# GIRF for Dichotomous models This function estimates the response functions of dichotomous models in a univariate framework using the method proposed by Lajaunie (2021). The response functions are based on the 4 specifications proposed by Kauppi & Saikkonen (2008). ```r GIRF_Dicho(Dicho_Y, Exp_X, Lag, Int, t_mod, horizon, shock_size, OC) ``` ## Arguments - `Dicho_Y`: Vector of the binary time series. - `Exp_X`: Vector or Matrix of explanatory time series. - `Lag`: Number of lags used for the estimation. - `Int`: Boolean value: TRUE for an estimation with intercept, and FALSE otherwise. - `t_mod`: Model number: 1, 2, 3 or 4. -> 1 for the static model: $$ P_{t-1}(Y_{t}) = F(\pi_{t})=F(\alpha + \beta'X_{t}) $$ -> 2 for the dynamic model with lag binary variable: $$ P_{t-1}(Y_{t}) = F(\pi_{t})=F(\alpha + \beta'X_{t} + \gamma Y_{t-l}) $$ -> 3 for the dynamic model with lag index variable: $$ P_{t-1}(Y_{t}) = F(\pi_{t})=F(\alpha + \beta'X_{t} + \eta \pi_{t-l}) $$ -> 4 for the dynamic model with both lag binary variable and lag index variable: $$ P_{t-1}(Y_{t}) = F(\pi_{t})=F(\alpha + \beta'X_{t} + \eta \pi_{t-l} + \gamma Y_{t-l}) $$ - `horizon`: Numeric variable corresponding to the horizon target for the GIRF analysis. - `shock_size`: Numeric variable equal to the size of the shock. It can be estimated with the Vector_Error function. - `OC`: Numeric variable equal to the Optimal Cut-off (threshold). This threshold can be considered arbitrarily, with a value between 0 and 1, or it can be estimated with one of the functions EWS_AM_Criterion, EWS_CSA_Criterion, or EWS_NSR_Criterion. ## Returns Matrix with 7 columns: - **column 1**: horizon - **column 2**: index - **column 3**: index with shock - **column 4**: probability associated to the index - **column 5**: probability associated to the index with shock - **column 6**: binary variable associated to the index - **column 7**: binary variable associated to the index with shock ## References Kauppi, Heikki, and Pentti Saikkonen. "Predicting US recessions with dynamic binary response models." The Review of Economics and Statistics 90.4 (2008): 777-791. Lajaunie, Quentin. Generalized Impulse Response Function for Dichotomous Models. No. 2852. Orleans Economics Laboratory/Laboratoire d'Economie d'Orleans (LEO), University of Orleans, 2021. ## Author(s) Jean-Baptiste Hasse and Quentin Lajaunie ## Examples ```r # NOT RUN { # Import data data("data_USA") # Data process Var_Y <- as.vector(data_USA$NBER) Var_X <- as.vector(data_USA$Spread) # Estimate the logit regression Logistic_results <- Logistic_Estimation(Dicho_Y = Var_Y, Exp_X = Var_X, Intercept = TRUE, Nb_Id = 1, Lag = 1, type_model = 1) # Vector of probabilities vector_proba <- as.vector(rep(0,length(Var_Y)-1)) vector_proba <- Logistic_results$prob # Vector of binary variables Lag <- 1 vector_binary <- as.vector(rep(0,length(Var_Y)-1)) vector_binary <- Var_Y[(1+Lag):length(Var_Y)] # optimal cut-off that maximizes the AM criterion Threshold_AM <- EWS_AM_Criterion(Var_Proba = vector_proba, Dicho_Y = vector_binary, cutoff_interval = 0.0001) # Estimate the estimation errors Residuals <- Vector_Error(Dicho_Y = Var_Y, Exp_X = Var_X, Intercept = TRUE, Nb_Id = 1, Lag = 1, type_model = 1) # Initialize the shock size_shock <- quantile(Residuals,0.95) # GIRF Analysis results <- GIRF_Dicho(Dicho_Y = Var_Y, Exp_X = Var_X, Lag = 1, Int = TRUE, t_mod = 1, horizon = 3, shock_size = size_shock, OC = Threshold_AM) # print results results #} ```

GIRF_Dichotomous_model function