions give the same results for $alpha$ and $beta$ as if you knew the quantities. If you want to know $alpha$ or $beta$ this is fine, but you won't identify $a$ this way.
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
$endgroup$
If prices are constant than quantities are proportional to expenditures. Consider :
$$ Y=AK^alphaL^beta = A(fracE_Kr)^alpha(fracE_Lw)^beta $$
$$ = (fracAr^alpha w^alpha)(E_K)^alpha(E_L)^beta $$
$$ = tildeA(E_K)^alpha(E_L)^beta $$
If prices don't vary too much this may be an acceptable approximation. However, notice that this is a log-additive function:
$$ lnY_t = y_t = a - alpha cdot r_t - beta cdot w_t + alpha cdot ln (E_K,t) + beta cdot ln (E_L,t)$$
If you estimate a regression with time fixed effects, it absorbs the $a - alpha cdot r_t - beta cdot w_t $ term and your expenditures regressions give the same results for $alpha$ and $beta$ as if you knew the quantities. If you want to know $alpha$ or $beta$ this is fine, but you won't identify $a$ this way.
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
answered 6 hours ago
BKayBKay
12.6k2 gold badges24 silver badges61 bronze badges
12.6k2 gold badges24 silver badges61 bronze badges
add a comment |
add a comment |
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