Econometric Applications - Science topic

Yes You can

It depends on how the shock influenced the treated and control unit.

If you can argue that the shock influenced all units in the same way, then the inclusion of two way fixed effects (particularly time fixed effects in this case) can help you to rule out the effects of such 'common' shock.

However, if there are reasons to think that the structural shock differently affected treated and control units, then this could result in potential biases in the estimation and identification of the average treatment effect.

There is a novel literature dealing with the correct identification of such effects. I would suggest you reading the following paper:

"VISUALIZATION, IDENTIFICATION, AND ESTIMATION IN THE LINEAR PANEL EVENT-STUDY DESIGN" from Simon Freyaldenhoven, Christian Hansen, Jorge Pérez Pérez and Jesse M. Shapiro. You can find the paper here: http://www.nber.org/papers/w29170

I particularly suggest you to read section 3.1. of the paper as long as accompanying the paper there is the Stata command "xtevent" which is particularly useful to deal with such econometric analyses.

Look at a scatterplots which may help but it seems that you don't have much of a relationship here. Best wishes David Booth

The difference between R squared in the ARDL model and R squared in the bounds test is that R squared in the ARDL model is about the rubostness of the overall model result and not about the robustness of the bounds test result only. This means R squared in the ARDL model will tell you how much the variability in Y or Ys (your dependent variable/variables) is/are explained by the ARDL model given Xs variables (your independent variables). On the other hand, R squared in the bounds test is specifically about the bounds test result within the ARDL model and not about the robustness of the overall model result. You need an ARDL model first to have a bounds test but not a bounds test to have the ARDL model. I hope it helps you.

I presume that you have real GDP and your energy consumption is in volume terms and that you are working with the log of both variables.

I would suggest that you go to your textbook and see if you can replicate the results of a lag selection example in the test book. It is difficult to give you a diagnosis without your data and your program. Otherwise, try a different econometric package (e.g. https://gretl.sourceforge.net/ which is free and user-friendly).

Treating 4 as maximum lags your criteria must be estimated using observations 5 to 29 as independent and 1 to 4 as lagged variables only, Treating 8 as maximum lags your criteria must be estimated using observations 9 to 29 as independent and 1 to 8 as lagged variables only, etc.

In ADF tests the maximum lag is often taken as

[the integer part of 12*(T/100)^0.25] which is 8 for 29 observations. See Hayashi, Econometrics page 592 and references therein. Many econometric packages used to use this as a maximum lag for determining lag length in this and other occasions. I would hope that with 29 observations it would specify a smaller number of lags as appropriate.

How can you justify economically that eight lags could possibly be valid? to add an extra lag to carry out this test. If you do not have cointegration then you use standard Granger tests and VAR in first differences. You will need strong economic arguments to justify the assumption that there are no other variables that are impacting both GDP and energy consumption. If there are such variables your test will not be valid.

How can you justify economically that eight lags could possibly be valid? There is something wrong with your model. The eight lags may be adjusting for autocorrelation caused by misspecification or an omitted variable. Unless there is something wrong with your calculations you need to rethink your model.

sir, i am doing research on labour market discrimination. help me to perform decomposition in unite level cross-section data.

I recommend that you use the free statistical program JAMOVI which allows the inclusion of multiple moderators and mediators.

Hello Jialing,

The fact that DVs are correlated is often one argument for choosing a multivariate method to analyze the data rather than generating a univariate model for each individual DV.

If what you are saying is that, causally or temporally, is that Y1 influences Y2, then perhaps you'd be better off evaluating a path model which incorporates such proposed relationships rather than simply allowing for correlations/covariances other than zero among the DV pairs in the multivariate regression.

Good luck with your work.

You should read the Global Burden of Disease articles on health care financing. Their appendices fully disclose their variables (& they've spent a lot of time & effort dettermining the best ones) and they provide their (sophisticated) statistical code. Lead author on most of that work is Joseph Dieleman or something like Global Burden of Disease Health Financing Collaborator Network. A full biblio of this work is at https://www.healthdata.org/about/joseph-dieleman if you click on the publications tab. The pubs are all open-access & most are on ResearchGate. :-)

I asked that question to the person who code that package, and he said C(9) coefficient does not have any meaning here, just ignore. It comes up because the package is written for the old version of Eviews and has not been updated that is why.

Index number is a measure of average (overall) change in a group of related variables.

It is to be defined clearly what is coefficient of index.

Hi there, I am using Eventus software and I am wondering how the software computes the Market index in order to calculate abnormal returns?

Hi Sultana Razia

I would recommend you read about the difference between EFA and PCA first. Whether or not you should run an EFA has nothing to do with the number of response options on the indicators, five or otherwise. In general, EFA is preferable to PCA as it is considered to be the 'real' factor analysis. The are many threads on RG on this issue.

Best

Marcel

Depending on you objective statement, if your objective is to compare variables that influence a particular problem, you can use the t- test to compare and them give justification.

