Dear all what is difference between ARDL and ARDL bound testing technique?
ARDL is the estimation and ARDL Bounds Testing is like Unit Roots+JJ to verify co-integration exists.
i have taken log returns (LN) of my stock prices, but the distribution of log returns is not normal. kurtosis is as high as 3000. what shall i do?
Atiq Rehman non-normality is not a big issue and there is no need to force data to normality, however, such a high kurtosis indicates outlier (s). These should be discarded
Hello! I have an urgent question to You. If I used lag 1 for Johansen coinyegration test, so does that mean that I have to use lag 1 in VECM too? Or I can use any another lag for VECM?
when we can employ johansen co-integration?
Sayed Hossain You can run Johansen test when variables are integrated of same order, that is I(1) or I(2) etc.
why our R square comes out smaller in cross sectional data?
and why in time series data we get higher R square ?
Noman Arshed Because there is more commonality between the variables in time series data, this commonality is called trend which leads to high R-squared. here is the catch most of the cases this high R-squared indicated spurious regressions.
What is mean by long run and short run ?
Muhammad Anees If I talk about long run than I mean sufficient time where I can say abi bahut time hay and I am sure I can do anything within this time period include building new businesses, plants, factories, changing capital, labour etc. I dont mention 5 years is along or 3 years. Only thing I consider is the feeling where I can do anything.
DIFFERENCES BETWEEN GLS AND GMM.
Professor Suborno Aditya commented as such >> GMM is a dynamic estimator correcting both hetero and serial corr however GLS is not a dynamic estimator but can correct for hetero, serial corr and cross sectional dependence. GMM cannot correct for CD. GLS cannot account for IV (and systems of equations) and differences data and hence can only estimate using data at level while GMM can do both at level and difference accounting for IV and systems of equations. Thus GLS is weaker with respect to endogeneity.
CURE OF HETRO AND AUTO
HETERO AND AUTOCORRELATION.
Professor Khan Saib commented as such> Hetero is solved by transformation of variables. Auto is cured by adding further variables or lags of the current variables.
++++++++++++++++++++++++++++++
how to read such kind of values?
In the above example of 1.25E+08, decmal has been shifted 8 points to the right, it was before 25, after shifting 8 points to the right, we have placed 6 zeros, i.e. 25 means 2 digits and 6 zeros means six digits, means total 8 points (digits) right.
and
e.g. we have 1.25E-08 then we have to place 7 zeros before 125 as we have only one digit before decimal i.e. 1, the resulting value will be 0.0000000125
Do we need stationarity checking for GMM?
from Sir Sayed Hossain to Hossain Academy wall.
Professor Hichem Ben Ammar Mediouni commented> GMM of Blundell and Bond (1998) dont require stationarity test (see Kapodar (2008)). After analysing GMM regression, I think two things need to be brought into effect i) Residual Autocorrelation test 1 and 2 ii) Validity of instrument test (see Roodman (2009).Can we ignore Multicolinearity ?
Tella Oluwatoba Ibrahim Multicolinearity is not the main interest of Econometricians but the "degree of multicollinearity. Multicollinearity can either be perfect or imperfect multicolinearity. Perfect multicolinearity go against the classical assumption which indicates that no independent variables must be a perfect function of another independent variable in a given regression model. When perfect multicollinearity occurred,the estimation of betas or coefficients become impossible. In Eviews, the software will show "error" because the matrix becomes a singular matrix. When two variables are imperfectly linearly related, we'll have what is called "Imperfect multicollinearity. One interesting fact about imperfect multicollinearity is that estimates will remain unbiased. Although, the standard error will rise. Since coefficient÷standard error=T-Score, the t-stat will fall. In addition, estimates will be sensitive changes in sample size as well as specification of the model but the overall fit of the equation and coefficient of non-linearly related variables will be largely unaffected. Common sense tells that the higher the sample size, the lower the variance of the estimated coefficients. Just kill the imperfect multicollinearity by increasing sample size(that's funny,right). I am not encouraging disaggregation of data cos in my country when you disaggregate annual time-series data, I am 100% certain that the problem of non-normallity will arise. When econometricians say do nothing to multicollinearity, they're talking about imperfect multicollinearity. In case of perfect multicollinearity one must do something because determinant of the matirix equals zero. Possible solution of such problem involve the use of correlation and Variance Inflation factor. Above 0.8 numerical value for correlation analysis while above 5 numerical value in VIF. When those numerical values is fulfilled, you need to drop one of the variables involved. All the best
what is cross dependence test?
