# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Environment # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Import libraries library(tidyverse) library(magrittr) library(janitor) library(rio) library(rlist) library(boot) library(broom) library(purrr) library(parallel) library(ebal) library(rootSolve) library(stargazer) library(haven) library(latex2exp) library(estimatr) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Constants # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Define basic constants for identification num_days <- 20 hourly_rate <- 50 max_hours <- 3 param_initial <- list( delta = 0.997, p_B = (hourly_rate / num_days) / 60 ) # Define constants for balance us_adults <- 255200373 avg_income <- 43.01 avg_college <- 0.3009 avg_male <- 0.4867 avg_white <- 0.73581 avg_age <- 47.6 avg_usage <- 186 # Define common random seed for bootstrap replicability size <- 2000 seed <- 5 RNGkind("L'Ecuyer-CMRG") set.seed(seed) # Define colors for plots maroon <- '#94343c' grey <- '#848484' skyblue <- '#87CEEB' black <- '#000000' deepskyblue <- '#B0C4DE' # Define base changes for parameters to be ported to tex # Note : tex names should not have symbols (_ or - or ,) and should not have numbers constants <- c('delta', 'p_B') name_changes <- list("omega" = "omegause", "omega_est" = "omegahat", "tau_L" = "tauL", "avg_use" = "avguse", "rho" = "rhohat", "lambda" = "lambdahat", "rho_res" = "rhoreshat", "lambda_res" = "lambdareshat", "delta" = "deltahat", "p_B" = "pB", "F_B" = "FB", "tau_B_1" = "tauBone", "tau_B_2" = "tauBtwo", "tau_B_3" = "tauBthree", "tau_B_4" = "tauBfour", "tau_B_5" = "tauBfive", "tau_tilde_B_3_2" = "tautildeBthreetwo", "tau_tilde_B_2_2" = "tautildeBtwotwo", "tau_tilde_L_3_2" = "tautildeLthreetwo", "tau_tilde_L_2_2" = "tautildeLtwotwo", "tau_L_2" = "tauLtwo", "tau_L_y" = "tauLy", "tau_B_y" = "tauBy", "tau_B_2_full" = "tauBtwofull", "tau_L_3" = "tauLthree", "mispredict" = "mispredict", "x_tilde" = "xtilde", "x_ss" = "xss", "limit_effect_last_week" = "limiteffectlastweek", "d_L" = "dL", "d_CL" = "dCL", "tau_tilde_B" = "tautildeB", "tau_tilde_L" = "tautildeL", "x_tilde_2_B" = "xtildetwoB", "v_B" = "vB", "v_L" = "vL", "attritionrate" = "attritionrate", "true_tau_tilde_L" = "truetautildeL", "MPL_S2" = "MPLStwo", "number_people_opted_out" = "numberpeopleoptedout", "percent_opted_out" = "percentoptedout", "gamma_spec_omega_hour" = "gammaspecomegahour", "alpha" = "alphahat", "alpha_res" = "alphares", "eta" = "etahat", "zeta" = "zetahat", "eta_hour" = "etahour", "zeta_hour" = "zetahour", "eta_res" = "etares", "zeta_res" = "zetares", "eta_res_hour" = "etareshour", "zeta_res_hour" = "zetareshour", "tau_B_2_desired" = "tauBtwodesired", "lambdarho" = "lambdarho", "lambdarhosquared" = "lambdarhosquared", "tauBthreehour" = "tauBthreehour", "pcttaubtwo" = "pcttaubtwo", "naivete" = "naivete", "gamma_L_effect" = "gammaLeffect", "gamma_tilde_L_effect" = "gammatildeLeffect", "gamma_L" = "gammaL", "gamma_tilde_L" = "gammatildeL", "gamma_B" = "gammaB", "gamma_tilde_B" = "gammatildeB", "gamma" = "gammacap", "gamma_tilde" = "gammatilde", "naivete_hour" = "naivetehour", "gamma_hour" = "gammahour", "gamma_tilde_B_hour" = "gammatildeBhour", "gamma_tilde_L_hour" = "gammatildeLhour", "gamma_tilde_hour" = "gammatildehour", "gamma_L_hour" = "gammaLhour", "gamma_B_hour" = "gammaBhour", "gamma_L_effect_omega_hour" = "gammaLeffectomegahour", "gamma_L_omega_hour" = "gammaLomegahour", "underestimatetemp" = "underestimatetemp", "attritionrate" = "attritionrate", "gamma_tilde_L_effect_omega" = "gammatildeLeffectomega", "gamma_L_effect_omega" = "gammaLeffectomega", "gamma_tilde_L_omega" = "gammatildeLomega", "gamma_L_omega" = "gammaLomega", "gamma_tilde_L_multiple" = "gammatildeLmultiple", "gamma_L_multiple" = "gammaLmultiple", "gamma_tilde_B_multiple" = "gammatildeBmultiple", "gamma_B_multiple" = "gammaBmultiple", "gamma_tilde_L_multiple_hour" = "gammatildeLmultiplehour", "gamma_L_multiple_hour" = "gammaLmultiplehour", "gamma_tilde_B_multiple_hour" = "gammatildeBmultiplehour", "gamma_B_multiple_hour" = "gammaBmultiplehour", "naivete_res" = "naiveteres", "underestimatetemp_res" = "underestimatetempres", "gamma_L_effect_res" = "gammaLeffectres", "gamma_tilde_L_effect_res" = "gammatildeLeffectres", "gamma_L_res" = "gammaLres", "gamma_B_res" = "gammaBres", "naivete_res_hour" = "naivetereshour", "gamma_tilde_L_effect_res_hour" = "gammatildeLeffectreshour", "gamma_L_res_hour" = "gammaLreshour", "gamma_B_res_hour" = "gammaBreshour", "gamma_L_effect_omega_res_hour" = "gammaLeffectomegareshour", "gamma_L_omega_res_hour" = "gammaLomegareshour", "gamma_tilde_L_effect_omega_res" = "gammatildeLeffectomegares", "gamma_L_effect_omega_res" = "gammaLeffectomegares", "gamma_L_omega_res" = "gammaLomegares", "gamma_L_multiple_res" = "gammaLmultipleres", "gamma_B_multiple_res" = "gammaBmultipleres", "gamma_L_effect_multiple_res" = "gammaLeffectmultipleres", "gamma_tilde_L_effect_multiple_res" = "gammatildeLeffectmultipleres", "gamma_L_multiple_res_hour" = "gammaLmultiplereshour", "gamma_B_multiple_res_hour" = "gammaBmultiplereshour", "gamma_L_effect_multiple_res_hour" = "gammaLeffectmultiplereshour", "gamma_tilde_L_effect_multiple_res_hour" = "gammatildeLeffectmultiplereshour", "x_ss_L_effect" = "xssLeffect", "x_ss_L_effect_eta_high" = "xssLeffectetahigh", "x_ss_L_effect_eta_low" = "xssLeffectetalow", "x_ss_B" = "xssB", "delta_x_cap" = "deltaxcap", "delta_x_cap_us" = "deltaxcapus", "delta_x_tilde_L" = "deltaxtildeL", "delta_x_tilde_L_us" = "deltaxtildeLus", "delta_x_tilde_B" = "deltaxtildeB", "delta_x_tilde_B_us" = "deltaxtildeBus", "x_ss_L" = "xssL", "mispredicthour" = "mispredicthour", "delta_x_L_multiple" = "deltaxLmultiple", "delta_B_multiple" = "deltaBmultiple", "delta_x_cap_omega" = "deltaxcapomega", "delta_x_L_omega" = "deltaxLomega", "x_ss_L_effect_res" = "xssLeffectres", "x_ss_L_effect_eta_high_res" = "xssLeffectetahighres", "x_ss_L_effect_eta_low_res" = "xssLeffectetalowres", "x_ss_B_res" = "xssBres", "delta_x_cap_res" = "deltaxcapres", "delta_x_cap_us_res" = "deltaxcapusres", "delta_x_tilde_L_res" = "deltaxtildeLres", "delta_x_tilde_L_us_res" = "deltaxtildeLusres", "delta_x_tilde_B_res" = "deltaxtildeBres", "delta_x_tilde_B_us_res" = "deltaxtildeBusres", "x_ss_L_res" = "xssLres", "delta_x_cap_multiple_res" = "deltaxcapmultipleres", "delta_x_L_multiple_res" = "deltaxLmultipleres", "delta_B_multiple_res" = "deltaBmultipleres", "delta_x_cap_omega_res" = "deltaxcapomegares", "delta_x_L_omega_res" = "deltaxLomegares", "delta_x_temptation" = "deltaxtemptation", "delta_x_naivete" = "deltaxnaivete", "delta_x_habit" = "deltaxhabit", "x_ss_temptation" = "xsstemptation", "x_ss_temptation_eta_high" = "xsstemptationetahigh", "x_ss_temptation_eta_low" = "xsstemptationetalow", "x_ss_naivete" = "xssnaivete", "x_ss_naivete_eta_high" = "xssnaiveteetahigh", "x_ss_naivete_eta_low" = "xssnaiveteetalow", "x_ss_habit" = "xsshabit", "x_ss_habit_eta_high" = "xsshabitetahigh", "x_ss_habit_eta_low" = "xsshabitetalow", "x_ss_habit_est" = "xsshabitest", "x_ss_habit_temptation" = "xsshabittemptation", "x_ss_habit_temptation_eta_high" = "xsshabittemptationetahigh", "x_ss_habit_temptation_eta_low" = "xsshabittemptationetalow", "x_ss_zero_temp" = "xsszerotemp", "delta_x_temptation_res" = "deltaxtemptationres", "delta_x_naivete_res" = "deltaxnaiveteres", "delta_x_habit_res" = "deltaxhabitres", "x_ss_temptation_res" = "xsstemptationres", "x_ss_temptation_eta_high_res" = "xsstemptationetahighres", "x_ss_temptation_eta_low_res" = "xsstemptationetalowres", "x_ss_naivete_res" = "xssnaiveteres", "x_ss_naivete_eta_high_res" = "xssnaiveteetahighres", "x_ss_naivete_eta_low_res" = "xssnaiveteetalowres", "x_ss_habit_res" = "xsshabitres", "x_ss_habit_eta_high_res" = "xsshabitetahighres", "x_ss_habit_eta_low_res" = "xsshabitetalowres", "x_ss_habit_est_res" = "xsshabitestres", "x_ss_habit_temptation_res" = "xsshabittemptationres", "x_ss_habit_temptation_eta_high_res" = "xsshabittemptationetahighres", "x_ss_habit_temptation_eta_low_res" = "xsshabittemptationetalowres", "x_ss_i_data" = "xssidata", "x_ss_spec" = "xssSpec", "tau_L_2_signed" = "tauLtwosignednotnice", "intercept_spec" = "interceptspec", "intercept_spec_hour" = "interceptspechour", "gamma_tilde_spec" = "gammatildespec", "gamma_spec" = "gammaspec", "delta_x_spec" = "deltaxspec", "gamma_tilde_spec_hour" = "gammatildespechour", "gamma_spec_hour" = "gammaspechour", "intercept_het_L_effect" = "intercepthetLeffect", "intercept_het_L_effect_eta_high" = "intercepthetLeffectetahigh", "intercept_het_L_effect_eta_low" = "intercepthetLeffectetalow", "intercept_het_B" = "intercepthetB", "intercept_het_L" = "intercepthetL", "intercept_het_B_hour" = "intercepthetBhour", "intercept_het_L_hour" = "intercepthetLhour", "intercept_het_L_effect_hour" = "intercepthetLeffecthour", "gamma_spec_omega_hour" = "gammaspecomegahour", "intercept_spec_omega_hour" = "interceptspecomegahour", "intercept_het_L_effect_omega_hour" = "intercepthetLeffectomegahour", "intercept_het_L_omega_hour" = "intercepthetLomegahour", "intercept_het_B_multiple" = "intercepthetBmultiple", "intercept_het_L_multiple" = "intercepthetLmultiple", "intercept_het_L_effect_omega" = "intercepthetLeffectomega", "intercept_het_L_omega" = "intercepthetLomega", "x_ss_spec_res" = "xssSpecres", "intercept_spec_res" = "interceptspecres", "intercept_spec_res_hour" = "interceptspecreshour", "gamma_tilde_spec_res" = "gammatildespecres", "gamma_spec_res" = "gammaspecwres", "delta_x_spec_res" = "deltaxspecres", "gamma_tilde_spec_res_hour" = "gammatildespecreshour", "gamma_spec_res_hour" = "gammaspechourres", "intercept_het_L_effect_res" = "intercepthetLeffectres", "intercept_het_L_effect_eta_high_res" = "intercepthetLeffectetahighres", "intercept_het_L_effect_eta_low_res" = "intercepthetLeffectetalowres", "intercept_het_B_res" = "intercepthetBres", "intercept_het_L_res" = "intercepthetLres", "intercept_het_B_res_hour" = "intercepthetBreshour", "intercept_het_L_res_hour" = "intercepthetLreshour", "intercept_het_L_effect_res_hour" = "intercepthetLeffectreshour", "gamma_spec_omega_res_hour" = "gammaspecomegareshour", "intercept_spec_omega_res_hour" = "interceptspecomegareshour", "intercept_het_L_effect_omega_res_hour" = "intercepthetLeffectomegareshour", "intercept_het_L_omega_res_hour" = "intercepthetLomegareshour", "intercept_het_L_effect_multiple_res" = "intercepthetLeffectmultipleres", "intercept_het_B_multiple_res" = "intercepthetBmultipleres", "intercept_het_L_multiple_res" = "intercepthetLmultipleres", "intercept_het_L_effect_omega_res" = "intercepthetLeffectomegares", "intercept_het_L_omega_res" = "intercepthetLomegares", "gamma_L_effect_res_hour" = "gammaLeffectreshour", "delta_x_temptation_wo_habit" = "deltaxtemptationwohabit", "delta_x_temptation_wo_habit_res" = "deltaxtemptationwohabitres", "DWLStatic" = "DWLStatic", "DWLStaticThreeWeeks" = "DWLStaticThreeWeeks", "YearlyWelfare" = "YearlyWelfare" ) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Utility functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ find_bottom <- function(x){ return(as.numeric(quantile(x, 0.025, na.rm=TRUE))) } find_top <- function(x){ return(as.numeric(quantile(x, 0.975, na.rm=TRUE))) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Data functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ import_data <- function(){ # Import data df <- import('input/final_data_sample.dta') # Clean data df %<>% mutate(L = ifelse(S2_LimitType != 0, 1, 0)) %>% mutate(B = ifelse(S3_Bonus == 1, 1, 0)) %>% mutate(S = as.character(Stratifier)) %>% mutate(w = 1) return(df) } balance_data <- function(df, magnitude=2){ cols_used <- c('balance_income', 'balance_college', 'balance_male', 'balance_white', 'balance_age') balance_df <- df[, c('UserID', cols_used)] balance_df$treat <- 0 avg_df <- data.frame(0, avg_income, avg_college, avg_male, avg_white, avg_age, 1) names(avg_df) <- c('UserID', cols_used, 'treat') balance_df <- rbind(balance_df, avg_df[rep(1, nrow(df)),]) ebal.out <- ebalance(Treatment = balance_df$treat, X = balance_df[,cols_used], print.level = 0) df$w <- ebal.out$w df$w <- sapply(df$w, function(x){ return(min(magnitude, x))}) df$w <- sapply(df$w, function(x){ return(max(1/magnitude, x))}) return(df) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Solve functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #solves for rho and lambda solve_sys_eq_1 <- function(param) { # Define tau_B_2 <- param[['tau_B_2']] tau_B_3 <- param[['tau_B_3']] tau_B_4 <- param[['tau_B_4']] tau_B_5 <- param[['tau_B_5']] # Solve a <- tau_B_2*tau_B_4 b <- tau_B_3*tau_B_4 - tau_B_2*tau_B_5 