I am trying to estimate the effect of a range of bank specific variables like Size, Risk leverage, Assets quality, Provision Coverage Ratio, NIM, non-Interest Income, Contingent Liabilities and Operating Efficiency on Stress level of banks. I have included GDP growth Rate, G-sec Yield, Call Money Rate, Stability, Inflation and USD-INR Exchange Rate as my macroeconomic control variables. My panel consists of 18 years from 2005-2022 and has got 39 banks. Hausman test indicates RE model to be appropriate.
I want to investigate whether, my dependent variable, i.e. Stress score follows any linear or quadratic time trend, by including c.year and then c.year##c.year, respectively. With linear time trend, the coefficient of timevar turned out to be insignificant. However, with quadratic time trend, the variable c.year##c.year was omitted citing multicollinearity as reason.
i) My first question is, why is this happening and should the outcome be interpreted as being "no quadratic trend in the dependent variable?"
Afterwards, I came across posts which mentioned, "if you don't expect a time trend so much as just haphazard shocks to outcome from year to year, then add i.time to the list of dependent variables". Further, in field like Finance, most of the time the shock is haphazard rather than following a time trend. Both these statements are attributed to Clyde Schechter. Assuming, my dependent variable, banking stress to be the outcome haphazard shocks to bank-specific and macroeconomic parameters, I re-ran my model by including i.year as one of the independent variable, as follows.
ii) For the years retained in the outcome, the corresponding p-values demonstrate insignificant coefficients. Further, certain omitted years have been omitted owing to collinearity. In this regard, what should I infer from this outcome?
iii) Even though my time period begins from 2005, why it is not included in the result ?
Any help/ insight would be sincerely appreciated.
Warm regards
pankaj
I want to investigate whether, my dependent variable, i.e. Stress score follows any linear or quadratic time trend, by including c.year and then c.year##c.year, respectively. With linear time trend, the coefficient of timevar turned out to be insignificant. However, with quadratic time trend, the variable c.year##c.year was omitted citing multicollinearity as reason.
Code:
. xtreg STRESS_SCORE LN_ASSETS RISK_LEV GNPA PCR NIM NONINT_INC CONT_LIAB OP_EFF GDP_GR GSEC_YLD WTAVG_CMR STABILITY C
> P_INFL USDINR_EXC c.Year##c.Year , re
note: c.Year#c.Year omitted because of collinearity.
Random-effects GLS regression Number of obs = 681
Group variable: BankID Number of groups = 39
R-squared: Obs per group:
Within = 0.5699 min = 15
Between = 0.6987 avg = 17.5
Overall = 0.6530 max = 18
Wald chi2(15) = 920.17
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
STRESS_SCORE | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
LN_ASSETS | 852.2561 170.0258 5.01 0.000 519.0116 1185.501
RISK_LEV | 27.7547 19.36566 1.43 0.152 -10.20129 65.71068
GNPA | 12.03832 18.77313 0.64 0.521 -24.75635 48.83298
PCR | -4.035505 4.591998 -0.88 0.380 -13.03566 4.964646
NIM | -906.5539 215.4158 -4.21 0.000 -1328.761 -484.3466
NONINT_INC | -748.1694 245.9966 -3.04 0.002 -1230.314 -266.0249
CONT_LIAB | .0054839 .0003396 16.15 0.000 .0048183 .0061496
OP_EFF | 479.4029 237.4127 2.02 0.043 14.08257 944.7232
GDP_GR | -64.94529 24.15464 -2.69 0.007 -112.2875 -17.60307
GSEC_YLD | 115.9559 260.1435 0.45 0.656 -393.9159 625.8278
WTAVG_CMR | 6.902367 116.1757 0.06 0.953 -220.7978 234.6026
STABILITY | .5993533 3.522829 0.17 0.865 -6.305264 7.503971
CP_INFL | -2.546553 49.51693 -0.05 0.959 -99.59795 94.50484
USDINR_EXC | 57.17443 26.12808 2.19 0.029 5.964339 108.3845
Year | -113.7963 62.55224 -1.82 0.069 -236.3965 8.803796
|
c.Year#c.Year | 0 (omitted)
|
_cons | 219487.2 123282.9 1.78 0.075 -22142.84 461117.2
--------------+----------------------------------------------------------------
sigma_u | 1586.1843
sigma_e | 1520.6156
rho | .5210955 (fraction of variance due to u_i)
-------------------------------------------------------------------------------
Afterwards, I came across posts which mentioned, "if you don't expect a time trend so much as just haphazard shocks to outcome from year to year, then add i.time to the list of dependent variables". Further, in field like Finance, most of the time the shock is haphazard rather than following a time trend. Both these statements are attributed to Clyde Schechter. Assuming, my dependent variable, banking stress to be the outcome haphazard shocks to bank-specific and macroeconomic parameters, I re-ran my model by including i.year as one of the independent variable, as follows.