Ade Kutu When applying the Pesaran CD (cross-sectional dependence) test, what you are looking for is to test whether the residuals are correlated across entities. The benchmark null hypotheses that are tested for the cross-sectional dependence are: Ho:α=1, there is no correlation of the residual.
H1:α≠1, there is correlation of the residual.
or
It is like people are getting confused as to the right meaning of cross-sectional dependence. In a simple language, cross-sectional dependence means for instance, Ade Kutu who is a Nigerian, he is based in South Africa and working in South Africa. He earns income in South Africa and send money to his family every month in Nigeria. Now, if Ade Kutu who is working in South Africa should lost his job, it means his family in Nigeria will be affected as he will no longer be able to send money to his family again every month. This means that there has been a cross-sectional dependence across entity between Ade Kutu in South Africa and his family in Nigeria. This simple analysis can be expanded to macro level. That is why the Pesaran CD (cross-sectional dependence) test is a test for the correlation of the residual.
or
Abu Subhi Suborno is right. Cross-sectional correlation and serial correlation are two different things. We can confirm that by taking an excerpt from a paper written by Frees (1995):
"there may exist important correlations between [cross-sectional] units ... These are called ‘cross-sectional’ correlations to distinguish them from autocorrelations, or correlations through time" (p. 394).
I tried to find the exact definition of cross-sectional correlation or dependence in my econometric texts but found nothing. However, in a recent article published in the Stata Journal, cross-sectional dependence can be defined as:
"some correlation structure in the error term between [cross-sectional] units” (Burdisso & Sangiácomo, 2016, p. 424).
This definition is different from the definition of serial correlation or autocorrelation. In Wooldridge's textbook, autocorrelation refers to "correlation between the errors in different time periods" (Wooldridge, 2013, p. 857).
References
Burdisso, T., & Sangiácomo, M. (2016). Panel time series. Review of the methodological evolution. The Stata Journal, 16(2), 424–442.
Frees, E. W. (1995). Assessing cross-sectional correlation in panel data. Journal of Econometrics, 69(2), 393-414.
Wooldridge, J. M. (2015). Introductory econometric: A modern approach. Nelson Education. What to do if we have multicollinearity problem?
Professor Moulana Naykrasyvishyy Cholovik commented as such > The best remedy for multicollinearity is ‘’do nothing’’ instead of torturing model with transformations or with poor ridge estimators or with deleting variables. Econometricians call the multicollinearity ‘'GOD’s will'’ thts beyond the boundary of mankind.
Taken from Blanchard, O. J. (1987). [Vector Autoregressions and Reality]: Comment. Journal of Business & Economic Statistics, 5(4), 449-451.
there are many independent variables which effect dependent variable, but we select some variables not all can any one tell why
Including too many explanatory variables has a cost. When you add more variables, you lose your degrees of freedom (number of observations). Fewer degrees of freedom make it difficult for you to get statistically significant coefficients. That is why many researchers omit some variables and only include variables that are likely the most important in determining the dependent variable.
Intresting question about ARDL cointegration
Why didn't ''Pesaran & Shin'' talk explicitly about the order of integration of dependent variable in their original paper ? what is the suitable methodology to estimate a long run relationship between a I(0) dependent and set of independent variables of mixed order of I(1) & I(0).
I can't change nor transform the variables because there is a strong theoretical support/reason for the specification i have chosen.
I have said explained in one of my posts that it is not possible to have cointegration between I(1) and I(0) variable because one is having bounded variance and one is having unbounded variance. But if you have more than two variables with at least two having highest order of integration, cointegration is possible. That is testable by any tests. However, the critical values need adjustment for the number of I(0) variables in the model. This type of adjustment is available only for ARDL. Therefore when you assume that there is mix of I(1) and I(0) variables, you can apply ARDL approach, provided, at least two variables are I(1). If only one variable is I(1), cointegration is not possible theoretically.
Moulana Naykrasyvishyy Cholovik thank you for your comment. i have 3 independent 2 are purely I(1) and 1 is weakly I(1). but the dependent variable is purely I(0). i still can apply ARDL ? i remember once #Noman Arshad said that dependent variable must be I(1).this made me confused. then i went through the pesaran's papers published in 2001. pesaran didn't say a single word about the order of integration for dependent variable. authors just talked about set of regressors of mixed orders.
your words ''Therefore when you assume that there is mix of I(1) and I(0) variables'' this mix in which side ? just in right side of the equation ? or in both sides ?
