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Estimate Fama-MacBeth Regressions

Source: R/estimate_fama_macbeth.R
estimate_fama_macbeth.Rd

Estimates Fama-MacBeth regressions (Fama and MacBeth, 1973) by first running cross-sectional regressions for each time period and then aggregating the results over time to obtain average risk premia and corresponding t-statistics.

Usage

estimate_fama_macbeth(
  data,
  model,
  vcov = "newey-west",
  vcov_options = NULL,
  data_options = NULL,
  detail = FALSE
)

Arguments

data

A data frame containing the data for the regression. It must include a column representing the time periods (defaults to date) and the variables specified in the model.

model

A character string describing the model to be estimated in each cross-section (e.g., "ret_excess ~ beta + bm + log_mktcap").

vcov

A character string indicating the type of standard errors to compute. Options are "iid" for independent and identically distributed errors or "newey-west" for Newey-West standard errors. Default is "newey-west".

vcov_options

A list of additional arguments to be passed to the NeweyWest() function when vcov = "newey-west". These can include options such as lag, which specifies the number of lags to use in the Newey-West covariance matrix estimation, and prewhite, which indicates whether to apply a prewhitening transformation. Default is an empty list.

data_options

A list of class tidyfinance_data_options (created via data_options()) specifying column name mappings. The date element is used to specify the date column. Uses data_options() default if NULL: "date" = "date".

detail

A logical value indicating whether to return additional summary statistics. If FALSE (default), the function returns only the coefficient estimates. If TRUE, it returns a list with two elements: coefficients (the usual estimates table) and summary_statistics (a one-row tibble with the average cross-sectional R-squared, the average cross-sectional adjusted R-squared, and the average number of observations per cross-section).

Value

If detail = FALSE (default), a tibble with columns factor, risk_premium, n (number of time periods), standard_error, and t_statistic.

If detail = TRUE, a named list with two elements:

coefficients

The same tibble described above.

summary_statistics

A one-row tibble with r_squared (mean cross-sectional R-squared), adj_r_squared (mean cross-sectional adjusted R-squared), and n_obs (mean cross-sectional observation count).

References

Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81(3), 607-636. doi:10.1086/260061

Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703-708. doi:10.2307/1913610

See also

Other estimation functions: estimate_betas(), estimate_model()

Examples

set.seed(1234)

data <- tibble::tibble(
  date = rep(seq.Date(from = as.Date("2020-01-01"),
                      to = as.Date("2020-12-01"), by = "month"), each = 50),
  permno = rep(1:50, times = 12),
  ret_excess = rnorm(600, 0, 0.1),
  beta = rnorm(600, 1, 0.2),
  bm = rnorm(600, 0.5, 0.1),
  log_mktcap = rnorm(600, 10, 1)
)

estimate_fama_macbeth(data, "ret_excess ~ beta + bm + log_mktcap")
#> # A tibble: 4 × 5
#>   factor     risk_premium     n standard_error t_statistic
#>   <chr>             <dbl> <dbl>          <dbl>       <dbl>
#> 1 intercept       0.0114     12        0.0362       0.314 
#> 2 beta            0.00175    12        0.0196       0.0893
#> 3 bm              0.0712     12        0.0132       5.39  
#> 4 log_mktcap     -0.00505    12        0.00318     -1.59  
estimate_fama_macbeth(
  data,
  "ret_excess ~ beta + bm + log_mktcap",
  vcov = "iid"
)
#> # A tibble: 4 × 5
#>   factor     risk_premium     n standard_error t_statistic
#>   <chr>             <dbl> <dbl>          <dbl>       <dbl>
#> 1 intercept       0.0114     12        0.0647        0.610
#> 2 beta            0.00175    12        0.0222        0.274
#> 3 bm              0.0712     12        0.0386        6.40 
#> 4 log_mktcap     -0.00505    12        0.00528      -3.31 
estimate_fama_macbeth(
  data,
  "ret_excess ~ beta + bm + log_mktcap",
  vcov = "newey-west",
  vcov_options = list(lag = 6, prewhite = FALSE)
)
#> # A tibble: 4 × 5
#>   factor     risk_premium     n standard_error t_statistic
#>   <chr>             <dbl> <dbl>          <dbl>       <dbl>
#> 1 intercept       0.0114     12        0.0324        0.351
#> 2 beta            0.00175    12        0.0145        0.121
#> 3 bm              0.0712     12        0.0205        3.47 
#> 4 log_mktcap     -0.00505    12        0.00403      -1.26 

# Return detailed output including R-squared and observation counts
estimate_fama_macbeth(
  data,
  "ret_excess ~ beta + bm + log_mktcap",
  detail = TRUE
)
#> $coefficients
#> # A tibble: 4 × 5
#>   factor     risk_premium     n standard_error t_statistic
#>   <chr>             <dbl> <dbl>          <dbl>       <dbl>
#> 1 intercept       0.0114     12        0.0362       0.314 
#> 2 beta            0.00175    12        0.0196       0.0893
#> 3 bm              0.0712     12        0.0132       5.39  
#> 4 log_mktcap     -0.00505    12        0.00318     -1.59  
#> 
#> $summary_statistics
#> # A tibble: 1 × 3
#>   r_squared adj_r_squared n_obs
#>       <dbl>         <dbl> <dbl>
#> 1    0.0761        0.0159    50
#> 

# Use different column name for date
data |>
  dplyr::rename(month = date) |>
  estimate_fama_macbeth(
    "ret_excess ~ beta + bm + log_mktcap",
    data_options = data_options(date = "month")
 )
#> # A tibble: 4 × 5
#>   factor     risk_premium     n standard_error t_statistic
#>   <chr>             <dbl> <dbl>          <dbl>       <dbl>
#> 1 intercept       0.0114     12        0.0362       0.314 
#> 2 beta            0.00175    12        0.0196       0.0893
#> 3 bm              0.0712     12        0.0132       5.39  
#> 4 log_mktcap     -0.00505    12        0.00318     -1.59