This is a program package to estimate the model used in

Sylvia Frühwirth-Schnatter and Sylvia Kaufmann,
"How do changes in monetary policy affect bank lending? An analysis of
Austrian bank data" 

Model

y_it = alpha*X^1_it + beta^G_S(i)*X^2_it + beta^R_S(i)*X^3_it*(I_t-1) + e_it

S(i)=1,2,...,K; e_it ~ N(0,sigma^2_i), sigma^2_(i)=sigma^2/lambda_i
i=1,...,N; t=1,...,T

ESTIMATION

start_model
    script file to run estimation
    set K (number of groups)
    set index0 (default is empty matrix, otherwise it is used if some
      parameters are set zero, not implemented in this version)
    set gr_fix (default is zero, (1) is used when groups are formed a priori 
      -- adjust ev. run_model_lagzins lines 123-127 and/or program group_fix)
    set not_switch (default is zero, (1) if a non-switching specification is 
      to be estimated)
    set true (default is zero, (1) is used to read-in true parameters when 
      testing the program)
    set lag_dir (number of lagged exogenous variables)
    set lag_dlo (number of lagged endogenous variables)
    set eta_different (default is zero, (1) is used when there are 
      group-specific state indicators with different transition
      probability matrices --- use another routine in runmcmc3mixture_neu2.m)
    set unit_spec_var ( (1) is used to estimate unit-specific variances) 
    set prm, prior mean of group-specific parameter if I_t==1;
    set scale of prior information (if scale lower, then lower information, 
      hence more diffuse prior
    change the name of the file to which MCMC output is saved

    calls run_model_lagzins
    calls run_lcm_MS

run_model_lagzins
    script file to read in data and design the explanatory matrices
    defines which banks to include and how to treat outliers (as missing 
      values or not, i.e. to exclude banks with outliers)
    indexb vector containing the units included in the analysis
    indexn vector containing the effective estimation sample (accounts for 
      autocorrelation of endogenous/exogenous variables)
    
    y TxN contains the dependent variable
    Z_dlolag TxUxN contains the U lagged endogenous variables (set with 
      lag_dlo)
    Zvar TxUxN contains the U variables with group-specific effects
    Z TxUxN contains in the first 'ill' (later defined as dd) columns the 
      variables with group-specific effects (the matrix Zvar), then the lagged 
      endogenous variables (Z_dlolag), the variables with fixed effects 
      (additional variables in Zwirt, dummy variables in Zdum and the 
      constant c).
    Z = [Zvar,Z_dlolag,Zwirt,Zdum,c]
    ZMS TxUxN contains the U variables with state-specific effects
    IMS 1x(T+1) starting value for I_t
    S 1xN defining S_i
    
    calls daten_read_b
          script file to read in data and construct an outlier matrix
          dlo_out TxN  matrix containing a 1 where there is an outlier (due 
	    to merger or statistics)
          Zbasis TxUxN (each column u contains a variable with group- and/or 
	    state-specific effect)
          BLZ Nx1 unit identifier
          Zdum TxUxN (each column contains a dummy variable, e.g. seasonals, 
	    break identifier etc.)
          c Tx1xN constant
          Zwirt TxUxN (each column contains a macro variable included in the 
	    regression, e.g. inflation GDP growth etc.)
          
       
    calls exclude_ind
          script file to exclude specific banks

run_lcm_MS
    script file to design the prior distribution, to set the starting values
      and to call the estimation program
    prseps inverse Gamma for error variance
    pralm  prior mean of parameter vector 
    pralinf prior information matrix
    e0 1xK vector of prior's hyperparameter for group probabilities
    e0MS 2x2 prior parameter for the transition probabilities
    
    seps0 starting value for error variance
    alpha0 starting value for the parameter vector [beta^G_1,...,beta^G_K,
      lagged endogenous,fixed effects,beta^R_1,...,beta^R_K]
    eta0 starting value for the group probabilities
    eta0MS starting value for the transition probabilities
    