c <- tau_B_4^2 - tau_B_3*tau_B_5 #solve for rho using the quadratic formula and choose the larger value rho <- ifelse((tau_B_2==0), tau_B_5/tau_B_4 - tau_B_4/tau_B_3, (-b + sqrt(b^2 - 4*a*c)) / (2*a)) lambda <- tau_B_4 / (rho*tau_B_3 + rho^2*tau_B_2) rho <- ifelse(rho<0, 0, rho) lambda <- ifelse(lambda<0, 0, lambda) # Solve for tau_b_2=0, i.e. restricted alpha=1 model rho_res <- tau_B_5/tau_B_4 - tau_B_4/tau_B_3 rho_res <- ifelse(rho_res<0, 0, rho_res) lambda_res <- tau_B_4 / (rho_res*tau_B_3) lambda_res <- ifelse(lambda_res<0, 0, lambda_res) # Return solution <- list( rho = rho, lambda = lambda, rho_res = rho_res, lambda_res = lambda_res ) return(solution) } # Solves for alpha, eta, zeta solve_sys_eq_2 <- function(param, display_warning=FALSE) { rho = param[['rho']] lambda = param[['lambda']] rho_res = param[['rho_res']] lambda_res = param[['lambda_res']] delta = param[['delta']] tau_B_2 = param[['tau_B_2']] tau_tilde_B = param[['tau_tilde_B']] tau_B_3 = param[['tau_B_3']] tau_B_4 = param[['tau_B_4']] tau_tilde_B_3_2 = param[['tau_tilde_B_3_2']] p_B = param[['p_B']] find_y <- function(alpha, s, rho=rho, lambda=lambda){ num <- -tau_B_4 + (1-alpha) * delta * (rho^2) * lambda * s denom <- rho * tau_B_3 + (rho^2) * tau_B_2 - (1-alpha) * delta * (rho^2) * (1 - lambda) * s return(num / denom) } find_x <- function(alpha, s, y, rho=rho, lambda=lambda){ x1 <- tau_B_3 - (1-alpha)*delta*(rho^2)*lambda*(rho*tau_B_2 + tau_B_3) x2 <- rho * tau_B_2 - (1-alpha)*delta*(rho^2)*(1 - lambda)*(rho*tau_B_2 + tau_B_3) return(x1 + y * x2) } solve_alpha <- function(alpha){ s <- (rho^2) * tau_B_2 + rho * tau_B_3 + tau_B_4 y <- find_y(alpha, s, rho=rho, lambda=lambda) x <- find_x(alpha, s, y, rho=rho, lambda=lambda) eta <- p_B / x zeta <- y * eta num_z <- eta*tau_B_2 den_z <- delta*rho*(-p_B + (eta - zeta)*tau_tilde_B + zeta * rho * tau_B_2) z <- (num_z / den_z) - (1-alpha) return(z) } #Unrestricted model print(tau_B_2) if (tau_B_2 >= 0){ alpha <- 1 } else { alpha <- uniroot(solve_alpha, interval=c(0,1.2))$root } alpha <- ifelse(alpha > 1, 1, alpha) alpha <- ifelse(alpha<0, 0, alpha) s <- (rho^2) * tau_B_2 + rho * tau_B_3 + tau_B_4 y <- find_y(alpha, s, rho=rho, lambda=lambda) x <- find_x(alpha, s, y, rho=rho, lambda=lambda) eta <- p_B / x zeta <- y * eta #Winsorise parameters at 0 eta <- ifelse(eta>0, 0, eta) zeta <- ifelse(zeta<0, 0, zeta) denom <- -eta - (1-alpha)*delta*rho*(zeta-eta)-zeta*((rho-(1-alpha)*delta*rho^2)/(1-rho)) #eta <- ifelse(denom <0, NA, eta) #zeta <- ifelse(denom <0, NA, zeta) #Restricted model # note: alpha=1 in restricted model alpha_res <- 1 eta_res <- p_B / tau_B_3 zeta_res <- (-eta_res*tau_B_4) / (rho_res*tau_B_3) #Winsorise parameters at 0 eta_res <- ifelse(eta_res>0, 0, eta_res) zeta_res <- ifelse(zeta_res<0, 0, zeta_res) # Display error for concavity assumptions if (display_warning){ if(rho*(1+lambda)>1){ stop("Concavity condition for rho(1+lambda) not satisfied") } } #Get hourly estimates eta_hour <- eta*3600 zeta_hour <- zeta*3600 eta_res_hour <- eta_res*3600 zeta_res_hour <- zeta_res*3600 #Export desired variables for in-text references lambdarho <- signif(lambda*rho, digits=2) lambdarhosquared <- lambda*rho^2 lambdarhosquared <- signif(lambdarhosquared, digits=1) tauBthreehour <- signif(tau_B_3/60, digits=3) find_y_tau <- function(tau_B_2){ s <- (rho^2) * tau_B_2 + rho * tau_B_3 + tau_B_4 num <- -tau_B_4 + delta * (rho^2) * lambda * s denom <- rho * tau_B_3 + (rho^2) * tau_B_2 - delta * (rho^2) * (1 - lambda) * s return(num / denom) } find_x_tau <- function(tau_B_2, y){ s <- (rho^2) * tau_B_2 + rho * tau_B_3 + tau_B_4 x1 <- tau_B_3 - delta*(rho^2)*lambda*(rho*tau_B_2 + tau_B_3) x2 <- rho * tau_B_2 - delta*(rho^2)*(1 - lambda)*(rho*tau_B_2 + tau_B_3) return(x1 + y * x2) } solve_tau <- function(tau_B_2){ y <- find_y_tau(tau_B_2) x <- find_x_tau(tau_B_2, y) left <- delta * rho * (-x + (1-y)*tau_tilde_B) right <- tau_B_2 * (1 - y * delta * rho^2) return(left - right) } tau_B_2_desired <- NA try(tau_B_2_desired <- uniroot(solve_tau, interval=c(-60,5))$root, silent = T) pcttaubtwo <- 100*(tau_B_2)/tau_B_2_desired oneminusalphapct <- (1-alpha)*100 # Return solution <- list( alpha = alpha, eta = eta, zeta = zeta, eta_hour = eta_hour, zeta_hour = zeta_hour, alpha_res = alpha_res, eta_res = eta_res, zeta_res = zeta_res, eta_res_hour = eta_res_hour, zeta_res_hour = zeta_res_hour, tau_B_2_desired = tau_B_2_desired, lambdarho = lambdarho, lambdarhosquared = lambdarhosquared, tauBthreehour = tauBthreehour, pcttaubtwo = pcttaubtwo, oneminusalphapct = oneminusalphapct, denom = denom ) # Return return(solution) } solve_sys_eq_3 <- function(param) { # Define rho <- param[['rho']] lambda <- param[['lambda']] rho_res <- param[['rho_res']] lambda_res <- param[['lambda_res']] alpha <- param[['alpha']] alpha_res <- param[['alpha_res']] delta <- param[['delta']] eta <- param[['eta']] zeta <- param[['zeta']] eta_res <- param[['eta_res']] zeta_res <- param[['zeta_res']] p_B <- param[['p_B']] F_B <- param[['F_B']] tau_B_2 <- param[['tau_B_2']] tau_B_3 <- param[['tau_B_3']] tau_tilde_B <- param[['tau_tilde_B']] tau_tilde_L <- param[['tau_tilde_L']] tau_L_2 <- param[['tau_L_2']] tau_L_y <- param[['tau_L_y']] tau_B_y <- param[['tau_B_y']] mispredict <- param[['mispredict']] d_L <- param[['d_L']] d_CL <- param[['d_CL']] v_L <- param[['v_L']] v_B <- param[['v_B']] x_ss <- param[['x_ss']] x_tilde_2_B <- param[['x_tilde_2_B']] # Compute estimated Omega omega_est <- (d_L - d_CL) / -d_CL omega <- 1 p <- p_B # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Unrestricted alpha # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Naivete term <- -eta + (1-alpha)*delta*(rho^2)*(eta*lambda + zeta*(1 - lambda)) naivete <- mispredict*term # Gamma-tilde-L gamma_tilde_L <- (2*v_L) / (-tau_tilde_L*(2-omega)) gamma_L <- naivete + gamma_tilde_L # Gamma-tilde-L omega gamma_tilde_L_omega <- (2*v_L) / (-tau_tilde_L*(2-omega_est)) gamma_L_omega <- naivete + gamma_tilde_L_omega # Gamma-tilde-L multiple good gamma_tilde_L_multiple <- v_L/-(tau_tilde_L*(2-omega)/2+tau_L_y) gamma_L_multiple <- naivete + gamma_tilde_L_multiple # Gamma-tilde-B term <- v_B - F_B + p*x_tilde_2_B gamma_tilde_B <- term / (-tau_tilde_B) gamma_B <- naivete + gamma_tilde_B # Gamma-tilde-B multiple good gamma_tilde_B_multiple <- (v_B - F_B + p*x_tilde_2_B)/-(tau_tilde_B+tau_B_y) gamma_B_multiple <- naivete + gamma_tilde_B_multiple # Gamma-L-effect num <- eta*tau_L_2/omega - (1-alpha)*delta*rho*(((eta-zeta)*tau_tilde_L/omega+zeta*rho*tau_L_2/omega) + (1+lambda)*mispredict*(-eta+(1-alpha)*delta*rho^2*((eta-zeta)*lambda+zeta))) denom <- 1 - (1-alpha)*delta*rho*(1+lambda) gamma_L_effect <- num/denom gamma_tilde_L_effect <- gamma_L_effect - naivete # Gamma-L-effect omega num_omega <- eta*tau_L_2/omega_est - (1-alpha)*delta*rho*(((eta-zeta)*tau_tilde_L/omega_est+zeta*rho*tau_L_2/omega_est) + (1+lambda)*mispredict*(-eta+(1-alpha)*delta*rho^2*((eta-zeta)*lambda+zeta))) gamma_L_effect_omega <- num_omega/denom gamma_tilde_L_effect_omega <- gamma_L_effect_omega - naivete # Select Gammas gamma_tilde <- gamma_tilde_L_effect gamma <- gamma_L_effect # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Restricted alpha=1 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Naivete naivete_res <- mispredict*(-eta_res) # Gamma-tilde-L gamma_tilde_L <- (2*v_L) / (-tau_tilde_L*(2-omega)) gamma_L_res <- naivete_res + gamma_tilde_L # Gamma-tilde-L omega gamma_tilde_L_omega <- (2*v_L) / (-tau_tilde_L*(2-omega_est)) gamma_L_omega_res <- naivete_res + gamma_tilde_L_omega # Gamma-tilde-L multiple goods gamma_tilde_L_multiple <- v_L/-(tau_tilde_L*(2-omega)/2+tau_L_y) gamma_L_multiple_res <- naivete_res + gamma_tilde_L_multiple # Gamma-tilde-B gamma_B_res <- naivete_res + gamma_tilde_B # Gamma tilde-B multiple goods gamma_B_multiple_res <- naivete_res + gamma_tilde_B_multiple # Gamma-L-effect gamma_L_effect_res <- eta_res*tau_L_2 gamma_tilde_L_effect_res <- gamma_L_effect_res - naivete_res # Gamma-L-effect omega gamma_L_effect_omega_res <- eta_res*tau_L_2/omega_est gamma_tilde_L_effect_omega_res <- gamma_L_effect_omega_res - naivete_res # Gamma-L-effect multiple goods (note: only for restricted case) gamma_L_effect_multiple_res <- (tau_L_2*p/tau_B_3)/(1+tau_L_y/tau_L_2) gamma_tilde_L_effect_multiple_res <- gamma_L_effect_multiple_res - naivete_res #Hourly variables for the tables naivete_hour <- naivete*60 gamma_hour <- gamma*60 gamma_L_hour <- gamma_L*60 gamma_B_hour <- gamma_B*60 gamma_tilde_hour <- gamma_tilde*60 gamma_tilde_B_hour <- gamma_tilde_B*60 gamma_tilde_L_hour <- gamma_tilde_L*60 gamma_L_effect_omega_hour <- gamma_L_effect_omega*60 gamma_L_omega_hour <- gamma_L_omega*60 underestimatetemp <- naivete_hour/gamma_hour*100 gamma_tilde_L_multiple_hour <- gamma_tilde_L_multiple*60 gamma_L_multiple_hour <- gamma_L_multiple*60 gamma_tilde_B_multiple_hour <- gamma_tilde_B_multiple*60 gamma_B_multiple_hour <- gamma_B_multiple*60 naivete_res_hour <- naivete_res*60 gamma_L_effect_res_hour <- gamma_L_effect_res*60 gamma_L_res_hour <- gamma_L_res*60 gamma_B_res_hour <- gamma_B_res*60 underestimatetemp_res <- naivete_res_hour/gamma_L_effect_res_hour*100 gamma_tilde_L_effect_res_hour <- gamma_tilde_L_effect_res*60 gamma_L_effect_omega_res_hour <- gamma_L_effect_omega_res*60 gamma_L_omega_res_hour <- gamma_L_omega_res*60 gamma_L_multiple_res_hour <- gamma_L_multiple_res*60 gamma_B_multiple_res_hour <- gamma_B_multiple_res*60 gamma_L_effect_multiple_res_hour <- gamma_L_effect_multiple_res*60 gamma_tilde_L_effect_multiple_res_hour <- gamma_tilde_L_effect_multiple_res*60 attritionrate <- (1-1933/2048) DWLStatic <- -(tau_L_2/60*gamma_L_effect_res_hour/2) DWLStaticThreeWeeks <- DWLStatic*21 YearlyWelfare <- DWLStaticThreeWeeks*52/3*0.24 # Return solution <- list( naivete = naivete, omega_est = omega_est, omega = omega, gamma_L_effect = gamma_L_effect, gamma_tilde_L_effect = gamma_tilde_L_effect, gamma_L = gamma_L, gamma_tilde_L = gamma_tilde_L, gamma_B = gamma_B, gamma_tilde_B = gamma_tilde_B, gamma = gamma, gamma_tilde = gamma_tilde, naivete_hour = naivete_hour, gamma_hour = gamma_hour, gamma_tilde_B_hour = gamma_tilde_B_hour, gamma_tilde_L_hour = gamma_tilde_L_hour, gamma_tilde_hour = gamma_tilde_hour, gamma_L_hour = gamma_L_hour, gamma_B_hour = gamma_B_hour, gamma_L_effect_omega_hour = gamma_L_effect_omega_hour, gamma_L_omega_hour = gamma_L_omega_hour, underestimatetemp = underestimatetemp, attritionrate = attritionrate, gamma_tilde_L_effect_omega = gamma_tilde_L_effect_omega, gamma_L_effect_omega = gamma_L_effect_omega, gamma_tilde_L_omega = gamma_tilde_L_omega, gamma_L_omega = gamma_L_omega, gamma_tilde_L_multiple = gamma_tilde_L_multiple, gamma_L_multiple = gamma_L_multiple, gamma_tilde_B_multiple = gamma_tilde_B_multiple, gamma_B_multiple = gamma_B_multiple, gamma_tilde_L_multiple_hour = gamma_tilde_L_multiple_hour, gamma_L_multiple_hour = gamma_L_multiple_hour, gamma_tilde_B_multiple_hour = gamma_tilde_B_multiple_hour, gamma_B_multiple_hour = gamma_B_multiple_hour, naivete_res = naivete_res, underestimatetemp_res = underestimatetemp_res, gamma_L_effect_res = gamma_L_effect_res, gamma_tilde_L_effect_res = gamma_tilde_L_effect_res, gamma_L_res = gamma_L_res, gamma_B_res = gamma_B_res, naivete_res_hour = naivete_res_hour, gamma_tilde_L_effect_res_hour = gamma_tilde_L_effect_res_hour, gamma_L_res_hour = gamma_L_res_hour, gamma_B_res_hour = gamma_B_res_hour, gamma_L_effect_omega_res_hour = gamma_L_effect_omega_res_hour, gamma_L_omega_res_hour = gamma_L_omega_res_hour, gamma_tilde_L_effect_omega_res = gamma_tilde_L_effect_omega_res, gamma_L_effect_omega_res = gamma_L_effect_omega_res, gamma_L_omega_res = gamma_L_omega_res, gamma_L_multiple_res = gamma_L_multiple_res, gamma_B_multiple_res = gamma_B_multiple_res, gamma_tilde_L_effect_multiple_res = gamma_tilde_L_effect_multiple_res, gamma_L_effect_multiple_res = gamma_L_effect_multiple_res, gamma_L_multiple_res_hour = gamma_L_multiple_hour, gamma_B_multiple_res_hour = gamma_B_multiple_res_hour, gamma_tilde_L_effect_multiple_res_hour = gamma_tilde_L_effect_multiple_res_hour, gamma_L_effect_multiple_res_hour = gamma_L_effect_multiple_res_hour, gamma_L_effect_res_hour = gamma_L_effect_res_hour, DWLStatic = DWLStatic, DWLStaticThreeWeeks = DWLStaticThreeWeeks, YearlyWelfare = YearlyWelfare ) return(solution) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate effects from different identification strategies # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ solve_effects <- function(param, df){ # Define eta <- param[['eta']] zeta <- param[['zeta']] eta_res <- param[['eta_res']] zeta_res <- param[['zeta_res']] alpha <- param[['alpha']] alpha_res <- param[['alpha_res']] rho <- param[['rho']] rho_res <- param[['rho_res']] lambda <- param[['lambda']] lambda_res <- param[['lambda_res']] delta <- param[['delta']] p_B <- param[['p_B']] naivete <- param[['naivete']] naivete_res <- param[['naivete_res']] mispredict <- param[['mispredict']] x_ss <- param[['x_ss']] intercept_het_L_effect <- param[['intercept_het_L_effect']] intercept_het_L_effect_eta_high <- param[['intercept_het_L_effect_eta_high']] intercept_het_L_effect_eta_low <- param[['intercept_het_L_effect_eta_low']] intercept_het_B <- param[['intercept_het_B']] intercept_het_L <- param[['intercept_het_L']] intercept_het_B_multiple <- param[['intercept_het_B_multiple']] intercept_het_L_multiple <- param[['intercept_het_L_multiple']] intercept_het_L_effect_omega <- param[['intercept_het_L_effect_omega']] intercept_het_L_omega <- param[['intercept_het_L_omega']] intercept_het_L_effect_res <- param[['intercept_het_L_effect_res']] intercept_het_L_effect_eta_high_res <- param[['intercept_het_L_effect_eta_high_res']] intercept_het_L_effect_eta_low_res <- param[['intercept_het_L_effect_eta_low_res']] intercept_het_B_res <- param[['intercept_het_B_res']] intercept_het_L_res <- param[['intercept_het_L_res']] intercept_het_L_effect_multiple_res <- param[['intercept_het_L_effect_multiple_res']] intercept_het_B_multiple_res <- param[['intercept_het_B_multiple_res']] intercept_het_L_multiple_res <- param[['intercept_het_L_multiple_res']] intercept_het_L_effect_omega_res <- param[['intercept_het_L_effect_omega_res']] intercept_het_L_omega_res <- param[['intercept_het_L_omega_res']] gamma_L_effect <- param[['gamma_L_effect']] gamma_tilde_L_effect <- param[['gamma_tilde_L_effect']] gamma_L_effect_res <- param[['gamma_L_effect_res']] gamma_tilde_L_effect_res <- param[['gamma_tilde_L_effect_res']] gamma_L_res <- param[['gamma_L_res']] gamma_L <- param[['gamma_L']] gamma_tilde_L <- param[['gamma_tilde_L']] gamma_B <- param[['gamma_B']] gamma_B_res <- param[['gamma_B_res']] gamma_tilde_B <- param[['gamma_tilde_B']] gamma_tilde_L_multiple <- param[['gamma_tilde_L_multiple']] gamma_L_multiple <- param[['gamma_L_multiple']] gamma_L_multiple_res <- param[['gamma_L_multiple_res']] gamma_tilde_B_multiple <- param[['gamma_tilde_B_multiple']] gamma_B_multiple <- param[['gamma_B_multiple']] gamma_B_multiple_res <- param[['gamma_B_multiple_res']] gamma_L_effect_multiple_res <- param[['gamma_L_effect_multiple_res']] gamma_tilde_L_effect_multiple_res <- param[['gamma_tilde_L_effect_multiple_res']] gamma_tilde_L_effect_omega <- param[['gamma_tilde_L_effect_omega']] gamma_L_effect_omega <- param[['gamma_L_effect_omega']] gamma_tilde_L_effect_omega_res <- param[['gamma_tilde_L_effect_omega_res']] gamma_L_effect_omega_res <- param[['gamma_L_effect_omega_res']] gamma_tilde_L_omega <- param[['gamma_tilde_L_omega']] gamma_L_omega <- param[['gamma_L_omega']] gamma_L_omega_res <- param[['gamma_L_omega_res']] # set price to zero p <- 0 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Unrestricted alpha model # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Estimating using gamma from limit effect x_ss_L_effect <- max(0, calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect)) delta_x_cap <- x_ss_L_effect - max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect)) delta_x_cap_us <- delta_x_cap * 365 * us_adults # Estimating using gamma from limit effect eta high (eta*1.1) and low (eta*0.9) x_ss_L_effect_eta_high <- max(0, calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect_eta_high, eta_scale=1.1)) x_ss_L_effect_eta_low <- max(0, calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect_eta_low, eta_scale=0.9)) # Estimating using gamma_tilde from limit valuation x_ss_L <- max(0, calculate_steady_state(param, gamma_tilde_L, gamma_L, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L)) delta_x_tilde_L <- x_ss_L - max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L)) delta_x_tilde_L_us <- delta_x_tilde_L * 365 * us_adults # Estimating using gamma_tilde from bonus valuation x_ss_B <- max(0, calculate_steady_state(param, gamma_tilde_B, gamma_B, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_B)) delta_x_tilde_B <- x_ss_B - max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_B)) delta_x_tilde_B_us <- delta_x_tilde_B * 365 * us_adults mispredicthour <- mispredict/60 # Estimating time effects using multiple goods moments x_ss_L_multiple <- max(0, calculate_steady_state(param, gamma_tilde_L_multiple, gamma_L_multiple, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_multiple)) delta_x_L_multiple <- max(0,x_ss_L_multiple - max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_multiple))) x_ss_B_multiple <- max(0, calculate_steady_state(param, gamma_tilde_B_multiple, gamma_B_multiple, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_B_multiple)) delta_B_multiple <- max(0,x_ss_B_multiple - max(0, calculate_steady_state(param, 0, 0, alpha, rho,lambda, 0, eta, zeta, intercept=intercept_het_B_multiple))) # Estimating time effects using omega hat moments # limit effect; omega_hat x_ss_L_effect_omega <- max(0, calculate_steady_state(param, gamma_tilde_L_effect_omega, gamma_L_effect_omega, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect_omega)) delta_x_cap_omega <- max(0,x_ss_L_effect_omega - max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_omega))) # limit valuation: omega_hat x_ss_L_omega <- max(0, calculate_steady_state(param, gamma_tilde_L_omega, gamma_L_omega, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_omega)) delta_x_L_omega <- max(0,x_ss_L_omega - max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_omega))) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Restricted alpha=1 model # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Estimating using gamma from limit effect x_ss_L_effect_res <- max(0, calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_res)) delta_x_cap_res <- x_ss_L_effect_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_res)) delta_x_cap_us_res <- delta_x_cap_res * 365 * us_adults # Estimating using gamma from limit effect eta high (eta*1.1) and low (eta*0.9) x_ss_L_effect_eta_high_res <- max(0, calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_high_res, eta_scale=1.1)) x_ss_L_effect_eta_low_res <- max(0, calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_low_res, eta_scale=0.9)) # Estimating using gamma_tilde from limit valuation (note: gamma_tilde_L is same for restricted and unrestricted models) x_ss_L_res <- max(0, calculate_steady_state(param, gamma_tilde_L, gamma_L_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_res)) delta_x_tilde_L_res <- x_ss_L_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_res)) delta_x_tilde_L_us_res <- delta_x_tilde_L_res * 365 * us_adults # Estimating using gamma_tilde from bonus valuation (note: gamma_tilde_B is same for restricted and unrestricted models) x_ss_B_res <- max(0, calculate_steady_state(param, gamma_tilde_B, gamma_B_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_B_res)) delta_x_tilde_B_res <- x_ss_B_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_B_res)) delta_x_tilde_B_us_res <- delta_x_tilde_B_res * 365 * us_adults # Estimating time effects using multiple goods moments x_ss_L_effect_multiple_res <- max(0, calculate_steady_state(param, gamma_tilde_L_effect_multiple_res, gamma_L_effect_multiple_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_multiple_res)) delta_x_cap_multiple_res <- max(0,x_ss_L_effect_multiple_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_multiple_res))) x_ss_L_multiple_res <- max(0, calculate_steady_state(param, gamma_tilde_L_multiple, gamma_L_multiple_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_multiple_res)) delta_x_L_multiple_res <- max(0,x_ss_L_multiple_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_multiple_res))) x_ss_B_multiple_res <- max(0, calculate_steady_state(param, gamma_tilde_B_multiple, gamma_B_multiple_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_B_multiple_res)) delta_B_multiple_res <- max(0,x_ss_B_multiple_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_B_multiple_res))) # Estimating time effects using omega hat moments (limit effects) x_ss_L_effect_omega_res <- max(0, calculate_steady_state(param, gamma_tilde_L_effect_omega_res, gamma_L_effect_omega_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_omega_res)) delta_x_cap_omega_res <- max(0,x_ss_L_effect_omega_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_omega_res))) x_ss_L_omega_res <- max(0, calculate_steady_state(param, gamma_tilde_L_omega, gamma_L_omega_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_omega_res)) delta_x_L_omega_res <- max(0,x_ss_L_omega_res - max(0, calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_omega_res))) #xero temp x_ss x_ss_zero_temp <- max(0, calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect)) # Return solution <- list( x_ss_L_effect = x_ss_L_effect, x_ss_L_effect_eta_high = x_ss_L_effect_eta_high, x_ss_L_effect_eta_low = x_ss_L_effect_eta_low, x_ss_B = x_ss_B, delta_x_cap = delta_x_cap, delta_x_cap_us = delta_x_cap_us, delta_x_tilde_L = delta_x_tilde_L, delta_x_tilde_L_us = delta_x_tilde_L_us, delta_x_tilde_B = delta_x_tilde_B, delta_x_tilde_B_us = delta_x_tilde_B_us, x_ss_L = x_ss_L, mispredicthour = mispredicthour, delta_x_L_multiple = delta_x_L_multiple, delta_B_multiple = delta_B_multiple, delta_x_cap_omega = delta_x_cap_omega, delta_x_L_omega = delta_x_L_omega, x_ss_L_effect_res = x_ss_L_effect_res, x_ss_L_effect_eta_high_res = x_ss_L_effect_eta_high_res, x_ss_L_effect_eta_low_res = x_ss_L_effect_eta_low_res, x_ss_B_res = x_ss_B_res, delta_x_cap_res = delta_x_cap_res, delta_x_cap_us_res = delta_x_cap_us_res, delta_x_tilde_L_res = delta_x_tilde_L_res, delta_x_tilde_L_us_res = delta_x_tilde_L_us_res, delta_x_tilde_B_res = delta_x_tilde_B_res, delta_x_tilde_B_us_res = delta_x_tilde_B_us_res, x_ss_L_res = x_ss_L_res, delta_x_cap_multiple_res = delta_x_cap_multiple_res, delta_x_L_multiple_res = delta_x_L_multiple_res, delta_B_multiple_res = delta_B_multiple_res, delta_x_cap_omega_res = delta_x_cap_omega_res, delta_x_L_omega_res = delta_x_L_omega_res, x_ss_zero_temp = x_ss_zero_temp ) return(solution) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate effects from different counterfactuals (heterogeneous) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ solve_counterfactuals <- function(param, df){ # Define alpha <- param[['alpha']] alpha_res <- param[['alpha_res']] rho <- param[['rho']] rho_res <- param[['rho_res']] eta <- param[['eta']] eta_res <- param[['eta_res']] zeta <- param[['zeta']] zeta_res <- param[['zeta_res']] lambda <- param[['lambda']] lambda_res <- param[['lambda_res']] delta <- param[['delta']] mispredict <- param[['mispredict']] x_ss <- param[['x_ss']] gamma_L_effect <- param[['gamma_L_effect']] gamma_tilde_L_effect <- param[['gamma_tilde_L_effect']] gamma_tilde_L_effect_res <- param[['gamma_tilde_L_effect_res']] intercept_het_L_effect <- param[['intercept_het_L_effect']] intercept_het_L_effect_eta_high <- param[['intercept_het_L_effect_eta_high']] intercept_het_L_effect_eta_low <- param[['intercept_het_L_effect_eta_low']] gamma_L_effect_res <- param[['gamma_L_effect_res']] intercept_het_L_effect_res <- param[['intercept_het_L_effect_res']] intercept_het_L_effect_eta_high_res <- param[['intercept_het_L_effect_eta_high_res']] intercept_het_L_effect_eta_low_res <- param[['intercept_het_L_effect_eta_low_res']] # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate effects for unrestricted model # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Remember the order of the arguments for calculate steady state is # calculate_steady_state(param, gamma_tilde, gamma, alpha, rho, mispredict, eta, zeta, intercept=NA, eta_scale=1){ x_ss_L_effect <- max(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect) ,0) x_ss_temptation <- max(calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect) ,0) x_ss_temptation_eta_high <- max(calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_eta_high, eta_scale=1.1) ,0) x_ss_temptation_eta_low <- max(calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_eta_low, eta_scale=0.9) ,0) x_ss_habit <- max(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, 0, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect) ,0) x_ss_habit_eta_high <- max(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, 0, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect_eta_high, eta_scale=1.1) ,0) x_ss_habit_eta_low <- max(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, 0, lambda, mispredict, eta, zeta, intercept=intercept_het_L_effect_eta_low, eta_scale=0.9) ,0) x_ss_naivete <- max(calculate_steady_state(param, gamma_L_effect, gamma_L_effect, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect) ,0) x_ss_naivete_eta_high <- max(calculate_steady_state(param, gamma_L_effect, gamma_L_effect, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_eta_high, eta_scale=1.1) ,0) x_ss_naivete_eta_low <- max(calculate_steady_state(param, gamma_L_effect, gamma_L_effect, alpha, rho, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_eta_low, eta_scale=0.9) ,0) x_ss_habit_temptation <- max(calculate_steady_state(param, 0, 0, alpha, 0, lambda, 0, eta, zeta, intercept=intercept_het_L_effect) ,0) x_ss_habit_temptation_eta_high <- max(calculate_steady_state(param, 0, 0, alpha, 0, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_eta_high, eta_scale=1.1) ,0) x_ss_habit_temptation_eta_low <- max(calculate_steady_state(param, 0, 0, alpha, 0, lambda, 0, eta, zeta, intercept=intercept_het_L_effect_eta_low, eta_scale=0.9) ,0) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate effects for restricted alpha=1 model # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Remember the order of the arguments for calculate steady state is # calculate_steady_state(param, gamma_tilde, gamma, alpha, rho, mispredict, eta, zeta, intercept=NA, eta_scale=1){ x_ss_L_effect_res <- max(calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_res) ,0) x_ss_temptation_res <- max(calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_res) ,0) x_ss_temptation_eta_high_res <- max(calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_high_res, eta_scale=1.1) ,0) x_ss_temptation_eta_low_res <- max(calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_low_res, eta_scale=0.9) ,0) x_ss_habit_res <- max(calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, 0, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_res) ,0) x_ss_habit_eta_high_res <- max(calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, 0, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_high_res, eta_scale=1.1) ,0) x_ss_habit_eta_low_res <- max(calculate_steady_state(param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, 0, lambda_res, mispredict, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_low_res, eta_scale=0.9) ,0) x_ss_naivete_res <- max(calculate_steady_state(param, gamma_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_res) ,0) x_ss_naivete_eta_high_res <- max(calculate_steady_state(param, gamma_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_high_res, eta_scale=1.1) ,0) x_ss_naivete_eta_low_res <- max(calculate_steady_state(param, gamma_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_low_res, eta_scale=0.9) ,0) x_ss_habit_temptation_res <- max(calculate_steady_state(param, 0, 0, alpha_res, 0, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_res) ,0) x_ss_habit_temptation_eta_high_res <- max(calculate_steady_state(param, 0, 0, alpha_res, 0, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_high_res, eta_scale=1.1) ,0) x_ss_habit_temptation_eta_low_res <- max(calculate_steady_state(param, 0, 0, alpha_res, 0, lambda_res, 0, eta_res, zeta_res, intercept=intercept_het_L_effect_eta_low_res, eta_scale=0.9) ,0) # Return solution <- list( delta_x_temptation = x_ss_L_effect - x_ss_temptation, delta_x_naivete = x_ss_L_effect - x_ss_naivete, delta_x_habit = x_ss_L_effect - x_ss_habit, delta_x_temptation_wo_habit = x_ss_habit - x_ss_habit_temptation, delta_x_temptation_wo_habit_res = x_ss_habit_res - x_ss_habit_temptation_res, x_ss_temptation = x_ss_temptation, x_ss_temptation_eta_high = x_ss_temptation_eta_high, x_ss_temptation_eta_low = x_ss_temptation_eta_low, x_ss_naivete = x_ss_naivete, x_ss_naivete_eta_high = x_ss_naivete_eta_high, x_ss_naivete_eta_low = x_ss_naivete_eta_low, x_ss_habit = x_ss_habit, x_ss_habit_eta_high = x_ss_habit_eta_high, x_ss_habit_eta_low = x_ss_habit_eta_low, x_ss_habit_temptation = x_ss_habit_temptation, x_ss_habit_temptation_eta_high = x_ss_habit_temptation_eta_high, x_ss_habit_temptation_eta_low = x_ss_habit_temptation_eta_low, delta_x_temptation_res = x_ss_L_effect_res - x_ss_temptation_res, delta_x_naivete_res = x_ss_L_effect_res - x_ss_naivete_res, delta_x_habit_res = x_ss_L_effect_res - x_ss_habit_res, x_ss_temptation_res = x_ss_temptation_res, x_ss_temptation_eta_high_res = x_ss_temptation_eta_high_res, x_ss_temptation_eta_low_res = x_ss_temptation_eta_low_res, x_ss_naivete_res = x_ss_naivete_res, x_ss_naivete_eta_high_res = x_ss_naivete_eta_high_res, x_ss_naivete_eta_low_res = x_ss_naivete_eta_low_res, x_ss_habit_res = x_ss_habit_res, x_ss_habit_eta_high_res = x_ss_habit_eta_high_res, x_ss_habit_eta_low_res = x_ss_habit_eta_low_res, x_ss_habit_temptation_res = x_ss_habit_temptation_res, x_ss_habit_temptation_eta_high_res = x_ss_habit_temptation_eta_high_res, x_ss_habit_temptation_eta_low_res = x_ss_habit_temptation_eta_low_res) return(solution) } solve_effects_individual <- function(x_ss_i_data, param, tau_tilde_L, tau_L_2, w){ rho <- param[['rho']] lambda <- param[['lambda']] rho_res <- param[['rho_res']] lambda_res <- param[['lambda_res']] delta <- param[['delta']] alpha <- param[['alpha']] alpha_res <- param[['alpha_res']] omega <- param[['omega']] omega_est <- param[['omega_est']] mispredict <- param[['mispredict']] d_L <- param[['d_L']] d_CL <- param[['d_CL']] eta <- param[['eta']] zeta <- param[['zeta']] naivete <- param[['naivete']] gamma_L_effect <- param[['gamma_L_effect']] gamma_tilde_L_effect <- param[['gamma_tilde_L_effect']] gamma_tilde_L_effect_omega <- param[['gamma_tilde_L_effect_omega']] gamma_L_effect_omega <- param[['gamma_L_effect_omega']] gamma_L <- param[['gamma_L']] gamma_tilde_L <- param[['gamma_tilde_L']] gamma_tilde_L_omega <- param[['gamma_tilde_L_omega']] gamma_L_omega <- param[['gamma_L_omega']] gamma_tilde_L_multiple <- param[['gamma_tilde_L_multiple']] gamma_L_multiple <- param[['gamma_L_multiple']] gamma_B <- param[['gamma_B']] gamma_tilde_B <- param[['gamma_tilde_B']] gamma_tilde_B_multiple <- param[['gamma_tilde_B_multiple']] gamma_B_multiple <- param[['gamma_B_multiple']] eta_res <- param[['eta_res']] zeta_res <- param[['zeta_res']] naivete_res <- param[['naivete_res']] gamma_L_effect_res <- param[['gamma_L_effect_res']] gamma_tilde_L_effect_res <- param[['gamma_tilde_L_effect_res']] gamma_tilde_L_effect_omega_res <- param[['gamma_tilde_L_effect_omega_res']] gamma_L_effect_omega_res <- param[['gamma_L_effect_omega_res']] gamma_tilde_L_effect_multiple_res <- param[['gamma_tilde_L_effect_multiple_res']] gamma_L_effect_multiple_res <- param[['gamma_L_effect_multiple_res']] gamma_L_res <- param[['gamma_L_res']] gamma_L_omega_res <- param[['gamma_L_omega_res']] gamma_L_multiple_res <- param[['gamma_L_multiple_res']] gamma_B_res <- param[['gamma_B_res']] gamma_B_multiple_res <- param[['gamma_B_multiple_res']] tau_L_2_signed <- param[['tau_L_2']]*-1 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate individual intercepts and steady states under different strategies - Unrestricted alpha # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Gamma-spec num <- eta*tau_L_2/omega - (1-alpha)*delta*rho*(((eta-zeta)*tau_tilde_L/omega+zeta*rho*tau_L_2/omega) + (1+lambda)*mispredict*(-eta+(1-alpha)*delta*rho^2*((eta-zeta)*lambda+zeta))) denom <- 1 - (1-alpha)*delta*rho*(1+lambda) num_omega <- eta*tau_L_2/omega_est - (1-alpha)*delta*rho*(((eta-zeta)*tau_tilde_L/omega_est+zeta*rho*tau_L_2/omega) + (1+lambda)*mispredict*(-eta+(1-alpha)*delta*rho^2*((eta-zeta)*lambda+zeta))) gamma_spec <- num/denom gamma_spec_omega <- num_omega/denom gamma_tilde_spec <- gamma_spec - naivete gamma_tilde_spec_omega <- gamma_spec_omega - naivete # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate individual intercepts and steady states under different strategies # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ intercept_spec <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_spec, gamma_spec, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_L_effect <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_B <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B, gamma_B, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_L <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L, gamma_L, alpha, rho, lambda, mispredict, eta, zeta) intercept_spec_omega <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_spec_omega, gamma_spec_omega, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_L_effect_omega <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_omega, gamma_L_effect_omega, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_L_omega <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_omega, gamma_L_omega, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_B_multiple <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B_multiple, gamma_B_multiple, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_L_multiple <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_multiple, gamma_L_multiple, alpha, rho, lambda, mispredict, eta, zeta) intercept_het_L_effect_eta_high <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta, eta_scale=1.1) intercept_het_L_effect_eta_low <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, lambda, mispredict, eta, zeta, eta_scale=0.9) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate individual counterfactuals # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ x_ss_spec <- calculate_steady_state(param, gamma_tilde_spec, gamma_spec, alpha, rho, lambda, mispredict, eta, zeta, intercept_spec) x_ss_zero_un <- calculate_steady_state(param, 0, 0, alpha, rho, lambda, 0, eta, zeta, intercept_spec) x_ss_zero <- ifelse(x_ss_zero_un<0, 0, x_ss_zero_un) delta_x <- x_ss_spec - x_ss_zero # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate individual intercepts and steady states under different strategies - Restricted alpha # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Gamma-spec gamma_spec_res <- eta_res*tau_L_2 gamma_spec_omega_res <- eta_res*tau_L_2/omega_est gamma_tilde_spec_res <- gamma_spec_res - naivete_res gamma_tilde_spec_omega_res <- gamma_spec_omega_res - naivete_res # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate individual intercepts and steady states under different strategies # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ intercept_spec_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_spec_res, gamma_spec_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_effect_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_B_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B, gamma_B_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L, gamma_L_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_spec_omega_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_spec_omega_res, gamma_spec_omega_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_effect_omega_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_omega_res, gamma_L_effect_omega_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_omega_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_omega, gamma_L_omega_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_effect_multiple_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_multiple_res, gamma_tilde_L_effect_multiple_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_B_multiple_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B_multiple, gamma_B_multiple_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_multiple_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_multiple, gamma_L_multiple_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res) intercept_het_L_effect_eta_high_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res, eta_scale=1.1) intercept_het_L_effect_eta_low_res <- calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_res, gamma_L_effect_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res, eta_scale=0.9) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Calculate individual counterfactuals # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ x_ss_spec_res <- calculate_steady_state(param, gamma_tilde_spec_res, gamma_spec_res, alpha_res, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res, intercept_spec_res) x_ss_zero_un_res <- calculate_steady_state(param, 0, 0, alpha_res, rho_res, lambda_res, 0, eta = eta_res, zeta = zeta_res, intercept_spec_res) x_ss_zero_res <- ifelse(x_ss_zero_un_res<0, 0, x_ss_zero_un_res) delta_x_res <- x_ss_spec_res - x_ss_zero_res # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Compute