Dear, conducting any standard model depends on an important factor, namely the number of observations included in the model, for example, if the observations are small, the Phelps-Peron test can be conducted to test the stability, and if the observations are large, the whooping-full test can be conducted, and in light of the stability results, we can determine the model that can be conducted Julius Hogan

Before deciding on the econometric model, you should go through the stationarity test (ADF test). If the data are stationary, OLS Regression with a log-linear model would be fine. But, if not, you may go for VAR or ARDL. You should also check the robustness of the model by going through residual tests such as Autocorrelation LM Test.

Regarding model specification, I think GMM is a good option here, given that N>T.

It seems a very small sample to apply microeconometric techniques. Having 27 seven observations and 10 covariates, at most, you will have 27 - 1 - 10 = 16 degrees of freedom. This is pretty low. If I had to decide to pursue a project based on that, I would try to avoid it.

It is really closer to multiple times series than panel data. Have a look at this link:

I notice the following about your specification. (1) Your inclusion of a constant (and its subsequent significance) means you allow for (and find) a trend in the real exchange rate independent of any trends in the other variables. Is that economically reasonable? (2) I assume the CRISIS variable is a zero-one dummy for time periods with a "crisis" of some sort. Apparently it is not in the cointegration vector. Why not? If it were, then I'd expect to find CRISIS differences in the error correction equation. Instead, you have it in levels. Thus you specify that a temporary crisis has a permanent effect of the level of the real exchange rate independent of the other variables. Is that what you intend? (3) You do not include the lagged difference of the real exchange rate in the error correction equation. Why not? Normally it would be there.

Ibrahim Niftiyev , probably the reviewer wants to see not only whether a variable affects or not the other (i.e. the results of the Granger causality tests), but also to which extent (the magnitude and temporality of the dynamic relationship, something you can obtain from the IRFs of a VAR model). If you want to apply a VAR but you have a small sample size/data limitations, you want to consider a Bayesian VAR. Bayesian VARs are very popular and Bayesian methods are valid in small samples.

Very nicely explained Renaud Di Francesco Thank you.

See these links:

Hello Md Rakib Hossain,

In an ordinary linear regression, if inclusion of an interaction (say, X*M) in a model that previously only had the individual variables as predictors (X, M), and the interaction was significant in the expanded model, but the individual predictor(s) was(were) not any longer, then to me this sounds like a classic case of moderation effect.

Good luck with your work.

I presume that your data is quarterly or monthly as otherwise, you have too few observations to make any reasonable inferences.

If you are trying to make causal inferences (e.g. you have an economic model that implies that x causes y and you wish to measure that effect). the CUMSUMSQ is one test that indicates that your model is not stable. Either the coefficients or the variance of the residuals is not stable. You have indicated that there is no heteroskedasticity so it is possible that the model coefficients are the problem. The test itself only indicates that there's instability and does not say what the instability is or what causes it. There are many possible causes of instability, (omitted variables, functional form, heteroskedasticity, autocorrelation, varying coefficients etc.) Your best procedure is to return to your economics and work out how your theory might lead to stability problems. Are there possible breaks in your data caused by policy changes, strikes, technological innovations, and similar. that might be covered with a dummy variable or a step dummy.

If you are doing forecasting (or projections) I would not be too concerned about specification tests. It is very unlikely that an unstable model will forecast well. You may achieve good forecasting results with a very simple model that need not be fully theory compliant.

Are you attempting prediction or are you trying to do some form of “causal” relationship. If you are estimating a ”causal“ model you conclusions are conditional on the model estimated. Strictly speaking, it would be better to use the adjusted degrees of freedom - particularly with your small sample. In this case, a non-significant coefficient does not necessarily imply that the coefficient is truly zero. It is more likely that your sample is too small t establish a significant result. Its p-value must not be very far from your significance level. If the estimate is of the sign and magnitude expected by theory I would accept the value and report the p-value. Esimating 5 coefficients is a big demand from a sample of 23 obs.

If you are simply doing prediction or forecasting and are not attributing explanatory power to your coefficients you might be better with a simpler model which might have better predictive ability.

Dear Ibrahim Niftiyev ,

Econometric models estimated with non-stationary data are profoundly invalid and misleading (Greene, 2002). An example of a simple scenario: - in a regression with one regressor, there are three variables that could be stationary or non-stationary; namely the dependent variable (Y), the regressor (X), and the disturbance term (u). A suitable econometric treatment of such a model depends critically on the pattern of stationarity and non-stationarity of these three variables (incl. the dependant variable). Since quite often variables can be non-stationary at I(0), it is important to understand the forces behind such non-stationarity, which largely include structural breaks, deterministic trends, and stochastic trends. Differencing (including the explained variable as in your case) is a common appropriate in nonstationary models, and this is often correct (Granger & Newbold, 1974; Green, 2002; and Stock, James & Watson, 2011).

