10-fold cross-validation predictions of ERCs

Part three of the code for Section 3: Heterogeneity in earnings response coefficients

Harm Schuett https://hschuett.github.io/ (Tilburg University)https://www.tilburguniversity.edu
2021-10-03 
library(tidyverse)
library(cmdstanr)
library(posterior)
library(patchwork)
library(rsample)
source("00-utils.R")
kable <- knitr::kable
theme_set(theme_prodgray())

1. Introduction and preliminaries

This markdown file contains all the code necessary to replicate the cross-validation prediction test from Section 3: Heterogeneity in earnings response coefficients of the Paper What Can Bayesian Inference Do for Accounting Research?. All the code can also be found in the repo. It contains 00-utils.R which contains a few helper functions for graphs and tables.

Note: I used the newer cmdstanr package instead of the older rstan package because it likely is the future of the R based Stan ecosystem. I also really like its api, which is very close to the api of the pystan package. An additional advantage (I hope) is thus that most model fitting code should be more or less directly transferable to pystan for those that want to work in python. Installing cmdstanr used to be tricky at times because one needs a working c++ toolchain. But it is much smoother now. Please see the cmdstanr doc for installation instructions

2. Loading the data

The data used here is generated via the 02-create-ERC-sample.R script found in the repo. Here, we just load it and do some last minute transformations like de-meaning, etc.

ea_data <- arrow::read_parquet("../data/ea-event-returns.pqt") 
ea_data <- 
  ea_data |> 
  mutate(
    ret_dm = AbEvRet - mean(AbEvRet),
    earn_surp_dm = earn_surp - mean(earn_surp)
    )
head(ea_data)

# A tibble: 6 x 15
  ticker permno fpend_date ea_date    actual_eps median_fcast_eps
  <chr>   <dbl> <date>     <date>          <dbl>            <dbl>
1 001N    14504 2014-12-31 2015-02-09       0.04            0.03 
2 001N    14504 2015-03-31 2015-05-05       0.06           -0.045
3 001N    14504 2015-06-30 2015-08-05       0.02           -0.015
4 001N    14504 2015-09-30 2015-11-04      -0.02            0.04 
5 002T    14503 2014-06-30 2014-08-07       0.19            0.235
6 002T    14503 2014-09-30 2014-11-04       0.18            0.34 
# ... with 9 more variables: num_forecasts <int>,
#   two_days_bef_ea <date>, Price <dbl>, earn_surp <dbl>,
#   ea_match_date <date>, AbEvRet <dbl>, firm_id <int>, ret_dm <dbl>,
#   earn_surp_dm <dbl>

3. Creating 10-fold CV datasets

This creates the 10 random splits of the sample

set.seed(3597)
folds <- vfold_cv(ea_data, v = 10)
glimpse(folds)

Rows: 10
Columns: 2
$ splits <list> [<vfold_split[60624 x 6736 x 67360 x 15]>], [<vfold_~
$ id     <chr> "Fold01", "Fold02", "Fold03", "Fold04", "Fold05", "Fo~

4. OLS OOS predictions

Next, loop through the 10 splits and train the OLS model on each train split and compute predictions for holdout part.

ols_fit <- function(.d){
  fit <- lm(ret_dm ~ earn_surp_dm, data = .d)
}

ols_pred <- function(.fit, .nd){
  # Note there are some singularity warnings in here. Mainly due to insufficient n.obs
  suppressWarnings(
  fit_pred <- broom::augment(.fit, newdata = .nd)
  )
}

ols_predictions <- vector("list", length = 10)
for (i in 1:10) {
  train_set <- analysis(folds$splits[[i]])
  holdout_set <- assessment(folds$splits[[i]])
  
  ea_data_train <- 
    train_set |>
    nest(data = -c(ticker, firm_id)) 
  
  ea_data_test <- 
    holdout_set |>
    nest(data = -c(ticker, firm_id)) |> 
    rename(test_data = data)
  
  data_slice <- 
    ea_data_train |> 
    inner_join(ea_data_test, by = c("ticker", "firm_id"))
  
  ols_predictions[[i]] <- 
    data_slice |>
    mutate(ols_fit = map(.x = data, .f = ~ols_fit(.))) |> 
    mutate(ols_pred = map2(.x = ols_fit, .y = test_data, .f = ols_pred)) |> 
    select(ticker, firm_id, ols_pred) |> 
    unnest(cols = c(ols_pred)) |> 
    select(ticker, firm_id, ea_date, ret_dm, ols_pred = .fitted)
}
ols_predictions <- bind_rows(ols_predictions)
write_csv(ols_predictions, file = "../out/results/ols-dump.csv")

5. Bayesian OOS prediction

Do the same for the Bayes model. Loop through the 10 splits and train the Bayes model on each train split and compute predictions for holdout part.

cat(read_lines("../Stan/erc-wkinfo-priors-oos.stan"), sep = "\n")

data{
  int<lower=1> N;                   // num obs
  int<lower=1> J;                   // num groups
  int<lower=1> K;                   // num coefficients
  int<lower=1, upper=J> GroupID[N]; // GroupID for obs, e.g. FirmID or Industry-YearID
  vector[N] y;                      // Response
  matrix[N, K] x;                   // Predictors (incl. Intercept)

