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  • Threshold Autoregression Model (TAR)

    Hello,

    I'm using Stata 14 and monthly time-series data for January 2000 to December 2015. My thesis is economics-related.
    I am trying to establish the long-run and short-run relationship between various retail rates (mthtd, dddr, savr, alvr, etc) and monetary policy rate (mpr).

    where,

    mthth - 3-month deposit rate
    dddr - demand deposit rate
    savr - savings rate
    avlr - average lending rate

    Each of these variables is used as a dependent variable in a series of regressions with the independent variables being:
    npl - non-performing loans
    crr - reserve requirement coefficient
    xcrate - exchange rate
    vix - VIX volatility index
    embi - EMBI spread
    a dummy for inflation targeting period is included in all regresions.

    The result after testing for unit root and co-integration led me to run ECM estimation, an example is shown below:

    Code:
    . vec avlr mpr crr vix xcrate dummyit
    Code:
    Vector error-correction model
    
    Sample:  1960m4 - 1976m4                        Number of obs     =    193
    AIC               =    10.43915
    Log likelihood =  -954.378                      HQIC              =    10.80199
    Det(Sigma_ml)  =  .0007949                      SBIC              =    11.33512
    
    Equation           Parms      RMSE     R-sq      chi2     P>chi2
    
    D_avlr                8     2.10038   0.2955   77.60149   0.0000
    D_mpr                 8     2.86624   0.2867   74.34033   0.0000
    D_crr                 8     .713627   0.2752   70.25058   0.0000
    D_vix                 8     3.00484   0.1464   31.73876   0.0001
    D_xcrate              8     .078599   0.1338    28.5696   0.0004
    D_dummyit             8     .073178   0.0093   1.738625   0.9880
    
    
        
    Coef.   Std. Err.      z    P>z     [95% Conf.    Interval]
        
    D_avlr       
    _ce1 
    L1.    .0269756   .0209137     1.29   0.197    -.0140145    .0679657
    
    avlr 
    LD.   -.3544857   .1617355    -2.19   0.028    -.6714815    -.03749
    
    mpr 
    LD.    -.047585   .1181624    -0.40   0.687     -.279179    .1840089
    
    crr 
    LD.    .6698698   .1950973     3.43   0.001     .2874861    1.052254
    
    vix 
    LD.   -.0210711   .0502179    -0.42   0.675    -.1194965    .0773543
    
    xcrate 
    LD.     .082976   1.891667     0.04   0.965    -3.624624    3.790576
    
    dummyit 
    LD.    .0003657   2.121369     0.00   1.000    -4.157442    4.158174
    
    _cons   -.0276036   .1556347    -0.18   0.859     -.332642    .2774347
        
    D_mpr        
    _ce1 
    L1.    .0605919   .0285395     2.12   0.034     .0046554    .1165283
    
    avlr 
    LD.   -.2348009   .2207096    -1.06   0.287    -.6673837    .197782
    
    mpr 
    LD.   -.2578047   .1612483    -1.60   0.110    -.5738455    .0582361
    
    crr 
    LD.    .6963436   .2662363     2.62   0.009     .1745301    1.218157
    
    vix 
    LD.    -.043976   .0685291    -0.64   0.521    -.1782905    .0903385
    
    xcrate 
    LD.   -.8315905   2.581432    -0.32   0.747    -5.891104    4.227923
    
    dummyit 
    LD.    .3711811   2.894891     0.13   0.898    -5.302701    6.045063
    
    _cons   -.0323948   .2123842    -0.15   0.879    -.4486602    .3838706
        
    D_crr        
    _ce1 
    L1.    -.008501   .0071057    -1.20   0.232    -.0224279    .0054259
    
    avlr 
    LD.    .0720169   .0549515     1.31   0.190     -.035686    .1797199
    
    mpr 
    LD.   -.0124776    .040147    -0.31   0.756    -.0911643    .0662092
    
    crr 
    LD.    -.438733   .0662866    -6.62   0.000    -.5686523    -.3088137
    
    vix 
    LD.    .0192707   .0170621     1.13   0.259    -.0141705    .0527119
    
    xcrate 
    LD.    .4796758   .6427159     0.75   0.455    -.7800242    1.739376
    
    dummyit 
    LD.    .2226528   .7207598     0.31   0.757    -1.190011    1.635316
    
