combined_df <- data.frame(
     Date = as.Date(as.yearmon(index(combined_m))),
     coredata(combined_m)
  ) %>%
  dplyr::rename(
    pop_m = POP,
    pce_m = PCEC96,
    dsp_m = DSPIC96,
    umcsent_m = UMCSENT,
    csu_m = CSUSHPISA,
    totalsl_m = TOTALSL
  ) %>%
  dplyr::mutate(
    # transform to base units
    pop_m = pop_m * 1e3,          # Thousands → persons
    pce_m = pce_m * 1e9,          # Billions → dollars
    dsp_m = dsp_m * 1e9,          # Billions → dollars
    totalsl_m = totalsl_m * 1e6,  # Millions → dollars

    # per-capita transformation
    pce_pc = pce_m / pop_m,
    dsp_pc = dsp_m / pop_m,
    totalsl_pc = totalsl_m / pop_m,

    # log transformation
    log_pce_pc = log(pce_pc),
    log_dsp_pc = log(dsp_pc),
    log_totalsl_pc = log(totalsl_pc),

    # diff-log transformation
    dlog_pce_pc = c(NA, diff(log_pce_pc)),
    dlog_dsp_pc = c(NA, diff(log_dsp_pc)),
    dlog_totalsl_pc = c(NA, diff(log_totalsl_pc)),

    # moving average transformation
    dlog_dsp_pc_lag1 = lag(dlog_dsp_pc, 1),
    ma3_dlog_dsp_pc = rollmean(dlog_dsp_pc_lag1, k = 3, align = "right", fill = NA),

    # covid dummy
    covid_dummy = ifelse(Date >= as.Date("2020-03-01") & Date <= as.Date("2021-06-30"), 1, 0)
  ) %>%
  na.omit()

model <- lm(dlog_pce_pc ~ ma3_dlog_dsp_pc * covid_dummy, data = combined_df)
summary(model)