population averages # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ x_ss_spec_w <- weighted.mean(x_ss_spec, w, na.rm=T) gamma_tilde_spec_w <- weighted.mean(gamma_tilde_spec, w, na.rm=T) gamma_spec_w <- weighted.mean(gamma_spec, w, na.rm=T) gamma_spec_omega_w <- weighted.mean(gamma_spec_omega, w, na.rm=T) delta_x_spec <- weighted.mean(delta_x, w, na.rm=T) x_ss_i_data <- weighted.mean(x_ss_i_data, w, na.rm=T) intercept_spec <- weighted.mean(intercept_spec, w, na.rm=T) intercept_spec_omega <- weighted.mean(intercept_spec_omega, w, na.rm=T) intercept_het_L_effect_omega <- weighted.mean(intercept_het_L_effect_omega, w, na.rm=T) intercept_het_L_effect <- weighted.mean(intercept_het_L_effect, w, na.rm=T) intercept_het_L_effect_eta_high <- weighted.mean(intercept_het_L_effect_eta_high, w, na.rm=T) intercept_het_L_effect_eta_low <- weighted.mean(intercept_het_L_effect_eta_low, w, na.rm=T) intercept_het_L_omega <- weighted.mean(intercept_het_L_omega, w, na.rm=T) intercept_het_B <- weighted.mean(intercept_het_B, w, na.rm=T) intercept_het_L <- weighted.mean(intercept_het_L, w, na.rm=T) intercept_het_B_multiple <- weighted.mean(intercept_het_B_multiple, w, na.rm=T) intercept_het_L_multiple <- weighted.mean(intercept_het_L_multiple, w, na.rm=T) x_ss_spec_w_res <- weighted.mean(x_ss_spec_res, w, na.rm=T) gamma_tilde_spec_w_res <- weighted.mean(gamma_tilde_spec_res, w, na.rm=T) gamma_spec_w_res <- weighted.mean(gamma_spec_res, w, na.rm=T) gamma_spec_omega_w_res <- weighted.mean(gamma_spec_omega_res, w, na.rm=T) delta_x_spec_res <- weighted.mean(delta_x_res, w, na.rm=T) intercept_spec_res <- weighted.mean(intercept_spec_res, w, na.rm=T) intercept_spec_omega_res <- weighted.mean(intercept_spec_omega_res, w, na.rm=T) intercept_het_L_effect_omega_res <- weighted.mean(intercept_het_L_effect_omega_res, w, na.rm=T) intercept_het_L_effect_res <- weighted.mean(intercept_het_L_effect_res, w, na.rm=T) intercept_het_L_effect_eta_high_res <- weighted.mean(intercept_het_L_effect_eta_high_res, w, na.rm=T) intercept_het_L_effect_eta_low_res <- weighted.mean(intercept_het_L_effect_eta_low_res, w, na.rm=T) intercept_het_L_omega_res <- weighted.mean(intercept_het_L_omega_res, w, na.rm=T) intercept_het_B_res <- weighted.mean(intercept_het_B_res, w, na.rm=T) intercept_het_L_res <- weighted.mean(intercept_het_L_res, w, na.rm=T) intercept_het_L_effect_multiple_res <- weighted.mean(intercept_het_L_effect_multiple_res, w, na.rm=T) intercept_het_B_multiple_res <- weighted.mean(intercept_het_B_multiple_res, w, na.rm=T) intercept_het_L_multiple_res <- weighted.mean(intercept_het_L_multiple_res, w, na.rm=T) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Compute hourly variables # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ intercept_spec_hour <- intercept_spec*60*-1 gamma_tilde_spec_hour <- gamma_tilde_spec_w*60 gamma_spec_hour <- gamma_spec_w*60 gamma_spec_omega_hour <- gamma_spec_omega_w*60 intercept_het_B_hour <- intercept_het_B*60*-1 intercept_het_L_hour <- intercept_het_L*60*-1 intercept_het_L_effect_hour <- intercept_het_L_effect*60*-1 intercept_spec_omega_hour <- intercept_spec_omega*60*-1 intercept_het_L_effect_omega_hour <- intercept_het_L_effect_omega*60*-1 intercept_het_L_omega_hour <- intercept_het_L_omega*60*-1 intercept_spec_res_hour <- intercept_spec_res*60*-1 gamma_tilde_spec_res_hour <- gamma_tilde_spec_w_res*60 gamma_spec_res_hour <- gamma_spec_w_res*60 gamma_spec_omega_res_hour <- gamma_spec_omega_w_res*60 intercept_het_B_res_hour <- intercept_het_B_res*60*-1 intercept_het_L_res_hour <- intercept_het_L_res*60*-1 intercept_het_L_effect_res_hour <- intercept_het_L_effect_res*60*-1 intercept_spec_omega_res_hour <- intercept_spec_omega_res*60*-1 intercept_het_L_effect_omega_res_hour <- intercept_het_L_effect_omega_res*60*-1 intercept_het_L_omega_res_hour <- intercept_het_L_omega_res*60*-1 # Return solution <- list( x_ss_i_data = x_ss_i_data, x_ss_spec = x_ss_spec_w, tau_L_2_signed = tau_L_2_signed, intercept_spec = intercept_spec, intercept_spec_hour = intercept_spec_hour, gamma_tilde_spec = gamma_tilde_spec_w, gamma_spec = gamma_spec_w, delta_x_spec = delta_x_spec, gamma_tilde_spec_hour = gamma_tilde_spec_hour, gamma_spec_hour = gamma_spec_hour, intercept_het_L_effect = intercept_het_L_effect, intercept_het_L_effect_eta_high = intercept_het_L_effect_eta_high, intercept_het_L_effect_eta_low = intercept_het_L_effect_eta_low, intercept_het_B = intercept_het_B, intercept_het_L = intercept_het_L, intercept_het_B_hour = intercept_het_B_hour, intercept_het_L_hour = intercept_het_L_hour, intercept_het_L_effect_hour = intercept_het_L_effect_hour, gamma_spec_omega_hour = gamma_spec_omega_hour, intercept_spec_omega_hour = intercept_spec_omega_hour, intercept_het_L_effect_omega_hour = intercept_het_L_effect_omega_hour, intercept_het_L_omega_hour = intercept_het_L_omega_hour, intercept_het_B_multiple = intercept_het_B_multiple, intercept_het_L_multiple = intercept_het_L_multiple, intercept_het_L_effect_omega = intercept_het_L_effect_omega, intercept_het_L_omega = intercept_het_L_omega, x_ss_spec_res = x_ss_spec_w_res, intercept_spec_res = intercept_spec_res, intercept_spec_res_hour = intercept_spec_res_hour, gamma_tilde_spec_res = gamma_tilde_spec_w_res, gamma_spec_res = gamma_spec_w_res, delta_x_spec_res = delta_x_spec_res, gamma_tilde_spec_res_hour = gamma_tilde_spec_res_hour, gamma_spec_res_hour = gamma_spec_res_hour, intercept_het_L_effect_res = intercept_het_L_effect_res, intercept_het_L_effect_eta_high_res = intercept_het_L_effect_eta_high_res, intercept_het_L_effect_eta_low_res = intercept_het_L_effect_eta_low_res, intercept_het_B_res = intercept_het_B_res, intercept_het_L_res = intercept_het_L_res, intercept_het_B_res_hour = intercept_het_B_res_hour, intercept_het_L_res_hour = intercept_het_L_res_hour, intercept_het_L_effect_res_hour = intercept_het_L_effect_res_hour, gamma_spec_omega_res_hour = gamma_spec_omega_res_hour, intercept_spec_omega_res_hour = intercept_spec_omega_res_hour, intercept_het_L_effect_omega_res_hour = intercept_het_L_effect_omega_res_hour, intercept_het_L_omega_res_hour = intercept_het_L_omega_res_hour, intercept_het_L_effect_multiple_res = intercept_het_L_effect_multiple_res, intercept_het_B_multiple_res = intercept_het_B_multiple_res, intercept_het_L_multiple_res = intercept_het_L_multiple_res, intercept_het_L_effect_omega_res = intercept_het_L_effect_omega_res, intercept_het_L_omega_res = intercept_het_L_omega_res ) return(solution) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Check functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ check_sys_eq_1 <- function(param) { # Define rho <- param[['rho']] lambda <- param[['lambda']] tau_B_2 <- param[['tau_B_2']] tau_B_3 <- param[['tau_B_3']] tau_B_4 <- param[['tau_B_4']] tau_B_5 <- param[['tau_B_5']] diff <- rho + lambda # Rho diff <- diff - tau_B_5 / (tau_B_4*(1 + lambda)) # Lambda diff <- diff - tau_B_4 / (rho*tau_B_3 + rho^2*tau_B_2) # Return return(diff) } calculate_steady_state <- function(param, gamma_tilde, gamma, alpha, rho, lambda, mispredict, eta, zeta, intercept=NA, eta_scale=1){ eta <- eta * eta_scale delta <- param[['delta']] # Calculate term1 <- intercept term2 <- (1-alpha)*delta*rho term3 <- (zeta-eta) * mispredict - gamma_tilde*(1+lambda) num <- term1 + term2*term3 + gamma terma <- -eta -((1-alpha)*delta*rho*(zeta-eta)) termb <- zeta*((rho - (1-alpha)*delta*(rho**2)) / (1-rho)) denom <- terma - termb x_ss_calc <- num /denom return(x_ss_calc) } calculate_x_ss_i_spec <- function(df){ x_ss_i_df <- df %>% mutate(x_ss_i_data = PD_P1_UsageFITSBY) return(x_ss_i_df$x_ss_i_data) } get_avg_use <- function(df){ estimate <- list(signif(weighted.mean(df$PD_P1_UsageFITSBY,df$w, na.rm=TRUE), digits=3)) names(estimate) <- c('avg_use') # Return return(estimate) } get_fb <- function(df){ df <- df %>% mutate(F_B_uncensored = 50*PD_P1_UsageFITSBY/20) %>% mutate(F_B_min = ifelse(F_B_uncensored<150, F_B_uncensored, 150)) %>% mutate(F_B = F_B_min/num_days) estimate <- list(signif(weighted.mean(df$F_B,df$w, na.rm=TRUE), digits=3)) names(estimate) <- c('F_B') # Return return(estimate) } calculate_intercept_spec <- function(x_ss_i_data, param, gamma_tilde, gamma, alpha, rho, lambda, mispredict, eta, zeta, eta_scale=1){ delta <- param[['delta']] eta <- eta*eta_scale terma <- (1-alpha)*delta*rho termb <- (rho - terma*rho) / (1-rho) term1 <- -eta -terma*(zeta-eta)-zeta*termb term2 <- terma*((zeta-eta)*mispredict - (1+lambda)*gamma_tilde) intercept <- x_ss_i_data*term1 - term2 - gamma return(intercept) } check_steady_state <- function(param){ # Define x_ss <- param[['x_ss']] gamma_L_effect <- param[['gamma_L_effect']] gamma_tilde_L_effect <- param[['gamma_tilde_L_effect']] mispredict <- param[['mispredict']] rho <- param[['rho']] alpha <- param[['alpha']] intercept_het_L_effect <- param[['intercept_het_L_effect']] intercept_het_L_effect_eta_high <- param[['intercept_het_L_effect_eta_high']] intercept_het_L_effect_eta_low <- param[['intercept_het_L_effect_eta_low']] print('||||||||||||| Initial calculation |||||||||||||') print(x_ss) #print('||||||||||||| Checked calculation rho_tilde=0 |||||||||||||') #print(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, mispredict, intercept = intercept_het_L_effect)) # print(paste0('alpha 1.0eta:', intercept_het_L_effect)) # print('||||||||||||| Checked calculation rho_tilde=0, eta*1.1 |||||||||||||') # print(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, mispredict, intercept = intercept_het_L_effect_eta_high)) # print(paste0('alpha 1.1eta:', intercept_het_L_effect_eta_high)) # print('||||||||||||| Checked calculation rho_tilde=0, eta*0.9 |||||||||||||') # print(calculate_steady_state(param, gamma_tilde_L_effect, gamma_L_effect, alpha, rho, mispredict, intercept = intercept_het_L_effect_eta_low)) # print(paste0('alpha 0.9eta:', intercept_het_L_effect_eta_low)) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Moment functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ get_bonus <- function(df, t) { # Specify regression dep_var <- sprintf('PD_P%s_UsageFITSBY', t) if (t == 1) { eq <- paste0(dep_var, '~ L + B + S') } else if (t > 1) { eq <- paste0(dep_var, '~ PD_P1_UsageFITSBY + L + B + S') } # Run regression fit <- lm(data = df, formula = eq, weights = w) estimate <- list(ifelse(fit$coefficients[['B']]>0, 0,fit$coefficients[['B']])) names(estimate) <- c(sprintf('tau_B_%s', t)) # Return return(estimate) } get_multiple_good_taus <- function(df) { # Run regression fit <- lm(data = df, formula = S4_Substitution_W ~ L+B+S, weights = w) estimate <- list(fit$coefficients[['L']], fit$coefficients[['B']]) names(estimate) <- c('tau_L_y', 'tau_B_y') return(estimate) } get_full_bonus_2 <- function(df, t) { # Run regression fit <- lm(data = df, formula = 'PD_P2_UsageFITSBY ~ PD_P1_UsageFITSBY + L + B + S', weights = w) estimate <- list(ifelse(fit$coefficients[['B']]>0, 0,fit$coefficients[['B']])) names(estimate) <- c('tau_B_2_full') # Return return(estimate) } get_bonus_2b <- function(df, full=FALSE) { if (full){ fit <- lm(data = df, formula = 'PD_P2_UsageFITSBY ~ PD_P1_UsageFITSBY + L + B + S', weights = w) estimate <- list(ifelse(fit$coefficients[['B']]>0, 0,fit$coefficients[['B']])) names(estimate) <- c('tau_B_2') } else{ days <- 33:42 fit <- lm(data = df %>% mutate(PD_P2b_Usage_FITSBY = rowSums(.