Basically ARDL bypasses the need of prior application of unit root test. You don't need to apply unit root test befor application of ardl. If test stat is is above upper bound, that verifies long run relationship without worrying about order of integration. Soame people recommend use of i(2) variables, but i(2) variables behave like explosive series and therefore not compatible with behavior of economic time series. Therefore if your test stat is greater than upper bound, you can trust your results without going into details of order of integration of individual series
How to remove serial correlation
Suborno Aditya There are several approaches to remove serial correlation. Alternative approaches include using lagged variables of the dependent variable however literatures suggest its suppressive effect on overall outcome. Other approach is using first difference of variables but by doing this you lose dynamism and critical information from your data and hence you may end up with wrong results.
Hence, it is better to use appropriate methods and techniques to manage serial correlation rather than removing it from the data while estimating panel regression. If it is AR of order 1, Panel regression with Cluster option (xtreg, cluster) should be alright. Or you can estimate using XTREGAR instead of XTREG command that by default manage serial correlation. In that case no need to use cluster option any more.
However, if serial correlation oforder 1 is present alongside heteroskedasticity or/and cross section dependence, using FGLS or PCSE is better. In most literatures, authors do no check for higher order or possibly moving average serial correlation. Thus, managing for only AR1 where your data actually has higher order or moving average autocorrelation, will not reveal efficient or accurate result. However, many authors overlook it and simply estimates equations managing AR1 and gets published. The challenge is determining whether higher order or MA autocorrelation exists in your data after you have already identified autocorrelation of AR1. If it can be identified, there are very specific techniques to manage that in panel estimation.
How to Remove serial and heteroskedasticity problem from panel data?
first of all we can cheak serial and HSK problem with the help of these two stata commands
xtserial for serial correlation and xtgls, panel(hetero) for heteroscedasticity.
Few researchers says that there is no need of auto-correlation test in case of Panel data as we just need this test in case of Time serious data. Here I am confuse.
Yes, if the timespan is not too big compared to n, evidence it will not produce biasedness in estimates.suupose according to wolrigde
What are the dimensions of your N and T (roughly?) Many of the routines that claim to correct for serial correlation and/or heteroskedasticity are only guaranteed to work (in the sense of eliminating the problems) when T is fairly large. If N is large and T is not very large, the "cluster" option after FE -- or, for that matter, RE -- is attractive. So xtreg y x1 ... xk, fe cluster(csid) where csid is the cross section identifier. The resulting standard errors are completely robust to any kind of serial correlation and/or heteroskedasticity. The other approaches assume parametric forms and, like I said, typically rely on large T approximations. Jeff Jeffrey M. Wooldridge University Distinguished Professor Department of Economics Michigan State University 110 Marshall-Adams Hall East Lansing, MI 48824-1038 Phone: 517-353-5972 Fax: 517-432-1068
How to Remove serial and heteroskedasticity problem from panel data?
first of all we can cheak serial and HSK problem with the help of these two stata commands
xtserial for serial correlation and xtgls, panel(hetero) for heteroscedasticity.
Few researchers says that there is no need of auto-correlation test in case of Panel data as we just need this test in case of Time serious data. Here I am confuse.
Yes, if the timespan is not too big compared to n, evidence it will not produce biasedness in estimates.suupose according to wolrigde
What are the dimensions of your N and T (roughly?) Many of the routines that claim to correct for serial correlation and/or heteroskedasticity are only guaranteed to work (in the sense of eliminating the problems) when T is fairly large. If N is large and T is not very large, the "cluster" option after FE -- or, for that matter, RE -- is attractive. So xtreg y x1 ... xk, fe cluster(csid) where csid is the cross section identifier. The resulting standard errors are completely robust to any kind of serial correlation and/or heteroskedasticity. The other approaches assume parametric forms and, like I said, typically rely on large T approximations. Jeff Jeffrey M. Wooldridge University Distinguished Professor Department of Economics Michigan State University 110 Marshall-Adams Hall East Lansing, MI 48824-1038 Phone: 517-353-5972 Fax: 517-432-1068
How to check panel unit root with the help of summary statistics
because panel data consist of many panel units (N) and times (T), we can use xtsum command - command to summarize variables according to panel dataset - and we can see that between variations mean variations across panel units, and within variations mean variations across times within a panel unit, therefore if within variations are greater than between, it is highly likely that the variables are non-stationary or have unit root
Yes normally. But to eliminate serial correlation from model we may change number of lags...So I can use lag 1 for Johansen cointegration test but change lag for VECM? Sayed Hossain Guideline is normally we need to follow lag selection criteria suggestion to choose lags but if serial correlation still exists then we can change lag number.
hlo dear friends i have run PANEL VECM , as panel VECM show long run and short run causality the question is that , can we still run pairwise causality as well.Thanks in advance
According to Sir Muhammad Anees Yes, GC has no dependence on VECM,, means u can run.