Code:
. xtreg STRESS_SCORE LN_ASSETS RISK_LEV GNPA PCR NIM NONINT_INC CONT_LIAB OP_EFF GDP_GR GSEC_YLD WTAVG_CMR STABILITY C
> P_INFL USDINR_EXC i.Year, re
note: 2017.Year omitted because of collinearity.
note: 2018.Year omitted because of collinearity.
note: 2019.Year omitted because of collinearity.
note: 2020.Year omitted because of collinearity.
note: 2021.Year omitted because of collinearity.
note: 2022.Year omitted because of collinearity.
Random-effects GLS regression Number of obs = 681
Group variable: BankID Number of groups = 39
R-squared: Obs per group:
Within = 0.5756 min = 15
Between = 0.6998 avg = 17.5
Overall = 0.6552 max = 18
Wald chi2(25) = 925.79
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
STRESS_SCORE | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
LN_ASSETS | 824.5139 171.8609 4.80 0.000 487.6728 1161.355
RISK_LEV | 34.37259 19.7128 1.74 0.081 -4.263789 73.00897
GNPA | 2.299177 20.09347 0.11 0.909 -37.08329 41.68165
PCR | -1.816186 4.874106 -0.37 0.709 -11.36926 7.736886
NIM | -915.265 228.8066 -4.00 0.000 -1363.718 -466.8124
NONINT_INC | -696.9691 251.4479 -2.77 0.006 -1189.798 -204.1403
CONT_LIAB | .0055769 .0003431 16.25 0.000 .0049043 .0062494
OP_EFF | 426.0327 246.092 1.73 0.083 -56.29879 908.3643
GDP_GR | -82.44671 31.5042 -2.62 0.009 -144.1938 -20.69962
GSEC_YLD | 335.9414 884.0082 0.38 0.704 -1396.683 2068.566
WTAVG_CMR | 204.2107 270.3801 0.76 0.450 -325.7246 734.146
STABILITY | 15.96176 34.55709 0.46 0.644 -51.76889 83.69242
CP_INFL | 265.7651 459.0772 0.58 0.563 -634.0097 1165.54
USDINR_EXC | -42.01288 48.95287 -0.86 0.391 -137.9587 53.93299
|
Year |
2006 | -584.4236 930.4732 -0.63 0.530 -2408.118 1239.27
2007 | -2037.475 2191.599 -0.93 0.353 -6332.929 2257.98
2008 | -2400.557 2484.468 -0.97 0.334 -7270.025 2468.911
2009 | -4409.829 4150.43 -1.06 0.288 -12544.52 3724.864
2010 | -3285.549 4798.677 -0.68 0.494 -12690.78 6119.686
2011 | -3744.712 4577.124 -0.82 0.413 -12715.71 5226.287
2012 | -5108.068 5756.694 -0.89 0.375 -16390.98 6174.845
2013 | -4399.575 4948.135 -0.89 0.374 -14097.74 5298.591
2014 | -3247.508 3938.395 -0.82 0.410 -10966.62 4471.604
2015 | -1828.772 2342.686 -0.78 0.435 -6420.353 2762.809
2016 | -706.4356 979.0437 -0.72 0.471 -2625.326 1212.455
2017 | 0 (omitted)
2018 | 0 (omitted)
2019 | 0 (omitted)
2020 | 0 (omitted)
2021 | 0 (omitted)
2022 | 0 (omitted)
|
_cons | -7901.26 5665.685 -1.39 0.163 -19005.8 3203.279
-------------+----------------------------------------------------------------
sigma_u | 1586.0957
sigma_e | 1522.2238
rho | .52054002 (fraction of variance due to u_i)
------------------------------------------------------------------------------
iii) Even though my time period begins from 2005, why it is not included in the result ?
Any help/ insight would be sincerely appreciated.
Warm regards
pankaj
help document describes "##" as "binary operator to specify full-factorial interactions". This is the proper way to perform interactions: conditional main effects of the term included in the interaction + the interaction itself.
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