Hi all,
This is my first post here in this forum, so please excuse potential newcomer mistakes. I estimate annual data for a panel with 138 countries from 1970 to 2011. I have two approaches. First, I collapse my data to 5 year averages. Second, I estimate with the annual data. I estimate both times a fixed effect model with "xtreg" and my stata Version is 12.1.
My question is about the Fair and Dominguez (1991) age coefficients and how to get a confidence interval for the underlying cohort coefficients. I have 17 cohort, while my cohorts are defined as 0-4, 5-9,...80+ from the UN. I express each cohort as percentage of the country’s total population I restrict all my cohort coefficients to lie on a third order polynomial, while all my cohort coefficients (alpha_j with j=1,...,17) sum to zero. Alpha_j is defined as:
alpha_j= gamma_0 + gamma_1*j + gamma_2*j2 + gamma_3*j3.
with the zero sum restriction I can recover gamma_0 by
gamma_0 = -(gamma_1/J) *sum(j) - (gamma_2/J) * sum(j2) - (gamma_3/J) * sum(j3).
Finally, the variables for the coefficients gamma_1, gamma_2 and gamma_3 are defined as
Z1_t = sum_j=1 ^J (jp_jt) - (1/J)*sum_j=1 ^J(j)* sum_j=1 ^J (p_jt)
Z2_t = sum_j=1 ^J (j2p_jt) - (1/J)*sum_j=1 ^J(j2)* sum_j=1 ^J (p_jt)
Z3_t = sum_j=1 ^J (j3p_jt) - (1/J)*sum_j=1 ^J(j3)* sum_j=1 ^J (p_jt)
Hence, my model ooks like
y_it = bet_0 + gamma_1 *Z1_t + gamma_2 * Z2_t + gamma_3 * Z3_t + X_it*B_i + u_it
with X_it*B_i as a vector for the control variables.
Since the Z's don't have an intuitive interpretation, i have to interpret the alphas. Unfortunately, I have no idea how to obtain confidence intervals for them. I assume that I can’t' just use the standard errors of the Z coefficients since I need all three Z's jointly to obtain my alphas.
I hope I was clear enogh. I would be very grateful, if you could help me with my problem.
Best
Janis Riedl
This is my first post here in this forum, so please excuse potential newcomer mistakes. I estimate annual data for a panel with 138 countries from 1970 to 2011. I have two approaches. First, I collapse my data to 5 year averages. Second, I estimate with the annual data. I estimate both times a fixed effect model with "xtreg" and my stata Version is 12.1.
My question is about the Fair and Dominguez (1991) age coefficients and how to get a confidence interval for the underlying cohort coefficients. I have 17 cohort, while my cohorts are defined as 0-4, 5-9,...80+ from the UN. I express each cohort as percentage of the country’s total population I restrict all my cohort coefficients to lie on a third order polynomial, while all my cohort coefficients (alpha_j with j=1,...,17) sum to zero. Alpha_j is defined as:
alpha_j= gamma_0 + gamma_1*j + gamma_2*j2 + gamma_3*j3.
with the zero sum restriction I can recover gamma_0 by
gamma_0 = -(gamma_1/J) *sum(j) - (gamma_2/J) * sum(j2) - (gamma_3/J) * sum(j3).
Finally, the variables for the coefficients gamma_1, gamma_2 and gamma_3 are defined as
Z1_t = sum_j=1 ^J (jp_jt) - (1/J)*sum_j=1 ^J(j)* sum_j=1 ^J (p_jt)
Z2_t = sum_j=1 ^J (j2p_jt) - (1/J)*sum_j=1 ^J(j2)* sum_j=1 ^J (p_jt)
Z3_t = sum_j=1 ^J (j3p_jt) - (1/J)*sum_j=1 ^J(j3)* sum_j=1 ^J (p_jt)
Hence, my model ooks like
y_it = bet_0 + gamma_1 *Z1_t + gamma_2 * Z2_t + gamma_3 * Z3_t + X_it*B_i + u_it
with X_it*B_i as a vector for the control variables.
Since the Z's don't have an intuitive interpretation, i have to interpret the alphas. Unfortunately, I have no idea how to obtain confidence intervals for them. I assume that I can’t' just use the standard errors of the Z coefficients since I need all three Z's jointly to obtain my alphas.
I hope I was clear enogh. I would be very grateful, if you could help me with my problem.
Best
Janis Riedl
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