    _cons    -.019047   .0528787    -0.36   0.719    -.1226873    .0845932
        
    D_vix        
    _ce1 
    L1.   -.1396939   .0299195    -4.67   0.000    -.1983351    -.0810527
    
    avlr 
    LD.    .4147958   .2313819     1.79   0.073    -.0387044    .868296
    
    mpr 
    LD.   -.3731921   .1690453    -2.21   0.027    -.7045149    -.0418693
    
    crr 
    LD.    -.595865     .27911    -2.13   0.033     -1.14291    -.0488195
    
    vix 
    LD.    .0705053   .0718427     0.98   0.326    -.0703039    .2113145
    
    xcrate 
    LD.   -2.792197   2.706256    -1.03   0.302     -8.09636    2.511967
    
    dummyit 
    LD.   -.0592391   3.034872    -0.02   0.984    -6.007478    5.889
    
    _cons   -.0182203   .2226539    -0.08   0.935    -.4546139    .4181733
        
    D_xcrate     
    _ce1 
    L1.   -.0001194   .0007826    -0.15   0.879    -.0016533    .0014145
    
    avlr 
    LD.    .0001613   .0060524     0.03   0.979    -.0117011    .0120238
    
    mpr 
    LD.    .0007353   .0044218     0.17   0.868    -.0079313    .0094019
    
    crr 
    LD.     .001499   .0073008     0.21   0.837    -.0128104    .0158084
    
    vix 
    LD.    .0009432   .0018792     0.50   0.616      -.00274    .0046264
    
    xcrate 
    LD.   -.2977891   .0707891    -4.21   0.000    -.4365331    -.1590451
    
    dummyit 
    LD.   -.0264471   .0793849    -0.33   0.739    -.1820386    .1291443
    
    _cons    .0236027   .0058241     4.05   0.000     .0121877    .0350177
        
    D_dummyit    
    _ce1 
    L1.    .0005587   .0007286     0.77   0.443    -.0008695    .0019868
    
    avlr 
    LD.    -.000468    .005635    -0.08   0.934    -.0115123    .0105763
    
    mpr 
    LD.    .0004337   .0041168     0.11   0.916    -.0076352    .0085026
    
    crr 
    LD.   -.0019113   .0067973    -0.28   0.779    -.0152338    .0114112
    
    vix 
    LD.   -.0004187   .0017496    -0.24   0.811    -.0038479    .0030105
    
    xcrate 
    LD.   -.0158339   .0659068    -0.24   0.810    -.1450089    .1133411
    
    dummyit 
    LD.    .0017346   .0739098     0.02   0.981    -.1431259    .1465951
    
    _cons    .0055801   .0054224     1.03   0.303    -.0050477    .0162078
        
    
    Cointegrating equations
    
    Equation           Parms    chi2     P>chi2
    
    _ce1                  5   47.47435   0.0000
    
    
    Identification:  beta is exactly identified
    
    Johansen normalization restriction imposed
        
    beta       Coef.   Std. Err.      z    P>z     [95% Conf.    Interval]
        
    _ce1         
    avlr           1          .        .       .            .    .
    mpr   -1.555906   .2998338    -5.19   0.000    -2.143569    -.9682423
    crr   -.6836976   1.468203    -0.47   0.641    -3.561322    2.193927
    vix    1.511256   .2750964     5.49   0.000     .9720773    2.050435
    xcrate    5.275661   2.164469     2.44   0.015      1.03338    9.517943
    dummyit   -17.77735   4.573427    -3.89   0.000     -26.7411    -8.813596
    _cons     30.2893          .        .       .            .    .
    In the long run the results showed an incomplete pass-through effect (1.0 is considered a perfect pass-through).

    I intend to test for asymmetric co-integration. That is, if the monetary policy rate is increased, the other retail rates also increase, and decrease when the monetary policy rate is decreased. There exists is symmetric co-integration if they respond in similar timeframe, and asymmetric if the change in one direction is faster than in the opposite direction.

    The literature mentions the use of TAR and M -TAR models but try as i may, i haven't found a way of doing this kind of estimation.

    Can anyone please help me with how to run a TAR or M-TAR specification or its equivalent in Stata?

    Thank you.
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