[paste0('PD_DailyUsageFITSBY_',days)], na.rm=TRUE)/length(days)), formula = 'PD_P2b_Usage_FITSBY ~ PD_P1_UsageFITSBY + L + B + S', weights = w) coef <- fit$coefficients[['B']] coef <- ifelse(coef>0, 0, coef) estimate <- list(coef) names(estimate) <- c('tau_B_2') } # Return return(estimate) } get_bonus_tilde <- function(df) { # Specify regression dep_var <- sprintf('S3_PredictUseNext_1_W') eq <- paste0(dep_var, '~ PD_P1_UsageFITSBY + L + B + S') # Run regression fit <- lm(data = df, formula = eq, weights = w) estimate <- list(fit$coefficients[['B']]) names(estimate) <- c(sprintf('tau_tilde_B_3_2', t)) # Return return(estimate) } get_limit_tilde <- function(df) { # Specify regression eq <- 'S3_PredictUseNext_1_W ~ L + B + S' # Run regression fit <- lm(data = df, formula = eq, weights = w) estimate <- list(ifelse(fit$coefficients[['L']]>0, 0,fit$coefficients[['L']])) names(estimate) <- c('tau_tilde_L') # Return return(estimate) } get_true_limit_tilde <- function(df) { # Specify regression eq <- 'S3_PredictUseNext_1_W ~ L + B + S' # Run regression fit <- lm(data = df, formula = eq, weights = w) estimate <- list(ifelse(fit$coefficients[['L']]>0, 0,fit$coefficients[['L']])) names(estimate) <- c('true_tau_tilde_L') # Return return(estimate) } get_limit_tildes <- function(df, t) { # Specify regression dep_var <- sprintf('S2_PredictUseNext_%s_W', t-1) eq <- paste0(dep_var, '~ PD_P1_UsageFITSBY + L + B + S') # Run regression fit <- lm(data = df, formula = eq, weights = w) estimate <- list(ifelse(fit$coefficients[['L']]>0, 0,fit$coefficients[['L']])) names(estimate) <- c(sprintf('tau_tilde_L_%s_2', t)) # Return return(estimate) } get_limit_2b <- function(df) { # Run regression fit <- lm(data = df , formula = 'PD_P2_UsageFITSBY ~ PD_P1_UsageFITSBY + L + B + S', weights = w) estimate <- list(ifelse(fit$coefficients[['L']]>0, 0,fit$coefficients[['L']])) names(estimate) <- c('tau_L_2') # Return return(estimate) } get_limit <- function(df) { #Ryb regressuib fit <- lm(data = df , formula = 'PD_P3_UsageFITSBY ~ PD_P1_UsageFITSBY + L + B + S', weights = w) estimate <- list(ifelse(fit$coefficients[['L']]>0, 0,fit$coefficients[['L']])) names(estimate) <- c('tau_L_3') # Return return(estimate) } get_MPL_tilde <- function(df) { regression_df <- df %>% mutate(S2_reduction = PD_P3_UsageFITSBY - S2_PredictUseInitial_W) %>% select(S2_reduction, S2_PredictUseInitial_W, S2_PredictUseBonus, PD_P3_UsageFITSBY, B, S, L, PD_P1_UsageFITSBY,w) # Run regression fit <- lm(data = regression_df, formula = S2_reduction ~ B + S + L + PD_P1_UsageFITSBY, weights = w) estimate <- list(fit$coefficients[['B']]) names(estimate) <- c(sprintf('MPL_S2')) # Return return(estimate) } get_limit_last_week <- function(df) { # Run regression eq <- 'PD_WeeklyUsageFITSBY_15 ~ PD_P1_UsageFITSBY + L + B + S' fit <- lm(data = df, formula = eq, weights = w) estimate <- list(fit$coefficients[['L']]) names(estimate) <- c('limit_effect_last_week') # Return return(estimate) } get_limit_avg <- function(df) { # Reshape data df %<>% select( UserID, w, L, B, S, PD_P1_UsageFITSBY, PD_P2_UsageFITSBY, PD_P3_UsageFITSBY, PD_P4_UsageFITSBY, PD_P5_UsageFITSBY ) df %<>% gather( key = 'period', value = 'usage', -UserID, -w, -L, -B, -S, -PD_P1_UsageFITSBY ) # Run regression eq <- 'usage ~ PD_P1_UsageFITSBY + L + B + S' fit <- lm(data = df, formula = eq, weights = w) estimate <- list(ifelse(fit$coefficients[['L']]>0, 0,fit$coefficients[['L']])) names(estimate) <- c('tau_L') # Return return(estimate) } get_taus <- function(df, winsorize=F, full=full) { # Bonus bonus <- 3:5 %>% map(~get_bonus(df, .)) %>% list.flatten # Bonus Tilde bonus_tilde <- get_bonus_tilde(df) # Bonus 2B bonus_2b <- get_bonus_2b(df, full=full) bonus_2_full <- get_full_bonus_2(df) #Get MPL MPL <- get_MPL_tilde(df) # Limit limit <- get_limit(df) limit_tilde <- get_limit_tilde(df) true_limit_tilde <- get_true_limit_tilde(df) limit_tilde[[1]] <- limit[[1]] # Limit Tilde limit_tildes <- 2:3 %>% map(~get_limit_tildes(df, .)) %>% list.flatten limit_2 <- get_limit_2b(df) limit_avg <- get_limit_avg(df) multiple_good_taus <- get_multiple_good_taus(df) # Return tau <- list.merge(bonus, bonus_tilde, bonus_2b, bonus_2_full, limit, limit_tilde, limit_tildes, limit_2,limit_avg, true_limit_tilde, MPL, multiple_good_taus) if (winsorize){ tau_tilde_limit <- -4 ratio_limit <- 0.18 tau$tau_tilde_L <- min(-2, tau$tau_tilde_L) tau$tau_B_5 <- min(tau$tau_B_5, tau$tau_B_4 - ratio_limit * tau$tau_B_3) } return(tau) } get_mispredict <- function(df) { # Filter to control df_unfiltered <- df df %<>% filter(B == 0, L == 0) # Reshape data names(df) <- gsub('PD_(.*)_UsageFITSBY', 'UsageActual_\\1', names(df)) names(df) <- gsub('S(.*)_PredictUseNext_1_W', 'UsagePredicted_P\\1', names(df)) df %<>% select( UserID, w, starts_with('UsagePredicted'), starts_with('UsageActual') ) %>% select( UserID, w, ends_with('P2'), ends_with('P3'), ends_with('P4') ) df %<>% gather(key = 'period', value = 'value', -UserID, -w) %>% separate(period, c('key', 'period'), sep = '_') %>% spread(key = 'key', value = 'value') # Get mean df %<>% mutate(mispredict = UsageActual - UsagePredicted) estimate <- list( weighted.mean(df$mispredict, df$w, na.rm = T), weighted.mean(df_unfiltered$PD_P1_UsageFITSBY, df_unfiltered$w, na.rm=T), weighted.mean(df$UsagePredicted, df$w, na.rm = T) ) names(estimate) <- c('mispredict', 'x_ss', 'x_tilde') # Return return(estimate) } get_ideal <- function(df) { # Reshape data df %<>% select( UserID, w, L, B, S3_PhoneUseChange ) df %<>% gather(key = 'key', value = 'value', -UserID, -w, -L, -B) # Get mean estimate <- list( weighted.mean(filter(df, L == 1)$value, filter(df, L == 1)$w, na.rm = T), weighted.mean(filter(df, L == 0)$value, filter(df, L == 0)$w, na.rm = T) ) names(estimate) <- c('d_L', 'd_CL') # Return return(estimate) } get_predict <- function(df) { # Filter to control df %<>% filter(B == 1) # Reshape data df %<>% select( UserID, w, ends_with('PredictUseInitial'), ends_with('PredictUseBonus') ) #reformats any winsorization names(df) <- gsub('(.*)_W', '\\1', names(df)) df %<>% gather(key = 'period', value = 'value', -UserID, -w) %>% separate(period, c('period', 'key'), sep = '_') %>% spread(key = 'key', value = 'value') # Get mean df %<>% mutate(PredictUseBonus = PredictUseInitial * (1 - (PredictUseBonus / 100))) %>% mutate(bonus_effect = PredictUseBonus - PredictUseInitial) %>% mutate(average = (PredictUseBonus + PredictUseInitial) / 2) estimate <- list( weighted.mean(df$bonus_effect, df$w, na.rm = T), weighted.mean(filter(df, period == 'S2')$average, filter(df, period == 'S2')$w, na.rm = T) ) names(estimate) <- c('tau_tilde_B', 'x_tilde_2_B') # Return return(estimate) } get_wtp <- function(df) { df %<>% select( UserID, w, ends_with('MPL'), ends_with('MPLLimit') ) df %<>% gather(key = 'period', value = 'value', -UserID, -w) %>% separate(period, c('period', 'key'), sep = '_') %>% spread(key = 'key', value = 'value') # Get mean estimate <- list( weighted.mean(df$MPL, df$w, na.rm = T) / num_days, weighted.mean(df$MPLLimit, df$w, na.rm = T) / num_days ) names(estimate) <- c('v_B', 'v_L') # Return return(estimate) } find_tau_spec <- function(df, save_reg=FALSE){ tau_data <- df %>% select( UserID, w, L, B, S, PD_P1_UsageFITSBY, PD_P2_UsageFITSBY, PD_P3_UsageFITSBY, PD_P4_UsageFITSBY, PD_P5_UsageFITSBY, PD_P2_LimitTightFITSBY ) tau_data %<>% gather( key = 'period', value = 'usage', -UserID, -w, -L, -B, -S, -PD_P1_UsageFITSBY, -PD_P2_LimitTightFITSBY ) fit <- tau_data %>% mutate(tightness=ifelse(L,PD_P2_LimitTightFITSBY, 0)) %>% lm(formula = 'usage ~ PD_P1_UsageFITSBY + L + tightness + B + S', weights = w) if(save_reg){ stargazer(fit, omit.stat = c("adj.rsq","f","ser"), covariate.labels = c("Period 1 Usage", "Limit Treatment", "Limit Treatment x Period 2 Limit Tightness", "Bonus Treatment"), dep.var.labels = "FITSBY Usage (mins/day)", title = "", omit = c("S1", "S2", "S3", "S4", "S5", "S6", "S7", "S8"), type = "latex", omit.table.layout = "n", float = FALSE, dep.var.caption = "", star.cutoffs = NA, out = "output/heterogeneity_reg.tex" ) } const <- fit$coefficients['L'] slope <- fit$coefficients['tightness'] return(const + slope * df$PD_P2_LimitTightFITSBY) } find_tau_L2_spec <- function(df, save_reg=FALSE){ tau_data <- df %>% select( UserID, w, L, B, S, PD_P1_UsageFITSBY, PD_P2_UsageFITSBY, PD_P3_UsageFITSBY, PD_P4_UsageFITSBY, PD_P5_UsageFITSBY, PD_P2_LimitTightFITSBY ) fit <- tau_data %>% mutate(tightness=ifelse(L,PD_P2_LimitTightFITSBY, 0)) %>% lm(formula = 'PD_P2_UsageFITSBY ~ PD_P1_UsageFITSBY + L + tightness + B + S', weights = w) const <- fit$coefficients['L'] slope <- fit$coefficients['tightness'] return(const + slope * df$PD_P2_LimitTightFITSBY) } find_tau_L3_spec <- function(df, save_reg=FALSE){ tau_data <- df %>% select( UserID, w, L, B, S, PD_P1_UsageFITSBY, PD_P2_UsageFITSBY, PD_P3_UsageFITSBY, PD_P4_UsageFITSBY, PD_P5_UsageFITSBY, PD_P2_LimitTightFITSBY ) fit <- tau_data %>% mutate(tightness=ifelse(L,PD_P2_LimitTightFITSBY, 0)) %>% lm(formula = 'PD_P3_UsageFITSBY ~ PD_P1_UsageFITSBY + L + tightness + B + S', weights = w) const <- fit$coefficients['L'] slope <- fit$coefficients['tightness'] return(const + slope * df$PD_P3_LimitTightFITSBY) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Model functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ estimate_model <- function(df, param, winsorize=F, full=F, display_warning=FALSE) { # Empirical moments param %<>% list.merge( #get_opt(df), get_taus(df, winsorize=winsorize, full=full), get_mispredict(df), get_ideal(df), get_predict(df), get_wtp(df), get_avg_use(df), get_fb(df), get_limit_last_week(df) ) # Solve system of equation #1 param %<>% solve_sys_eq_1 %>% as.list %>% list.merge(param) # Solve system of equations #2 param %<>% solve_sys_eq_2(display_warning=display_warning) %>% as.list %>% list.merge(param) # Solve system of equations #3 param %<>% solve_sys_eq_3 %>% as.list %>% list.merge(param) # Solve for individual effects tau_L_2_spec <- find_tau_L2_spec(df) tau_tilde_spec <- find_tau_L3_spec(df) x_ss_i_data <- calculate_x_ss_i_spec(df) param %<>% solve_effects_individual(x_ss_i_data= x_ss_i_data, tau_tilde_L=tau_tilde_spec, tau_L_2=tau_L_2_spec, w=df$w)%>% as.list %>% list.merge(param) # Solve for effects param %<>% solve_effects(df) %>% as.list %>% list.merge(param) # Solve for counterfactuals param %<>% solve_counterfactuals(df) %>% as.list %>% list.merge(param) # Return return(param) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Plotting functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ plot_time_effects <- function(median, bottom, top, filename=""){ order_results_time <- function(df1){ r <- c(df1[['delta_x_cap_res']], df1[['delta_x_tilde_B_res']], df1[['delta_x_tilde_L_res']], df1[['delta_x_spec_res']]) return(r) } order_results_time_est <- function(df1){ r <- c(df1[['delta_x_cap']], df1[['delta_x_tilde_B']], df1[['delta_x_tilde_L']], df1[['delta_x_spec']]) return(r) } x <- c('Limit\n effect', 'Bonus \n valuation', 'Limit \n valuation', 'Heterogeneous\n limit effect') names <- rep(factor(x, levels=x),2) counterfactuals_zero <- order_results_time(param_full) lower_counterfactuals_zero <- order_results_time(bottom) upper_counterfactuals_zero <- order_results_time(top) counterfactuals_est <- order_results_time_est(param_full) lower_counterfactuals_est <- order_results_time_est(bottom) upper_counterfactuals_est <- order_results_time_est(top) df <- data.frame(names, counterfactuals_zero, lower_counterfactuals_zero, upper_counterfactuals_zero, counterfactuals_est, lower_counterfactuals_est, upper_counterfactuals_est) cols <- c("No projection bias"=maroon, "Perceived projection bias"=grey) a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals_zero, colour="No projection bias"), stat="identity", position = position_nudge(x = -.1)) + geom_point(aes(y=counterfactuals_est, colour="Perceived projection bias"), stat="identity", position = position_nudge(x = .1))+ geom_errorbar(aes(ymin=lower_counterfactuals_zero, ymax=upper_counterfactuals_zero), stat="identity", colour=maroon, position = position_nudge(x = -.1)) + geom_errorbar(aes(ymin=lower_counterfactuals_est, ymax=upper_counterfactuals_est), stat="identity", colour=grey, position=position_nudge(x = .1)) + scale_y_continuous(name="Time effect (minutes/day)") + theme_classic() + labs(x = "") + scale_colour_manual(name = "", values=cols, labels = unname(TeX(c(paste0("Zero projection bias", " (", "$\\alpha=1$", ")"), paste0("Estimated projection bias", " (" ,"$\\alpha=\\hat{\\alpha}$", ")") ))))+ theme(legend.text.align = 0, legend.key.height = unit(1, "cm"), legend.position="bottom") + theme(legend.margin=margin(0,0,0,0), legend.box.margin=margin(-10,-10,-10,-10)) + theme(axis.text.x = element_text(colour="black")) coord_cartesian(ylim = c(0, 180)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } plot_time_effects_bal <- function(param_full, param_balanced, bottom, top, bottom_bal, top_bal, filename=""){ order_results_time <- function(df1){ r <- c(df1[['delta_x_cap_res']], df1[['delta_x_tilde_B_res']], df1[['delta_x_tilde_L_res']], df1[['delta_x_spec_res']]) return(r) } x <- c('Limit\n effect', 'Bonus \n valuation', 'Limit \n valuation', 'Heterogeneous\n limit effect') names <- rep(factor(x, levels=x),2) counterfactuals_zero <- order_results_time(param_full) lower_counterfactuals_zero <- order_results_time(bottom) upper_counterfactuals_zero <- order_results_time(top) counterfactuals_est <- order_results_time(param_balanced) lower_counterfactuals_est <- order_results_time(bottom_bal) upper_counterfactuals_est <- order_results_time(top_bal) df <- data.frame(names, counterfactuals_zero, lower_counterfactuals_zero, upper_counterfactuals_zero, counterfactuals_est, lower_counterfactuals_est, upper_counterfactuals_est) cols <- c("No perceived habit formation"=maroon , "Perceived habit