# Compute nonlinear impulse responses for panel data This function estimates nonlinear impulse responses by using local projections for panel data with an identified shock. The data can be separated into two states by a smooth transition function as applied in Auerbach and Gorodnichenko (2012), or by a simple dummy approach. ```r lp_nl_panel( data_set = NULL, data_sample = "Full", endog_data = NULL, cumul_mult = TRUE, shock = NULL, diff_shock = TRUE, panel_model = "within", panel_effect = "individual", robust_cov = NULL, robust_method = NULL, robust_type = NULL, robust_cluster = NULL, robust_maxlag = NULL, use_gmm = FALSE, gmm_model = "onestep", gmm_effect = "twoways", gmm_transformation = "d", c_exog_data = NULL, l_exog_data = NULL, lags_exog_data = NaN, c_fd_exog_data = NULL, l_fd_exog_data = NULL, lags_fd_exog_data = NaN, switching = NULL, use_logistic = TRUE, use_hp = FALSE, lag_switching = TRUE, lambda = NULL, gamma = NULL, confint = NULL, hor = NULL ) ``` ## Arguments - `data_set`: A data.frame , containing the panel data set. The first column has to be the variable denoting the cross section. The second column has to be the variable denoting the time section. - `data_sample`: Character or numeric. To use the full sample set value to "Full" (default). To estimate a subset, you have to provide a sequence of dates. This sequence has to be in the same format as the second column (time-section). - `endog_data`: Character. The column name of the endogenous variable. You can only provide one endogenous variable at a time. - `cumul_mult`: Boolean. Estimate cumulative multipliers? TRUE (default) or FALSE. If TRUE, cumulative responses are estimated via: $$ y_{(t+h)} - y_{(t-1)}, $$ where h = 0,..., H-1. - `shock`: Character. The column name of the variable to shock with. - `diff_shock`: Boolean. Take first differences of the shock variable? TRUE (default) or FALSE. Note that when using this option both shock and instrument are used in first differences - `panel_model`: Character. Type of panel model. The default is "within" (fixed effects). Other options are "random", "ht", "between", "pooling" or "fd". See vignette of the plm package for details. - `panel_effect`: Character. The effects introduced in the model. Options are "individual" (default), "time", "twoways", or "nested". See the vignette of the plm-package for details. - `robust_cov`: NULL or Character. The character specifies the method how to estimate robust standard errors: Options are "vcovBK", "vcovDC", "vcovG", "vcovHC", "vcovNW", "vcovSCC". For these options see vignette of plm package. Another option is "Vcxt". For details see Miller (2017) If "use_gmm = TRUE", this option has to be NULL. - `robust_method`: NULL (default) or Character. The character is an option when robust_cov = "vcovHC". See vignette of the plm package for details. - `robust_type`: NULL (default) or Character. The character is an option when robust_cov = "vcovBK", "vcovDC", "vcovHC", "vcovNW" or "vcovSCC". See vignette of the plm package for details. - `robust_cluster`: NULL (default) or Character. The character is an option when robust_cov = "vcovBK", "vcovG" or "vcovHC". See vignette of the plm package for details. - `robust_maxlag`: NULL (default) or Character. The character is an option when robust_cov = "vcovNW" or "vcovSCC". See vignette of the plm package for details. - `use_gmm`: Boolean. Use GMM for estimation? TRUE or FALSE (default). See vignette of plm package for details. If TRUE, the option "robust_cov" has to be set to NULL. - `gmm_model`: Character. Either "onestep" (default) or "twosteps". See vignette of the plm package for details. - `gmm_effect`: Character. The effects introduced in