  // data for the oos test
  int<lower=1> N_test;              // num obs in test sample
  matrix[N_test, K] x_test;              // Predictors (incl. Intercept)
  int<lower=1, upper=J> GroupID_test[N_test]; // GroupID for  for test sample obs
}
parameters{
  matrix[K, J] z;                  // standard normal sampler
  cholesky_factor_corr[K] L_Omega; // hypprior coefficient correlation
  vector<lower=0>[K] tau;          // hypprior coefficient scales
  vector[K] mu_b;                  // hypprior mean coefficients
  real<lower=0> sigma;             // error-term scale
}
transformed parameters{
  matrix[J, K] b;                  // coefficient vector
  // The multivariate non-centered version:
  b = (rep_matrix(mu_b, J) + diag_pre_multiply(tau,L_Omega) * z)';
}
model{
  to_vector(z) ~ normal(0, 1);
  L_Omega ~ lkj_corr_cholesky(2);
  mu_b[1]  ~ normal(0, 0.1);
  mu_b[2]  ~ normal(0, 40);
  sigma ~ exponential(1.0 / 0.08);   // exp: 0.08 (std (abnormal returns))
  tau[1] ~ exponential(1.0 / 0.1);   // exp: 0.1
  tau[2] ~ exponential(1.0 / 40);    // exp: 40
  y ~ normal(rows_dot_product(b[GroupID] , x), sigma);
}
generated quantities {
  vector[N_test] y_pred = rows_dot_product(b[GroupID_test] , x_test);
}
model_wkinfo_priors <- cmdstan_model("../Stan/erc-wkinfo-priors-oos.stan")

Beware, the following code chunk can take a long time

bay_predictions <- vector("list", length = 10)
for (i in 1:10){
  train_set <- analysis(folds$splits[[i]])
  holdout_set <- assessment(folds$splits[[i]])
  
  input_data <- list(
    N = nrow(train_set),
    J = max(ea_data$firm_id),  # important! Needs to refer to full sample
    K = 2,
    GroupID = train_set$firm_id,
    y = train_set$AbEvRet,
    x = as.matrix(data.frame(int = 1, esurp = train_set$earn_surp)),
    
    N_test = nrow(holdout_set),
    x_test = as.matrix(data.frame(int = 1, esurp = holdout_set$earn_surp)),
    GroupID_test = holdout_set$firm_id
  )
  
  fit_wkinfo_priors <- model_wkinfo_priors$sample(
    data = input_data,
    iter_sampling = 1000,
    iter_warmup = 1000,
    chains = 4,
    parallel_chains = 4,
    seed = 1234,
    refresh = 1000
  )
  
  posterior_ypred <- summarise_draws(
    fit_wkinfo_priors$draws(c("y_pred")), 
      posterior_mean = mean,
      posterior_median = median, 
      posterior_sd = sd,
      ~quantile2(., probs = c(0.05, 0.25, 0.75, 0.95))
    )
  
   bay_predictions[[i]] <- 
     cbind(select(holdout_set, ticker, firm_id, ea_date, ret_dm), 
           posterior_ypred
           )
   
   rm(posterior_ypred, train_set, holdout_set, input_data)
}

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bay_predictions <- bind_rows(bay_predictions)
write_csv(bay_predictions, file = "../out/results/bay-dump.csv")

ols_predictions <- read_csv("../out/results/ols-dump.csv")
bay_predictions <- read_csv("../out/results/bay-dump.csv")

6. Table 2

tab2.A <- bind_rows(
  yardstick::mae(bay_predictions, truth = ret_dm, estimate = posterior_mean),
  yardstick::rmse(bay_predictions, truth = ret_dm, estimate = posterior_mean),
  yardstick::rsq(bay_predictions, truth = ret_dm, estimate = posterior_mean),
) |> 
  mutate(case = c("Bayes (Full sample)", "Bayes (Full sample)", "Bayes (Full sample)"),
         .estimate = round(.estimate, 4)
         ) |> 
  select(-.estimator) |> 
  pivot_wider(names_from = .metric, values_from = .estimate)
tab2.A$N <- nrow(bay_predictions)
kable(tab2.A)
case mae rmse rsq N
Bayes (Full sample) 0.0575 0.0768 0.0339 67360 
both_predictions <- 
  bay_predictions |> 
  ungroup() |> 
  inner_join(select(ols_predictions, ticker, ea_date, ols_pred), 
             by = c("ticker", "ea_date"))

tab2.B <- bind_rows(
  yardstick::mae(both_predictions, truth = ret_dm, estimate = posterior_mean),
  yardstick::mae(both_predictions, truth = ret_dm, estimate = ols_pred),
  yardstick::rmse(both_predictions, truth = ret_dm, estimate = posterior_mean),
  yardstick::rmse(both_predictions, truth = ret_dm, estimate = ols_pred),
  yardstick::rsq(both_predictions, truth = ret_dm, estimate = posterior_mean),
  yardstick::rsq(both_predictions, truth = ret_dm, estimate = ols_pred)
)|> 
  mutate(
    case = c("Bayes (OLS sample)", "OLS", "Bayes (OLS sample)", "OLS", "Bayes (OLS sample)", "OLS"),
    .estimate = round(.estimate, 4)) |> 
  select(-.estimator) |> 
  pivot_wider(names_from = .metric, values_from = .estimate)
tab2.B$N <- nrow(both_predictions)
kable(tab2.B)
case mae rmse rsq N
Bayes (OLS sample) 0.0575 0.0767 0.0339 67031
OLS 0.0669 0.4048 0.0000 67031 
bind_rows(tab2.A, tab2.B) |> write_csv("../out/results/tab2.csv")

Corrections

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Text and figures are licensed under Creative Commons Attribution CC BY 4.0. Source code is available at https://github.com/hschuett/BayesForAccountingResearch, unless otherwise noted. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".