formation"=skyblue) a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals_zero, colour="No perceived habit formation"), stat="identity", position = position_nudge(x = -.1)) + geom_point(aes(y=counterfactuals_est, colour="Perceived habit formation"), stat="identity", position = position_nudge(x = .1))+ geom_errorbar(aes(ymin=lower_counterfactuals_zero, ymax=upper_counterfactuals_zero), stat="identity", colour=maroon, position = position_nudge(x = -.1)) + geom_errorbar(aes(ymin=lower_counterfactuals_est, ymax=upper_counterfactuals_est), stat="identity", colour=skyblue, position=position_nudge(x = .1)) + scale_y_continuous(name="Time effect (minutes/day)") + theme_classic() + labs(x = "") + scale_colour_manual(name = "", values=cols, labels = c("Unweighted sample", "Weighted toward U.S. adults"))+ theme(legend.text.align = 0, legend.key.height = unit(1, "cm"), legend.position="bottom") + theme(legend.margin=margin(0,0,0,0), legend.box.margin=margin(-10,-10,-10,-10)) + theme(axis.text.x = element_text(colour="black")) + coord_cartesian(ylim = c(0, 165)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } plot_time_effects_both <- function(param_full, param_balanced, bottom, top, bottom_bal, top_bal, filename=""){ order_results_time <- function(df1){ r <- c(df1[['delta_x_cap_res']], df1[['delta_x_tilde_B_res']], df1[['delta_x_tilde_L_res']], df1[['delta_x_cap_multiple_res']], df1[['delta_B_multiple_res']], df1[['delta_x_L_multiple_res']], df1[['delta_x_cap_omega_res']], df1[['delta_x_L_omega_res']], df1[['delta_x_spec_res']]) return(r) } order_results_bal <- function(df1){ r <- c(df1[['delta_x_cap_res']]) return(r) } x <- c('Limit effect', 'Bonus valuation', 'Limit valuation', 'Limit effect \n multiple-good model', 'Bonus valuation \n multiple-good model', 'Limit valuation \n multiple-good model', 'Limit effect \n w=w', 'Limit valuation \n w=w', 'Heterogeneous limit effect' ) names <- factor(x, levels=x) x_bal <- c( 'Limit effect \n reweighted sample') names_bal <- factor(x_bal, levels=x_bal) counterfactuals <- order_results_time(param_full) lower_counterfactuals <- order_results_time(bottom) upper_counterfactuals <- order_results_time(top) counterfactuals_bal <- order_results_bal(param_balanced) lower_counterfactuals_bal <- order_results_bal(bottom_bal) upper_counterfactuals_bal<- order_results_bal(top_bal) df_normal <- data.frame(names, counterfactuals,lower_counterfactuals, upper_counterfactuals) df_bal <- data.frame(names_bal, counterfactuals_bal, lower_counterfactuals_bal, upper_counterfactuals_bal) %>% rename(names = names_bal, counterfactuals = counterfactuals_bal, lower_counterfactuals = lower_counterfactuals_bal, upper_counterfactuals = upper_counterfactuals_bal) df <- rbind(df_normal, df_bal) xaxislabels <- c('Limit effect', 'Bonus valuation', 'Limit valuation', 'Limit effect, \n multiple-good model', 'Bonus valuation, \n multiple-good model', 'Limit valuation, \n multiple-good model', unname(TeX(paste0("Limit effect,", "$\\omega = \\hat{\\omega}$"))), unname(TeX(paste0("Limit valuation,", "$\\omega = \\hat{\\omega}$"))), 'Heterogeneous limit effect', 'Limit effect, \n weighted sample') a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals), colour=maroon)+ geom_errorbar(aes(ymin=lower_counterfactuals, ymax=upper_counterfactuals), colour=maroon) + scale_y_continuous(name="Effect of temptation on FITSBY use (minutes/day)") + theme_classic() + labs(x = "") + theme(axis.text.x = element_text(colour="black")) + coord_cartesian(ylim = c(0, 180)) + theme(axis.text.x = element_text(angle = 45, hjust = 1)) + scale_x_discrete(labels= xaxislabels)+ theme(axis.title.y = element_text(size = 10)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } # plot_time_effects_robust <- function(param_full, bottom, top, filename=""){ # order_results_time <- function(df1){ # r <- c(df1[['delta_x_cap']], # df1[['delta_x_tilde_B']], # df1[['delta_x_tilde_L']], # df1[['delta_x_cap_multiple']], # df1[['delta_x_L_multiple']], # df1[['delta_B_multiple']], # df1[['delta_x_cap_omega']], # df1[['delta_x_L_omega']], # df1[['delta_x_spec']]) # return(r) # } # x <- c( 'Limit effect', # 'Bonus valuation', # 'Limit valuation', # 'Limit effect \n multiple-good model', # 'Limit valuation \n multiple-good model', # 'Bonus valuation \n multiple-good model', # 'Limit effect \n w=w', # 'Limit valuation \n w=w', # 'Heterogeneous limit effect' ) # names <- factor(x, levels=x) # counterfactuals <- order_results_time(param_full) # lower_counterfactuals <- order_results_time(bottom) # upper_counterfactuals <- order_results_time(top) # df <- data.frame(names, counterfactuals) # xaxislabels <- c('Limit effect', # 'Bonus valuation', # 'Limit valuation', # 'Limit effect \n multiple-good model', # 'Limit valuation \n multiple-good model', # 'Bonus valuation \n multiple-good model', # unname(TeX(paste0("Limit effect,", "$\\omega = \\hat{\\omega}$"))), # unname(TeX(paste0("Limit valuation,", "$\\omega = \\hat{\\omega}$"))), # 'Heterogeneous limit effect') # a <- ggplot(df, aes(x=names, width=.2)) + # geom_point(aes(y=counterfactuals), colour=maroon)+ # geom_errorbar(aes(ymin=lower_counterfactuals, ymax=upper_counterfactuals), colour=maroon) + # scale_y_continuous(name="Effect of temptation on FITSBY use (minutes/day)") + # theme_classic() + # labs(x = "") + # theme(axis.text.x = element_text(colour="black")) + # #coord_cartesian(ylim = c(-50, 200)) + # theme(axis.text.x = element_text(angle = 45, hjust = 1)) + # scale_x_discrete(labels= xaxislabels)+ # theme(axis.title.y = element_text(size = 10)) # ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") # } plot_time_effects_both_est <- function(param_full, bottom, top, filename=""){ order_results_time <- function(df1){ r <- c(df1[['delta_x_cap']], df1[['delta_x_tilde_B']], df1[['delta_x_tilde_L']], df1[['delta_B_multiple']], df1[['delta_x_L_multiple']], df1[['delta_x_cap_omega']], df1[['delta_x_L_omega']], df1[['delta_x_spec']]) return(r) } x <- c('Limit effect', 'Bonus valuation', 'Limit valuation', 'Bonus valuation, \n multiple-good model', 'Limit valuation, \n multiple-good model', 'Limit effect \n w=w', 'Limit valuation \n w=w', 'Heterogeneous limit effect' ) names <- factor(x, levels=x) counterfactuals <- order_results_time(param_full) lower_counterfactuals <- order_results_time(bottom) upper_counterfactuals <- order_results_time(top) df <- data.frame(names, counterfactuals) xaxislabels <- c('Limit effect', 'Bonus valuation', 'Limit valuation', 'Bonus valuation, \n multiple-good model', 'Limit valuation, \n multiple-good model', unname(TeX(paste0("Limit effect,", "$\\omega = \\hat{\\omega}$"))), unname(TeX(paste0("Limit valuation,", "$\\omega = \\hat{\\omega}$"))), 'Heterogeneous limit effect') a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals), colour=maroon)+ geom_errorbar(aes(ymin=lower_counterfactuals, ymax=upper_counterfactuals), colour=maroon) + scale_y_continuous(name="Effect of temptation on FITSBY use (minutes/day)") + theme_classic() + labs(x = "") + theme(axis.text.x = element_text(colour="black")) + coord_cartesian(ylim = c(0, 200)) + theme(axis.text.x = element_text(angle = 45, hjust = 1)) + scale_x_discrete(labels= xaxislabels)+ theme(axis.title.y = element_text(size = 10)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } plot_decomposition_boot <- function(median, bottom, top, filename){ order_results_zero <- function(df1){ r <- c(df1[['x_ss_L_effect_res']], df1[['x_ss_naivete_res']], df1[['x_ss_temptation_res']], df1[['x_ss_habit_res']], df1[['x_ss_habit_temptation_res']]) return(r) } order_results_est <- function(df1){ r <- c(df1[['x_ss_L_effect']], df1[['x_ss_naivete']], df1[['x_ss_temptation']], df1[['x_ss_habit']], df1[['x_ss_habit_temptation']]) return(r) } x <- c('Baseline','No naivete', 'No temptation', 'No habit\nformation', 'No temptation\n or habit formation') names <- rep(factor(x, levels=x),2) counterfactuals_zero <- order_results_zero(param_full) lower_counterfactuals_zero <- order_results_zero(bottom) upper_counterfactuals_zero <- order_results_zero(top) counterfactuals_est <- order_results_est(param_full) lower_counterfactuals_est <- order_results_est(bottom) upper_counterfactuals_est <- order_results_est(top) df <- data.frame(names, counterfactuals_zero, lower_counterfactuals_zero, upper_counterfactuals_zero, counterfactuals_est, lower_counterfactuals_est, upper_counterfactuals_est) cols <- c("No projection bias"=maroon , "Perceived projection bias"=grey) a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals_zero, colour="No projection bias"), stat="identity", position = position_nudge(x = -.1)) + geom_point(aes(y=counterfactuals_est, colour="Perceived projection bias"), stat="identity", position = position_nudge(x = .1))+ geom_errorbar(aes(ymin=lower_counterfactuals_zero, ymax=upper_counterfactuals_zero), stat="identity", colour=maroon, position = position_nudge(x = -.1)) + geom_errorbar(aes(ymin=lower_counterfactuals_est, ymax=upper_counterfactuals_est), stat="identity", colour=grey, position=position_nudge(x = .1)) + scale_y_continuous(name="FITSBY use (minutes/day)") + theme_classic() + #theme(axis.text.x = element_text(angle = 45, hjust = 1)) + labs(x = "") + scale_colour_manual(name = "", values=cols, labels = unname(TeX(c(paste0("Restricted model", " (", "$\\alpha$", "$=$", "$1$", ")"), paste0("Unrestricted model", " (" ,"$\\alpha$", "$=$", "$\\hat{\\alpha}$", ")") ))))+ theme(legend.text.align = 0, legend.key.height = unit(1, "cm"), legend.position="bottom") + theme(legend.margin=margin(0,0,0,0), legend.box.margin=margin(-10,-10,-10,-10)) + theme(axis.text.x = element_text(colour="black")) + coord_cartesian(ylim = c(0, 200)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } plot_decomposition_boot_etas <- function(median, bottom, top, filename){ order_results_zero <- function(df1){ r <- c(df1[['x_ss_L_effect_res']], df1[['x_ss_naivete_res']], df1[['x_ss_temptation_res']], df1[['x_ss_habit_res']], df1[['x_ss_habit_temptation_res']]) return(r) } order_results_zero_eta_high <- function(df1){ r <- c(df1[['x_ss_L_effect_eta_high_res']], df1[['x_ss_naivete_eta_high_res']], df1[['x_ss_temptation_eta_high_res']], df1[['x_ss_habit_eta_high_res']], df1[['x_ss_habit_temptation_eta_high_res']]) return(r) } order_results_zero_eta_low <- function(df1){ r <- c(df1[['x_ss_L_effect_eta_low_res']], df1[['x_ss_naivete_eta_low_res']], df1[['x_ss_temptation_eta_low_res']], df1[['x_ss_habit_eta_low_res']], df1[['x_ss_habit_temptation_eta_low_res']]) return(r) } x <- c('Baseline','No naivete', 'No temptation', 'No habit\nformation', 'No temptation\n or habit formation') names <- rep(factor(x, levels=x),2) counterfactuals_zero <- order_results_zero(param_full) lower_counterfactuals_zero <- order_results_zero(bottom) upper_counterfactuals_zero <- order_results_zero(top) counterfactuals_zero_eta_high <- order_results_zero_eta_high(param_full) lower_counterfactuals_zero_eta_high <- order_results_zero_eta_high(bottom) upper_counterfactuals_zero_eta_high <- order_results_zero_eta_high(top) counterfactuals_zero_eta_low <- order_results_zero_eta_low(param_full) lower_counterfactuals_zero_eta_low <- order_results_zero_eta_low(bottom) upper_counterfactuals_zero_eta_low <- order_results_zero_eta_low(top) df <- data.frame(names, counterfactuals_zero, lower_counterfactuals_zero, upper_counterfactuals_zero, counterfactuals_zero_eta_high, lower_counterfactuals_zero_eta_high, upper_counterfactuals_zero_eta_high, counterfactuals_zero_eta_low, lower_counterfactuals_zero_eta_low, upper_counterfactuals_zero_eta_low) cols <- c("eta_0.9"=deepskyblue, "eta_1.0"=maroon, "eta_1.1"=grey) a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals_zero_eta_low, colour="eta_0.9"), stat="identity", position = position_nudge(x = -.3))+ geom_point(aes(y=counterfactuals_zero, colour="eta_1.0"), stat="identity", position = position_nudge(x = -.1)) + geom_point(aes(y=counterfactuals_zero_eta_high, colour="eta_1.1"), stat="identity", position = position_nudge(x = .1)) + geom_errorbar(aes(ymin=lower_counterfactuals_zero_eta_low, ymax=upper_counterfactuals_zero_eta_low), stat="identity", colour=deepskyblue, position=position_nudge(x = -.3)) + geom_errorbar(aes(ymin=lower_counterfactuals_zero, ymax=upper_counterfactuals_zero), stat="identity", colour=maroon, position = position_nudge(x = -.1)) + geom_errorbar(aes(ymin=lower_counterfactuals_zero_eta_high, ymax=upper_counterfactuals_zero_eta_high), stat="identity", colour=grey, position=position_nudge(x = .1)) + scale_y_continuous(name="FITSBY use (minutes/day)") + theme_classic() + #theme(axis.text.x = element_text(angle = 45, hjust = 