Why we use Hausman test?
Noman Arshed Hausman test is actually used to compare consistent versus efficient estimates. It is not specially designed for ols it can be used any where when we are comparing consistent vs efficient method. Examples
1) fe v re
2) 2sls v ols
3) mg v pmg Etc.Hlo dear friends, i want to run granger causality ,as i have core purpose to test directional relationship ,so should i first run regression then granger causality or direct?
ans by sir Muhammad Anees Run VAR and then GCause
proceduere : go quick--group statistic--granger cusality
What is the main difference between static and dynamic models?
Answer:
For static models, the dependent variable responds immediately to changes in the independent variable.Whereas for dynamic models, the dependent variable does not respond instantaneously to a change in the independent variable during the period in which the change occurs. In other words, the independent variables have a lagged (dynamic) effect on the dependent variable.
Distributed lag and autoregressive models are general examples for dynamic models
use one less lag in vecm, suppose if we found optimal lags length 4 then use 3 in vecm...
Sayed Hossain Saeed Aas Khan Meo it is actually suggested by a group of econometricians. They argue, VECM model automatically converts all variables into first differences but VAR estimation can not do it. So while use VECM, use 1 less lag suggested by optimal one.Hlo Hi friend i want to know impact of macroeconomic variables effect on stock returns volatility how to do?
Noman Arshed It can be done using
1) moving standard deviation
2) arch garch modelshould i used first difference data or level form data.
Sayed Hossain commented about VAR and VECM model as such >> If you want to use unrestricted VAR then use differenced data as VAR can not convert variables automatically to first differenced. But if you want to run restricted VAR that is VECM, use non stationary data that is level data and EVIEWS or STATA will convert them to first differenced automatically.
What is the difference between U and ê ?
The terms RESIDUAL and ERROR, even what they represent the same thing but actualy they are not exactly the same e.g Y=B0 +B1X +U This is PRF and y=b0 +b1x +e this is SRF SO we can say that u is the population term which is not observeble and e is sample reg term and is observble I.E e=Y-Y^ ,,,,e is the estimate of u
how to remove serial correlation from panel data?
if cross sections are more than time then add more variables or try trend variable. if time is more than cross sections then it means variables might be non stationary, check that and use the panel ARDL.
PANEL ARDL
Professor Abu Subhi commented as below>>
Both Pedroni and Kao cointegration tests assume all variables are integrated of order one. You could try Dynamic Fixed Effects (DFE) as your short and long run coefficients may be homogeneous across individuals.
Note:
MG allows short and long run coefficients to differ across individuals. PMG only allows short run coefficients to differ while the long run are assumed to be homogeneous across individuals.
what is difference between VAR, SVAR, ARCH
Muhammad Anees If I have a model with three variables like x1, x2 and x3 and would like to estimate it with VAR, then the regression system when each of X will be once a DepVar and others as IndepVars, it can be considered as simultaneous equations system estimated through vector auto regression approach. If this regression becomes different between two time spans for the same sample like before 1980s, it behaved differently than after 1980s while estimation approach is still VAR, we can consider it as Structural VAR. The third approach becomes slighly different. Consider I have to model Y only. If the residuals of this model becomes of specific structure that its standard deviations and means behave like autocorrelation is there, the estimation of such models can be through ARCH.
Hlo friends what is difference between chow test and multiple break point test.?
Both are the same, the different between them that Chow test assume that the break dates (points) are already known.
halo friends, I have check structural brake in my data , I have data from 1980-2014 but confusion is that test showed three years 2003 ,2007, and 2008 , so how to give value to dummy variables.use three dummies for the three possible structural break (years), the dummy that is significant in your regression indicate a structural break at that year. for example if the dummy of the year 2007 is significant, year 2003 is not significant and the dummy of the year 2008 is significant, then you have structural break at 2007 and 2008 BUT there is no structural brek at year 2003.
sir i have cheacked multiple breaks one by one in all vriables and i found 3 break in first varibale ,2 in second ,and 1 in third so how many dummy variables i should use as independent
Then you add 6 dummies in your model and regress, after regressing if there any dummy that is insignificant drop it and re estimate your model again.