    set M number of iterations
    set it0 number of burn-in iterations
    set it0cov number of retained posterior moments (for Bayes factor
      evaluation, not implemented for the present specification)
    set it0b number of retained I^T and S^N (default is set to 100).
    set perm=100 to use random permutation sampler
    set perm=0 to use restricted permutation sampler (set the appropriate
      restriction in the procedure 'mixture3mcmc_samIt.m' (line 357) 
    
    calls runmcmc3mixture_neu2
        script to call the estimation procedure 'mixture3mcmc_samIt.m'
        

EVALUATION/IDENTIFICATION

load first the file with the saved MCMC output (load *****.mat)

run run_model_lagzins to read in relevant data and index definitions (note:
  ev. adjust daten_Read.m for the right exogenous variable)
set ifig=1 (index to number the figures) on the command line

run plotgroupR_ranperm, displays scatter plots of the elements of beta^R_k
  against each other and against persistence of 1st state
decide with which element in beta^R_k to identify the states 
    
set group=  0 (no group-specific sorting) on the command line
set eta_restr= (default is 0, (1) is used to identify the states by means of 
  the state persistence) on the command line

run a first time Permut_MS
    set indexMSsort=[1]    set with which element in beta^R_k to identify
      the state (relevant if eta_restr=0)
    set indexMIXsort=[1]   set with which element to identify the groups 
      (not relevant in the first permutation round)
    
run plotgroupalpha, displays scatter plots of the elements of beta^G_k 
  against each other 
decide with which element in beta^G_k (or in beta^R_k) to identify the groups
    
set group=   1 (group-specific sorting according to an element in beta^G_k)
             2 (group-specific sorting according to an element in beta^R_k)
	       on the command line
run a second time Permut_MS
    set indexMSsort=[1]    set with which element in beta^R_k to identify
      the state
    set indexMIXsort=[1]   set with which element to identify the groups 

       
run plotprob
    displays a graph for bank classification, 
    ev. a scatter plot of size against liquidity of specific bank groups
      (adjust lines 77-98)
    and a plot of the state indicator (adjust procedure plotprob_MS.m, ev.
      for the end date on line 13 and for the variable dyr and Zbasis)

    a group indicator for each bank is found in the matrix class
     (1st group ... last group excluded banks); [BLZ class] relates the
     indicators to the units

run plotrd
    displays marginal posterior distribution of the group-specific parameters
      when I_t=1 (beta^G_k) and when I_t=0 (beta^G_k-beta^R_k),
    of the state-specific parameter beta^R_k, of the fixed parameters, of the
      group and the transition probabilities.
    
the command
    plot(mean(sepsmc(:,ones(1,size(lambmc,2)))./lambmc,1)')
    displays the unit-specific estimated variances
the procedure
    boxlamb.m 
    displays boxplots of selected lambda's
    
define file='filename.txt' on the command line
    output_rel_parms (output_rel_parms_ns) writes a table in latex-format
      with mean and shortest confidence interval for group- and
    state-specific parameters, tabulates some group characteristics
      of interest (see lines 93-116), and mean and confidence interval
    of state persistence parameters.
    

to view the estimated missing data
    run first run_model_lagzins
    run daten_view_miss

    
FORECAST EVALUATION
run start_prognose.m
    loads the MCMC file
    calls run_model_lagzins_prognose (reads in data with daten_read_prognose)
    calls prognose_applecon.m to compute the forecasts
    the results are stored in matrix biasall and mseall, both of dimension
      imodel x forecast horizon x 3
    imodel = 1 (a priori grouping), 2,3,4 (K=2,3,4)
    forecast horizon=12
    3: first matrix: unweighed errors, second: weighted with lamdba_i,
      third: weighted with size
    
run plotmse.m to obtain the numbers of table 4, and the graphs of figure 7.