1 Matlab Mincer Wage Earnings Equation with Experience, Education and Gamma Shocks

Go to the MLX, M, PDF, or HTML version of this file. Go back to fan’s MEconTools Package, Matlab Code Examples Repository (bookdown site), or Math for Econ with Matlab Repository (bookdown site).

1.1 Define a Wage Equation with Partial Income for Part-time Workss

Individuals might work part or full time. Define a mincer wage equation that is a function of experienc, education and other individual characteristics. This is partly based on the wage equation from Hai and Heckman (2017).

First define parameters.

% cognitive and non-cognitive latent types
theta_cogntv = 0.1;
theta_noncog = 0.1;
% parameters mapping latent types to wage
COEF_alpha_cog_wage_hsh = 0.0529;
COEF_alpha_cog_wage_clg = 0.0529;
COEF_alpha_cog_wage_grd = 0.1433;
COEF_alpha_ncg_wage_hsh = 0.0275;
COEF_alpha_ncg_wage_clg = 0.0512;
COEF_alpha_ncg_wage_grd = 0.0892;
% Experience
COEF_beta_psi_0 = 1.8884;
COEF_beta_psi_k = 0.0767;
COEF_beta_psi_kk = -0.2683;
% Education
COEF_beta_psi_e0 = 0.0465;
COEF_beta_w_e_1 = 0.1432;
COEF_beta_w_e_2 = 0.1435;
COEF_beta_w_e_3 = 0.2806;
% for part time
COEF_beta_w_part_0 = -0.0082;
COEF_beta_w_part_1 = -0.4863;

Second define the log wage equation. This wage equation is a function of the parameters defined above, and also Education (ED), experience (EX) and the wage shcok (EPS_w).

% Log of wage
f_log_psi = @(ED, EX, EPS_w) ...
((COEF_alpha_cog_wage_hsh.*theta_cogntv + COEF_alpha_ncg_wage_hsh.*theta_noncog).*(ED < 12) ...
+ (COEF_alpha_cog_wage_clg.*theta_cogntv + COEF_alpha_ncg_wage_clg.*theta_noncog).*(ED >= 12).*(ED < 16) ...
+ (COEF_alpha_cog_wage_grd.*theta_cogntv + COEF_alpha_ncg_wage_grd.*theta_noncog).*(ED >= 16) ...
+ COEF_beta_psi_0 ...
+ COEF_beta_psi_k.*EX ...
+ COEF_beta_psi_kk.*(EX.^2/100) ...
+ COEF_beta_psi_e0.*(ED - 12) ...
+ COEF_beta_w_e_1.*(ED == 12) ...
+ COEF_beta_w_e_2.*(ED > 12).*(ED < 16) ...
+ COEF_beta_w_e_3.*(ED >= 16) ...
+ EPS_w);

Third, define wage, which might differ depending on work status as well as schooling status. D_e is schooling or not, which can take values of 0 or 1. D_k is work status, which can take values or 0, 0.5 (part-time work) and 1 (full-time work).

% Per hour wage considering part time, part time wage differ if also schooling
f_hr_wage = @(D_e, D_k, ED, EX, EPS_w) ...
exp(f_log_psi(ED, EX, EPS_w)).*exp((D_k==0.5).*(COEF_beta_w_part_0 + COEF_beta_w_part_1.*D_e));
% Total wage
f_wage = @(D_e, D_k, ED, EX, EPS_w) ...
f_hr_wage(D_e, D_k, ED, EX, EPS_w).*(2080.*(D_k == 1) + 1040.*(D_k == 0.5) + 0.*(D_k == 0));

Fourth, test the wage equation by calling it with different work and schooling choices, along with different education, experience, and shock levels.

% no experience, education, not school, not work
disp(['f_wage(0,0,0,0,0)=' num2str(f_wage(0,0,0,0,0))]);

f_wage(0,0,0,0,0)=0

% no experience, education, part-time
disp(['f_wage(0,0.5,0,0,0)=' num2str(f_wage(0,0.5,0,0,0))]);

f_wage(0,0.5,0,0,0)=3933.229

% no experience, education, full-time
disp(['f_wage(0,1,0,0,0)=' num2str(f_wage(0,1,0,0,0))]);

f_wage(0,1,0,0,0)=7931.2281

With the anonymous function defined, we can supply a vector of education values (as a column), and a vector of experience levles (as a row), and generate a matrix of wages for full-time workers, simulated at one particular shock level. Graph using FF_GRAPH_GRID from MEconTools.

The graph shows that higher education corresponds to higher wages, there are different levels by education tiers, and there is a quadratic structure to experience

% 1 to 16 years of educations
ar_edu = 1:1:20;
% 1 to 20 years of experiences
ar_exp = 1:1:20;