What does it mean when I find that there is cointegration among variables but then I get the long run coeffients, they turn out to be not significant. Cointegration means that there is a long run relationship but i find them not significant for my variables
Some time could be the case that there exist a cointegration among variables, but it is just by CHANCE !! in addition be sure that your model is correct specified.
BUt the series should be stationary and not autocorrelated. But even after taking the first difference you need to be sure that there is no auto correlation. The auto corr. is important in ARDL not because the standard errors and so one as we know normally , but in case of ARDL if there is auot corr. the estimated coefficients will be biased.You add trend to ensure that you not get a spurios regression.
VAR models tells bout long run or short run?
VAR model tells about short run results, How Do I Interpret the P-Values in Linear Regression Analysis?
The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.
Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.
In the output below, we can see that the predictor variables of South and North are significant because both of their p-values are 0.000. However, the p-value for East (0.092) is greater than the common alpha level of 0.05, which indicates that it is not statistically significant.
multicollinearity effects and solutions
In general, multicollinearity is a problem in any econometric framework. For instance, it causes standard errors to be large even if the underlying specification is correct (in which case the estimates will be unbiased). The risk of Type II error is thus increased. There are no hard and fast rules on how to deal with it but possible solutions include excluding, combining, centering or standardizing the problematic variables or just obtaining more data.That's right. In general, it is practical to accept values below or around 5 as fine when the sample size is relatively small, and values below or around 10 as fine for relatively large samples. What is a large or a small sample is totally up to you. In your specific case, 5.16 might be just acceptable.
how to make decision about multicollinearity exit or not via VIF
A general rule is that the VIF should not exceed 10 (Belsley, Kuh, & Welsch, 1980). When Xj is orthogonal to the remaining predictors, its variance inflation factor will be 1.
(Bandura, A. (1997). Self-efficacy: The Exercise of Self-Control. New York: Freeman. Belsley, D. A., Kuh, E. & Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley.)
How to take log of negative values
Find minimum value of the variable and add it as a constant to the entire series, then take log
now what if i have negative values in my data which is minimum in series so ans is with following example.Muhammad Ali Shuja Lets assume that minimum value of your series is -11.556. Then you should add 12 (rounding to the right) then the whole series will become positive and it will be perfectly collinear with your original series which means that it will not lose its properties. Once you have positive values then you can use all functions that require a variable to be positive.
HOW MUCH WE CAN TAKE MAXIMUM LAGS.
Monthly data: 12-36, Quarterly data: 4 to 12 and yearly data: 3 to 5. Not a scientific rule but an observation commonly found.
What are the differences between ARCH, GARCH, SVAR, and Co integration
Let me explain with a simple trick. Assume you have three persons and you asked them to jump. You see one of them and find him he jumps like frequently with similar patters like some small jumps together and some long jumps with no visible pattern. If you model this persons attitude, you can use the ARCH. If the person is found to have systematic pattern where small jumps are followed by some small jumps and long jumps followed by long, then you can use GARCH. Now, see if the three persons are seen together and you find them jumping like. Assume initially they were jumlping with small patterns but suddenly you found they started long jumping. This can be modelled with SVAR. Now again if you see the three persons are mumping similar without the first two patterns strongly visible but still you see a pattern, then you need Co-integration. Now find the differences in each other.
Should we make the selection of best among various type of GARCH model on the BASIC of AIC or SIC or Log-likelihood values?
Yes, most of the times ARCH/ARIMA models are to be selected with the aim of being the most parsimonious model and hence AIC will not give it so SIC is the criteria to be preferred. If your objective is not the parsimony of your model, then go for the AIC.
what should i do when i use 2 CointEq i.e. CointEq1 and CointEq 2 in a VECM. which one is the speed or ajusment or, or how can i specify the ECM ecuation
For simplicity sake and easy interpretation, enter only 1 co-integrating equation in your VECM specification regardless of the no of co-integrating equations you got via your Johansen cointegration test.
Sayed Hossain 2 CE can not show speed of adjustment. you need 1 CE to show it.
Dear Josef
You do not need to report the results of all the cointegrating equations. You should only take the first equation where only dependent variable is normalized. The number of cointegrating equations only tell you that there is long run relationship.andThe error correcting coefficients are your adjustment coefficients .