1)) + labs(x = "") + scale_colour_manual(name = "", values=cols, labels = unname(TeX(c(paste0("$\\eta$", "$=0.9\\hat{\\eta}$", " ,(", "$\\alpha$", "$=1$", ")"), paste0("$\\eta$", "$=1.0\\hat{\\eta}$", " ,(", "$\\alpha$", "$=1$", ")"), paste0("$\\eta$", "$=1.1\\hat{\\eta}$", " ,(", "$\\alpha$", "$=1$", ")") )))) + theme(legend.text.align = 0, legend.key.height = unit(1, "cm"), legend.position="bottom") + theme(legend.margin=margin(0,0,0,0), legend.box.margin=margin(-10,-10,-10,-10)) + theme(axis.text.x = element_text(colour="black")) + coord_cartesian(ylim = c(0, 200)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } plot_decomposition_boot_unique <- function(median, bottom, top, filename){ order_results_zero <- function(df1){ r <- c(df1[['x_ss_L_effect_res']], df1[['x_ss_temptation_res']], df1[['x_ss_habit_res']], df1[['x_ss_habit_temptation_res']]) return(r) } x <- c('Baseline', 'No temptation', 'No habit\nformation', 'No temptation\n or habit formation') names <- rep(factor(x, levels=x),2) counterfactuals_zero <- order_results_zero(param_full) lower_counterfactuals_zero <- order_results_zero(bottom) upper_counterfactuals_zero <- order_results_zero(top) df <- data.frame(names, counterfactuals_zero, lower_counterfactuals_zero, upper_counterfactuals_zero) cols <- c("No perceived habit formation"=maroon) a <- ggplot(df, aes(x=names, width=.2)) + geom_point(aes(y=counterfactuals_zero, colour="No perceived habit formation"), stat="identity", position = position_nudge(x = -.1)) + geom_errorbar(aes(ymin=lower_counterfactuals_zero, ymax=upper_counterfactuals_zero), stat="identity", colour=maroon, position = position_nudge(x = -.1)) + scale_y_continuous(name="FITSBY use (minutes/day)") + theme_classic() + #theme(axis.text.x = element_text(angle = 45, hjust = 1)) + labs(x = "") + scale_colour_manual(name = "", values=cols, labels = unname(TeX(c(paste0("Restricted model", " (", "$\\alpha$ ", "$=1$", ")") ))))+ theme(legend.text.align = 0, legend.key.height = unit(1, "cm"), legend.position="bottom") + theme(legend.margin=margin(0,0,0,0), legend.box.margin=margin(-10,-10,-10,-10)) + theme(axis.text.x = element_text(colour="black")) + coord_cartesian(ylim = c(0, 165)) ggsave(sprintf('output/%s.pdf', filename), plot=a, width=6.5, height=4.5, units="in") } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Bootstraps functions # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ run_boot_procedure <- function(fun){ results <- mclapply(1:(size*1.1), fun, mc.set.seed = TRUE) results %<>% bind_rows nrowsunfiltered <- nrow(results) winsortaubtwopre <- nrow(results %>% filter(tau_B_2 ==0)) winsortaubthreepre <- nrow(results %>% filter(tau_B_3 ==0)) percenttaubthreepre <- winsortaubthreepre/nrowsunfiltered*100 percenttaubthreepre <- signif(percenttaubthreepre, digits=2) winsortaubfourpre <- nrow(results %>% filter(tau_B_4 ==0)) percenttaubfourpre <- winsortaubfourpre/nrowsunfiltered*100 percenttaubfourpre <- signif(percenttaubfourpre, digits=2) winsortaubfivepre <- nrow(results %>% filter(tau_B_5 ==0)) percenttaubfivepre <- winsortaubfivepre/nrowsunfiltered*100 percenttaubfivepre <- signif(percenttaubfivepre, digits=2) winsortaultwopre <- nrow(results %>% filter(tau_L_2 ==0)) percenttaultwopre <- winsortaultwopre/nrowsunfiltered*100 percenttaultwopre <- signif(percenttaultwopre, digits=2) winsortautildelpre <- nrow(results %>% filter(tau_tilde_L ==0)) percenttautildelpre <- winsortautildelpre/nrowsunfiltered*100 percenttautildelpre <- signif(percenttautildelpre, digits=2) winsortautildebthreewtwopre <- nrow(results %>% filter(tau_tilde_B_3_2 ==0)) percenttautildebthreewtwopre <- winsortautildebthreewtwopre/nrowsunfiltered*100 percenttautildebthreewtwopre <- signif(percenttautildebthreewtwopre, digits=2) winsoreta <- nrow(results %>% filter(eta ==0)) percenteta <- winsoreta/nrowsunfiltered*100 percenteta <- signif(percenteta, digits=2) winsorzeta <- nrow(results %>% filter(zeta ==0)) percentzeta <- winsorzeta/nrowsunfiltered*100 percentzeta <- signif(percentzeta, digits=2) winsorlambda <- nrow(results %>% filter(lambda ==0)) percentlambda <- winsorlambda/nrowsunfiltered*100 percentlambda <- signif(percentlambda, digits=2) winsorlambdares <- nrow(results %>% filter(lambda_res ==0)) percentlambdares <- winsorlambdares/nrowsunfiltered*100 percentlambdares <- signif(percentlambdares, digits=2) winsorrho <- nrow(results %>% filter(rho ==0)) percentrho <- winsorrho/nrowsunfiltered*100 percentrho <- signif(percentrho, digits=2) winsoretares <- nrow(results %>% filter(eta_res ==0)) percentetares <- winsoretares/nrowsunfiltered*100 percentetares <- signif(percentetares, digits=2) winsorzetares <- nrow(results %>% filter(zeta_res ==0)) percentzetares <- winsorzetares/nrowsunfiltered*100 percentzetares <- signif(percentzetares, digits=2) winsorrhores <- nrow(results %>% filter(rho_res ==0)) percentrhores <- winsorrhores/nrowsunfiltered*100 percentrhores <- signif(percentrhores, digits=2) #dropdrawsdenom <- nrow(results %>% filter(is.na(rho_tilde))) #percentdenom <- dropdrawsdenom/nrowsunfiltered*100 # percentdenom <- signif(percentdenom, digits=2) # dropdrawsdenomstm <- nrow(results %>% filter(is.na(rho_tilde_658))) #percentdenomstm <- dropdrawsdenomstm/nrowsunfiltered*100 #percentdenomstm <- signif(percentdenomstm, digits=2 winsortauspre <- nrow(results %>% filter(tau_tilde_B_3_2==0 | tau_tilde_L==0 | tau_L_2==0 |tau_B_3 ==0 | tau_B_5 ==0 | tau_B_4 ==0)) paramwinsorisepre <- nrow(results %>% filter(eta==0 | lambda ==0 | zeta==0 | rho==0 | alpha==1 | eta_res==0 | zeta_res==0 |rho_res==0)) percenttaubtwopre <- winsortaubtwopre/nrowsunfiltered*100 percenttaubtwopre <- signif(percenttaubtwopre, digits=2) alphapre <- nrow(results %>% filter(alpha == 0 | alpha == 1)) percentalphapre <- alphapre/nrowsunfiltered*100 percentalphapre <- signif(percentalphapre, digits=2) dropdrawsdenom <- nrow(results %>% filter(is.na(eta))) NegSSDenom <- dropdrawsdenom/nrowsunfiltered*100 NegSSDenom <- signif(NegSSDenom, digits=2) alphaundefined <- nrow(results %>% filter(is.na(alpha))) percentalphaundefined <- alphaundefined/nrowsunfiltered*100 percentalphaundefined <- signif(percentalphaundefined, digits=2) percenttauspre <- winsortauspre/nrowsunfiltered*100 percenttauspre <- signif(percenttauspre, digits=2) percentparampre <- paramwinsorisepre/nrowsunfiltered*100 percentparampre <- signif(percentparampre, digits=2) xsszeropre <- nrow(results %>% filter(x_ss_zero_temp==0)) xsszeropre <- xsszeropre/nrowsunfiltered*100 xsszeropre <- signif(xsszeropre, digits=2) combined <- list(nrowsunfiltered, percenttaubtwopre, percenttauspre, percentparampre, xsszeropre, percenttaubthreepre, percenttaubfourpre, percenttaubfivepre, percenttaultwopre, percenttautildelpre, percenttautildebthreewtwopre,percenteta, percentzeta, percentlambda, percentrho, percentetares, percentzetares, percentlambdares, percentrhores, percentalphapre, alphapre, NegSSDenom, dropdrawsdenom, paramwinsorisepre, percentalphaundefined) names(combined) <- c("nrowsunfiltered", "percenttaubtwopre", "percenttauspre", "percentparampre", "xsszeropre", "percenttaubthreepre", "percenttaubfourpre", "percenttaubfivepre", "percenttaultwopre", "percenttautildelpre", "percenttautildebthreewtwopre","percenteta", "percentzeta", "percentlambda", "percentrho", "percentetares", "percentzetares", "percentlambdares", "percentrhores", "percentalphapre", "alphapre", "NegSSDenom", "dropdrawsdenom", "paramwinsorisepre", "percentalphaundefined") save_nrow(combined, filename ="bootsdrawsnumbers", suffix="") return(results) } run_boot_iter <- function(s) { if (s %% 50 == 0){ print(s) } sample <- sample_n(df, nrow(df), replace = T) sample %<>% mutate(UserID = 1:n()) param <- param_initial #You can chose to print statements that display warning when concavity conditions are not met when estimating the model try(param <- estimate_model(sample, param, display_warning=F)) return(param) } run_boot_iter_full <- function(s) { if (s %% 50 == 0){ print(s) } sample <- sample_n(df, nrow(df), replace = T) sample %<>% mutate(UserID = 1:n()) param <- param_initial try(param <- estimate_model(sample, param, full=T)) return(param) } run_boot_iter_bal2 <- function(s) { if (s %% 50 == 0){ print(s) } sample <- sample_n(df, nrow(df), replace = T) sample %<>% mutate(UserID = 1:n()) sample %<>% balance_data(magnitude=2) param <- param_initial try(param <- estimate_model(sample, param, winsorize=T)) return(param) } run_boot_iter_bal <- function(s) { if (s %% 50 == 0){ print(s) } sample <- sample_n(df, nrow(df), replace = T) sample %<>% mutate(UserID = 1:n()) sample %<>% balance_data(magnitude=3) param <- param_initial try(param <- estimate_model(sample, param, winsorize=T)) return(param) } run_boot_iter_bal4 <- function(s) { if (s %% 50 == 0){ print(s) } sample <- sample_n(df, nrow(df), replace = T) sample %<>% mutate(UserID = 1:n()) sample %<>% balance_data(magnitude=4) param <- param_initial try(param <- estimate_model(sample, param, winsorize=T)) return(param) } run_boot_iter_bal5 <- function(s) { if (s %% 50 == 0){ print(s) } sample <- sample_n(df, nrow(df), replace = T) sample %<>% mutate(UserID = 1:n()) sample %<>% balance_data(magnitude=5) param <- param_initial try(param <- estimate_model(sample, param, winsorize=T)) return(param) } # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Latex saving functions for different formating numbers # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ signnumber <- function(x){ significant <- ifelse(x==0, sprintf("0"),sprintf(paste0("%0.", pmax(floor(3 - log(abs(x)+0.001, 10)), 0), "f"), x)) return(significant) } signnumber2 <- function(x){ significant <- ifelse(x==0, sprintf("0"),sprintf(paste0("%0.", pmax(floor(2 - log(abs(x)+0.01, 10)), 0), "f"), x)) return(significant) } save_tex <- function(param, filename, suffix=""){ tex_string <- "" for(x in names(param)){ name <- x if (x %in% names(name_changes)){ name <- name_changes[[x]] } new_line <- (sprintf("\\newcommand{\\%s%s}{%s}", name, suffix, signnumber(param[[x]]))) tex_string <- sprintf("%s\n%s", tex_string, new_line) } # saves it as a .tex file sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) } save_tex_nice <- function(param, filename, suffix=""){ tex_string <- "" for(x in names(param)){ name <- x if (x %in% names(name_changes)){ name <- name_changes[[x]] } new_line <- (sprintf("\\newcommand{\\%s%s}{%s}", name, suffix, signif(param[[x]], digits=2))) tex_string <- sprintf("%s\n%s", tex_string, new_line) } # saves it as a .tex file sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) } save_tex_one <- function(param, filename, suffix=""){ tex_string <- "" for(x in names(param)){ name <- x if (x %in% names(name_changes)){ name <- name_changes[[x]] } new_line <- (sprintf("\\newcommand{\\%s%s}{%s}", name, suffix, format(param[[x]], digits=1))) tex_string <- sprintf("%s\n%s", tex_string, new_line) } # saves it as a .tex file sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) } save_tex2 <- function(param, filename, suffix=""){ tex_string <- "" for(x in names(param)){ name <- x if (x %in% names(name_changes)){ name <- name_changes[[x]] } new_line <- (sprintf("\\newcommand{\\%s%s}{%s}", name, suffix, signnumber2(param[[x]]))) tex_string <- sprintf("%s\n%s", tex_string, new_line) } # saves it as a .tex file sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) } save_boot_tex <- function(median, se, filename, suffix=""){ tex_string <- "" for(x in names(median)){ name <- x if (x %in% names(name_changes)){ name <- name_changes[[x]] } if (x %in% constants){ new_line <- (sprintf("\\newcommand{\\%s%s}{%s}", name, suffix, signnumber(median[[x]]))) } else { new_line <- (sprintf("\\newcommand{\\%s%s}{%s\\:(%s)}", name, suffix, signnumber(median[[x]]), signnumber(se[[x]]))) } tex_string <- sprintf("%s\n%s",tex_string, new_line) } sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) } save_boot_tex_percentile <- function(bottom, top, filename, suffix=""){ tex_string <- "" for(x in names(bottom)){ name <- x if (x %in% names(name_changes)){ name <- name_changes[[x]] } new_line <- (sprintf("\\newcommand{\\%s%s}{[%s, %s]}", name, suffix, signnumber(bottom[[x]]), signnumber(top[[x]]))) tex_string <- sprintf("%s\n%s",tex_string, new_line) } sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) } save_nrow <- function(nrows_list, filename, suffix=""){ tex_string <- "" for(x in names(nrows_list)){ name <- x new_line <- (sprintf("\\newcommand{\\%s%s}{%s}", name, suffix, nrows_list[[x]])) tex_string <- sprintf("%s\n%s",tex_string, new_line) } sink(file=sprintf('output/%s.tex', filename)) cat(tex_string) sink(NULL) }