the model: "twoways" (default) or "individual". See vignette of the plm-package for details. - `gmm_transformation`: Character. Either "d" (default) for the "difference GMM" model or "ld" for the "system GMM". See vignette of the plm package for details. - `c_exog_data`: NULL or Character. Name(s) of the exogenous variable(s) with contemporaneous impact. - `l_exog_data`: NULL or Character. Name(s) of the exogenous variable(s) with lagged impact. - `lags_exog_data`: Integer. Lag length for the exogenous variable(s) with lagged impact. - `c_fd_exog_data`: NULL or Character. Name(s) of the exogenous variable(s) with contemporaneous impact of first differences. - `l_fd_exog_data`: NULL or Character. Name(s) of exogenous variable(s) with lagged impact of first differences. - `lags_fd_exog_data`: NaN or Integer. Number of lags for variable(s) with impact of first differences. - `switching`: Character. Column name of the switching variable. If "use_logistic = TRUE", this series can either be decomposed by the Hodrick-Prescott filter (see Auerbach and Gorodnichenko, 2013) or directly plugged into the following smooth transition function: $$ F_{z_t} = \frac{exp(-\gamma z_t)}{1 + exp(-\gamma z_t)}. $$ The data for the two regimes are lagged by default: Regime 1 = (1-`F(z\_{t-1}))*y\_{(t-p)}`, Regime 2 = `F(z\_{t-1})*y\_{(t-p)}`. This option can be suppressed with "lag_switching = FALSE". - `use_logistic`: Boolean. Use logistic function to separate states? TRUE (default) or FALSE. If FALSE, the values of the switching variable have to be binary (0/1). - `use_hp`: Boolean. Use HP-filter? TRUE or FALSE (default). - `lag_switching`: Boolean. Use the first lag of the values of the transition function? TRUE (default) or FALSE. - `lambda`: Double. Value of $\lambda$ for the Hodrick-Prescott filter (if "use_hp = TRUE"). - `gamma`: Double. Positive value for $\gamma$, used in the transition function. - `confint`: Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. - `hor`: Integer. Number of horizons for impulse responses. ## Returns A list containing: - **irf_lin_mean**: A matrix , containing the impulse responses. The columns are the horizons. - **irf_lin_low**: A matrix , containing all lower confidence bands. The columns are the horizons. - **irf_lin_up**: A matrix , containing all upper confidence bands. The columns are the horizons. - **reg_outputs**: Full regression output (plm object) for each horizon. - **reg_summaries**: Summary of regression output for each horizon. In case of robust covariance estimators, this only includes the t-tests. - **xy_data_sets**: Data sets with endogenous and exogenous variables for each horizon. - **specs**: A list with data properties for e.g. the plot function. ## Examples ```r #--- Info # This example is based on a STATA code that has been provided on # Òscar Jordà's website (https://sites.google.com/site/oscarjorda/home/local-projections) # It estimates impulse reponses of the ratio of (mortgage lending/GDP) to a # +1% change in the short term interest rate #--- Get data # Go to the website of the 'The MacroFinance and MacroHistory Lab' # Download the Excel-Sheet of the 'Jordà-Schularick-Taylor Macrohistory Database': # URL: https://www.macrohistory.net/database/ # Then uncomment and run the code below... #--- Code ## Load libraries to download and read excel file from the website # library(lpirfs) # library(readxl) # library(dplyr) # # Load JST Macrohistory Database # jst_data <- read_excel("JSTdatasetR5.xlsx", sheet = "Data") # ## Choose years <= 2013. Swap the first two columns so that 'country' is the ## first (cross section) and 'year' the second (time section) column # jst_data <- jst_data %>% # dplyr::filter(year <= 2013) %>% # dplyr::select(country, year, everything()) # ## Prepare variables. This is based on the 'data.do' file # data_set <- jst_data %>% # mutate(stir = stir) %>% # mutate(mortgdp = 100*(tmort/gdp)) %>% # mutate(hpreal = hpnom/cpi) %>% # group_by(country) %>% # mutate(hpreal = hpreal/hpreal[year==1990][1]) %>% # mutate(lhpreal = log(hpreal)) %>% # # mutate(lhpy = lhpreal - log(rgdppc)) %>% # mutate(lhpy = lhpy - lhpy[year == 1990][1]) %>% # mutate(lhpreal = 100*lhpreal) %>% # mutate(lhpy = 100*lhpy) %>% # ungroup() %>% # # mutate(lrgdp = 100*log(rgdppc)) %>% # mutate(lcpi = 100*log(cpi)) %>% # mutate(lriy = 100*log(iy*rgdppc)) %>% # mutate(cay = 100*(ca/gdp)) %>% # mutate(tnmort = tloans - tmort) %>% # mutate(nmortgdp = 100*(tnmort/gdp)) %>% # dplyr::select(country, year, mortgdp, stir, ltrate, lhpy, # lrgdp, lcpi, lriy, cay, nmortgdp) # # ## Use data_sample from 1870 to 2013 and exclude observations from WWI and WWII # data_sample <- seq(1870, 2016)[!(seq(1870, 2016) %in% # c(seq(1914, 1918), # seq(1939, 1947)))] # ## Estimate panel model # results_panel <- lp_nl_panel(data_set = data_set, # data_sample = data_sample, # endog_data = "mortgdp", # cumul_mult = TRUE, # # shock = "stir", # diff_shock = TRUE, # panel_model = "within", # panel_effect = "individual", # robust_cov = "vcovSCC", # # switching = "lrgdp", # lag_switching = TRUE, # use_hp = TRUE, # lambda = 6.25, # gamma = 10, # # c_exog_data = "cay", # c_fd_exog_data = colnames(data_set)[c(seq(4,9),11)], # l_fd_exog_data = colnames(data_set)[c(seq(3,9),11)], # lags_fd_exog_data = 2, # # confint = 1.67, # hor = 5) # ## Plot irfs # plot(results_panel) # # ## Plot values of the transition function for USA between 1950 and 2016 # library(ggplot2) # # data_set %>% # mutate(fz = results_panel$fz$fz) %>% # select(country, year, fz) %>% # filter(country == "USA" & year > 1950 & year <= 2016) %>% # ggplot()+ # geom_line(aes(x = year, y = fz)) + # scale_x_continuous(breaks = seq(1950, 2016, 5)) # # ############################################################################## ### Use GMM ### ############################################################################## # ## Use a much smaller sample to have fewer T than N # data_sample <- seq(2000, 2012) # # ## Estimate panel model with gmm ## This example (please uncomment) gives a warning at each iteration. ## The data set is not well suited for ## GMM as GMM is based on N-asymptotics and the data set only contains 27 countries # # results_panel <- lp_nl_panel(data_set = data_set, # data_sample = data_sample, # endog_data = "mortgdp", # cumul_mult = TRUE, # # shock = "stir", # diff_shock = TRUE, # # use_gmm = TRUE, # gmm_model = "onestep", # gmm_effect = "twoways", # gmm_transformation = "ld", # # switching = "lrgdp", # lag_switching = TRUE, # use_hp = TRUE, # lambda = 6.25, # gamma = 10, # # l_exog_data = "mortgdp", # lags_exog_data = 1, # # confint = 1.67, # hor = 5) # ## Create and plot irfs # plot(results_panel) ``` ## References Croissant, Y., Millo, G. (2008). “Panel Data Econometrics in R: The plm Package.” **Journal of Statistical Software**, 27(2), 1-43. doi: 10.18637/jss.v027.i02. Jordà, Ò. (2005). "Estimation and Inference of Impulse Responses by Local Projections." **American Economic Review**, 95 (1): 161-182. Jordà, Ò., Schualrick, M., Taylor, A.M. (2018). "Large and State-Dependent Effects of Quasi-Random Monetary Experiments", **NBER** working paper 23074, **FRBSF** working paper 2017-02. Millo, G. (2017). “Robust Standard Error Estimators for Panel Models: A Unifying Approach.” **Journal of Statistical Software**, 82(3), 1-27. doi: 10.18637/jss.v082.i03. ## Author(s) Philipp Adämmer

lp_nl_panel function