Kerry Green McCullough You should include all the co-integrating relationships in a multivariate VECM...that is, if Trace and ME say there are 5 relationships, these should be in the VECM together these describe what is going on in the model. This is because the the vector of disequilibrium terms contains one for each co-integrating vector (Alexander, 2008, Vol.2, pg. 246). Asteriou and Hall (2011 pg 378) specifically note that the number of cointegrating equations including in the VECM is determined in the previous step (Trace and ME tests). In the worked example by Brooks (2008 pg 373) he notes that keeping the number of cointegrating equations to 1 (when Trace and ME have found more) is done in that particular example context only for simplicity. You could use Brooks as a reference supporting starting with 1 for simplicity's sake. If you come across any other references for why one may use 1 rather than the number found in Trace and ME I would be very appreciative if you were to share the references....I would love to learn more about this approach and Brooks does not give a full set of reasons for this method.
T test and F test
It is like t test and F test. t test talk about individual significancy while F test talk about joint significancy. Suppose X1 is alone significant as per t statistics but X1 and X2 are not jointly significant as per F statistics.
what if BOUND TEST value F value fall between upper bound and lower bound
You pointed interesting thing. Actually you are right. According to Banrjee et all, pesaran et all, Muhammad Amine if F-statisic is between the upper bound and lower bound. Then you need to rely on error correction term. If it is significant and negative, then you have long run connection among the variables
Difference between Var and granger causality .
Granger causality is JUST (JUST) a F-TEST of the coefficients obtained from VAR model. Telling us if the the coefficients of X and lags of X are jointly(F-TEST) causing Y AND if the coefficients og Y and all lags of Y are jointly(F-TEST) causing X. When you use STATA for example, you can not use the command og granger before using the command of VAR!! and when you use the command of granger you get a table with p-values; this table as i mentioned is JUST a table of F-TEST of the coefficients in VAR model. Good Luck
what is meaning of giving a shock
That you can say a dhakka-start to the economic system in question like we normally see the new taxes in Pakistan which acts like a shock for the whole economy and every sector gets affected.
Why we use adjusted R^2
Normally, R^2 increases when add more variables, but that does not necessary means that R^2 is high because your model is very good. To solve this problem we consider/use adjusted R^2 that adds panelty for any additional variable. This gives correct picture/information about how good is your model to explain the dependent variable.
What is R and R2
Dear Naina Baloch and all others:The difference between R-squared and Adj. R-squared is that the latter is adjusted for degrees of freedom while R2 is not.In a multiple regression model whenever you add another explanatory variable in the model, R2 will always increase with the inclusion of every additional variable in the model but the Adj.R2 may or may not increase. If the additional variable does not add anything to the explanatory power of the model Adj. R2 will decrease although R2 will still increase. If the additional variable also adds to the explanatory power of the model then both R2 and Adj-R2 will increase. In order to compare various models we have to use Adj.R-squared instead of R-squared. Since different models have different degrees of freedom we can't use simple R2 to compare those model. So we will have to use Adj.R-squared because it is adjusted for degrees of freedom.
What if I have expect coefficient but residual not normally Distributed and having HSK
Even the residual is not normally distributed we can accept the model as OLS estimators are still BLUE. Bit if there is heteroscedsaticity we can not accept the model as OLS estimators are no longer bLUE.
Why we take log
If you convert the variable into natural log and run the model, probably heteroscedasticity problem will not arise in the regression model. it is useful also for the interpretation, if you use log on both sides, then the coefficients indicates the elasticity. Also, log-transformations of dependent variables greatly reduce the variances and skewness and kurtosis statistics (see Cameron and Trivedi 2010). Log-scale informs on relative changes (multiplicative), while linear-scale informs on absolute changes (additive). When you care about relative changes, use the log-scale; when you care about absolute changes, use linear-scale. In log transformation you use natural logs of the values of the variable rather than the original raw values. Log transformation works for data where you can see that the residuals get bigger for bigger values of the dependent variableECM OR EVEC
Normally I convert all variables into natural log so that heteroscedasticity problem may not arise after running regression model to remove serial correlation from model.
Engle Granger or Johansen test
When two variables you can use ether Engle Granger or Johansen test but when more than two variables use Johansen only.
Model must be backed
One other serious problem which I observe while I check M.Phil and Ph.D student synopses, theses and dissertations is that most of the times they write equations and models to be estimated which are not backed or supported by economic theory, logic or inuition. As many as 50-70 % of the students (not well guided by their respective advisers) have equations in their theses/synopses not based on economic theory. As such, I call such equations hanging in the air with any support. So what you need to do? Whatever you want to do, you must read relevant literature and try to dig out what economic theory says about your topic or relationship among your variables of interest. This is very important. So, Economic theory comes first, and empirical testing and evidence come next. If Economic theory is silent about your topic of interest, you can find out what other learned researchers and economists have reported about such research. Literature review helps you in this regard. It may help you word your objectives, hypotheses and even defining your methodology and econometric model as well. I request all teachers to correctly guide your students. After all, your students are your ambassadors and they will propagate you. If you help of them they will portray you in a positive way and vice versa.
Interpreting Regression Output
As a teacher, examiner, and researcher I have observed that many students, researchers and even some teachers try to show that their R-squared must be close to 1 in regression. You must keep in mind that in case of time series R-squared could be high but in cross-sectional data it may not be high. It is not a problem at all; although higher the R2 better the explanatory power of the model.So we must not only be interested in getting or reporting a high R2. What is most important is that we must look at the p-values and algebraic signs of explanatory variables. First of all, we must see whether the signs of the coefficients are in agreement with economic theory, logic or intuition. If not then we may think again. May be there is something wrong with our data or functional form or any other problem. Second, we may look at statistical significance of the partial regression coefficients. If most of our coefficients are statistically significant, that is a good sign. Next we may look at other diagnostics tests. We may also see if F-stat is statistically significant too. If yes it shows that the over all equation/model is significant.After that we may also check normality, heteroscedasticity and serial auto-correlation of the error term. If you are thinking of submitting your article for publication consideration, you may give at least 4 to 5 different estimated models and conclude which model best suits the data and situation
Student problem
An M.Phil student from another university visited my office who was so upset. When I asked him what is your problem. He said that he was conducting research on factors affecting inflation in Pakistan. His research is based on time series. In his synopsis, there were three equations and all the three equation had the problem of endogeniety as well as simultaneity. The student was advised by two other teachers totally in a different ways. One teacher told him to this and the other told him to do this. Both the teachers advice was totally opposite to each other. Surprisingly, none of the three teachers (the student adviser, another teacher and one more teacher) advised her the first step (to check stationarity). In addition, all these teachers suggested this student to estimate these equations as OLS (I mean single equation) rather then what is required. I was so upset to know the state of academic affairs. If the teachers themselves know what is the right approach and if they cant spare time for student guidance, what will be the standard of their students. Its a pity, isn't it? Why should I allow my students to work on a topic on which I am not clear myself. It is better to produce one or two students with good work rather then producing 10 where none has not done a well researched work. We may prefer quality to quantity.
What test must be
For those of you who analyse time series data for your thesis research. Keep in mind that time series data are usually non-stationary at level. So before modeling your data, you must check the time series for unit root. If your time series variable are stationary at level, then you may go for OLS estimation. If your variables are non-stationary at level but stationary at first difference that is it is I(1), then check cointegration. If there is co-integration among your series based on Johansen Cointegration test, then use VECM. If there is no conintegration among your variables, the do VAR analysis. The coefficients will then be of short term rather than long term. If some of your series are I(0) and some are I(1), then you will use Autoregressive Distributed Lag model
What if data not stationary even 1ST difference
You must apply other test like we normally use Dickey fuller test, but If we have trending data we must chose other tests
ECM notce
If ECM is +ve means no convergence to equilibrium b/c it shows the the shortrun nature of the variables as well as how they move towards longrunECM term should be negative to say that model is stable and it converges to long term. EC term should be negative and statistically sig at the same time
Random of fixed effect model
dear Sara Nasir.... both models are static models....and normally uses when time period less or short period....by fixed effect model we means residual of model is fixed for all cross section while in randome effect model residual of model is changes with cross sections.. dear Sara Nasir......there are many things which can be explained....like fixed effect model have individuals intercept for in regression equation while in random effect model....different residuals......in fixed effect model it can also be one-way fixed effect model and two-way fixed effect model...it can be discus..
What if R square is listen sixty percent
If R SQURE is less than sixty but if F statistics is significant then we conclude that our model is accept able and its thumb of rule.
The properties of ARDL
The bounds test approach to cointegration has certain econometric advantages in comparison to other single equation cointegration procedures. As pointed out by Emran et al. (2007), the bounds test approach to cointegration is preferred to other conventional cointegration tests because Monte Carlo evidence shows that it has several important advantages over other conventional tests. The approach effectively corrects for a possible endogeneity of explanatory variables and the estimates derived from the approach exhibit desirable small sample properties. Another important advantage of the ARDL approach is that one can avoid the uncertainties created by unit root pre-testing as the test can be applied regardless of whether the series are I(0) or I(1). An added bonus of this approach is that unlike other conventional tests for cointegration, it can be applied to studies that have a small sample size (Narayan, 2005).
What is the acceptable range of skewness and kurtosis for normal distribution of data?
The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). George, D., & Mallery, M. (2010). SPSS for Windows Step by Step: A Simple Guide and Reference, 17.0 update (10a ed.) Boston: Pearson.The acceptable range for skewness or kurtosis below +1.5 and above -1.5 (Tabachnick & Fidell, 2013). If not, you have to consider transferring data and considering outliers.
What must be Reliability value of variables Cronbach's Alpha
A scale is reliable if the coefficient value is more than 0.600 (Hair et al., 1998).
What must be the value of normality of the data Skewness and kurtosis
According to George and Mallery (2006, p. 99), a skewness or kurtosis value between +1.0 is regarded as an excellent value and hence, the data for this study is normally distributed.Kurtosis is a measure of the “peakedness” or “flatness” of a distribution. A kurtosis value near 0 indicates a distribution shape close to normal. A negative kurtosis indicates a shape flatter than normal, and a positive value indicates more peaked than normal. An extreme kurtosis (e.g. |k| > 5.0) indicates a distribution where more of the values are in the tails of the distribution than around the mean. A kurtosis value between +1 is considered excellent, but a value between +2 is acceptable in many analyses in the life sciences
As kurtosis the value of skewness between +1 is considered excellent, but a value between +2 is acceptable in many analyses in the life sciences
Degrees of Freedoms
: Let me briefly say that the term, “degrees of freedom” refers to the number of (logically) independent pieces of information in a sample of data. Let me offer a simple example, suppose that we have a sample in which there are five values {3, 6, 8, 10, 13} whose sum is 40. In this particular example I can freely choose 4 values but the fifth one must be such that it will make the sum of these five numbers equal to 40. Thus there are n-1 = 5-1= 4 degrees of freedom. The value of the unknown fifth sample value is implicitly being determined from the other four values, and the constraint. That is, once the constraint is introduced, there are only four logically independent pieces of information in the sample. That’s to say, there are only four "degrees of freedom", once the sample total is revealed. Spencer Sáúll and Laxmi Narayan
Great detail of model selection on the base of data
let's suppose that we have a set of time-series variables, and we want to model the relationship between them, taking into account any unit roots and/or cointegration associated with the data. First, note that there are three straightforward situations that we're going to put to one side, because they can be dealt with in standard ways:1. We know that all of the series are I(0), and hence stationary. In this case, we can simply model the data in their levels, using OLS estimation, for example.
2. We know that all of the series are integrated of the same order (e.g., I(1)), but they are not cointegrated. In this case, we can just (appropriately) difference each series, and estimate a standard regression model using OLS.
3. We know that all of the series are integrated of the same order, and they are cointegrated. In this case, we can estimate two types of models: (i) An OLS regression model using the levels of the data. This will provide the long-run equilibrating relationship between the variables. (ii) An error-correction model (ECM), estimated by OLS. This model will represent the short-run dynamics of the relationship between the variables.
1. Now, let's return to the more complicated situation mentioned above. Some of the variables in question may bestationary, some may be I(1) or even fractionally integrated, and there is also the possibility of cointegration among some of the I(1) variables. In other words, things just aren't as "clear cut" as in the three situations noted above.
Cautions for ARDL
We need a road map to help us. Here are the basic steps that we're going to follow (with details to be added below):
Ø Make sure than none of the variables are I(2), as such data will invalidate the methodology.
Formulate an "unrestricted" error-correction model (ECM). This will be a particular type of ARDL model.
Ø Determine the appropriate lag structure for the model in step 2.
Ø Make sure that the errors of this model are serially independent.
Ø Make sure that the model is "dynamically stable".
Ø Perform a "Bounds Test" to see if there is evidence of a long-run relationship between the variables.
Ø If the outcome at step 6 is positive, estimate a long-run "levels model", as well as a separate "restricted" ECM.
Ø Use the results of the models estimated in step 7 to measure short-run dynamic effects, and the long-run equilibrating relationship between the variables.
Endogenous
Endogenous variable: A factor in a causal model or causal system whose value is determined by the states of other variables in the system; contrasted with an exogenous variable
Exogenous
Exogenous variable (see also endogenous variable): A factor in a causal model or causal system whose value is independent of the states of other variables in the system; a factor whose value is determined by factors or variables outside the causal system under stud
Stochastic
The stochastic variable is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense).
Monotonically
A monotonically increasing function
Asymptotic
The term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve that is asymptotic to given curve is called the asymptote of
Autoregressive model.
If the model includes one or more lagged values of the dependent variable among
Its explanatory variables, it is called an autoregressive model
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