Granger, C. W. J., and Paul Newbold. 1974. Spurious Regressions in Econometrics. Journal of Econometrics, 2(2):111-120.

Greene, W. 2002. Time series Models. (pp. 608-662) In Econometric Analysis, 5th edition. Prentice Hall, Upper Saddle Rive, NJ.

Stock, James H., and Mark Watson. 2011. Introduction to Econometrics. 3rd ed. Boston: Pearson Education/Addison Wesley.

You can access IO Tables for Pakistan over the period of 2010-2017 from following link :

Check if the bivariate scatterplots are linear or at least monotonically increasing or decreasing.

Dear Ibrahim Niftiyev ,

Thank you for the response and information shared on your PCA analysis – quite helpful.

Sincere apologies if I might have used the term “threshold” loosely. What I mean by “threshold” is the minimum score/loading a variable should have under a particular component. In other words, it is the minimum loading or score size which you have set as a criterion to regard and select a variable as significant for classifying a variable under a particular Component. For Instance, results in your Pattern Matric show that scores of variable FR_CULT as 0.774 under Component 1 and 0.414 under Component 2, so if you have set your minimum score size at 0.5 to regard a variable as significant, then you classify FR_CULT under Component 1. Using the same criterion of 0.5 as the minimum score, the variable FR_PROF loading with scores of 0.645 under Component 1 and 0.621 under Component 2 suggest that FR_PROF has a complex structure since it is loading with high scores in more than 1 component, and therefore the respective variables should be eliminated – unless a different analytical procedure is applied.

To probably reach at a conclusion on your analysis, I have a few suggestions:

(1). Could you please first compute and share results of the correlations between the variables. Correlations between variables should as much low as possible to avoid the potential problem of multicollinearity (Steven, 2002).

(2). Your Scree Plot shows that the number of components was extracted based on the Eigenvalues greater than 1 – thanks. But please advise how you determined your Maximum Iterations for Convergence – by default at 25 or you did input a pre-determined number? Such information can help understand the complete procedure you adopted in the determination of the number of components in your PCA. Probably you can read Huang and Tseng (1992) on the procedure for determining the number of components in PCA – full reference herein below.

(3). If your data is time-series, please assess and share the distributions of each of your variables.

(4). Sample size as one of the factors that influences the accuracy of procedures in PCA (Velicer, Eaton & Fava, 2000). I am NOT implying that your sample size is small, but I am not sure if the sample size of 26 relative to the number of variables (7) that you did run PCA is good enough, – you can read Velicer, Eaton & Fava (2000) with full reference provided below.

(5). Variable-to-component ratio (v:c) is an important feature in evaluation of PCA results. In your Pattern Matrix results, despite the complex structure demonstrated by FR_PROF, the distribution of number of variables in Component 2 relative to Component 1 raises some questions. The number of variables per component (which is measured counting the number of variables correlated with each component in the population conditions) influences the accuracy of the results, with more variables per component producing more stable results. If we exclude FR_PORF (due to complex structure) from your results, Component 1 will contain 5 variables while Component 2 will contain only one variable (FR_LI).

Suggested Readings:

Huang, D-Y. and Tseng, S-T. (1992). A decision procedure for determining the number of components in principal component analysis. J. Statist. Plan. Inf., 30, 63–71.

Stevens, J. (2002). Applied multivariate statistics for the social sciences. Mahwah. NJ: Lawrence Erlbaum Associates.

Velicer, F. W., Eaton, C. A., & Fava, J. L. (2000). Construct Explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components. In R. D. Goffin, & E. Helmes (Eds.), Problems and solutions in human assessment (pp. 42 -71). Boston: Kluwer Academic Publishers.

Dear all,

you can use as much as you whish but be carefull to the multicolinearity

best

In this case, you can check cointegration in the presence of structural break by using Gregory Hansen cointegration test.

You can also perform the Toda- Yamamoto causality test, because it can apply without checking the cointegration, and applicable for admixture of stationary and non-stationary series.

Dear Ibrahim,

I also recommend Greg. N Gregorios and Raven Pascalau @Hamid Muili and google for more materials on non-linear relationship.

Regards

Hello,

Please follow this procedure

1. select your data

2. right-click and select open as equation

3. select cointegration regression

4. Go ahead and choose FMOLS, DOLS, and CCR

Good Luck with your research

Partial F-test will be useful hear. After the 1st variable is in, you add other variables ONE at a time. after 2nd bariable is added you have your y-variable as function of 2 variables giving model with 2 d.f. & certain Sum of Squares (SS). from 2-variable SS subtract 1-variable SS. that change in SS will have 1d.f. cost. So extra variable SS divided by '1' is the "Change in regression mean squares (regMS). Further, divide 2-variable residual SS (RSS) by 2-variable residual d.f to get Residual mean Squares (resMS). Now divide Change in regMS by resMS to get partial F-value & look up Tables for probability of partial F-value. If significant keep the 2nd variable in & do the same for any further independent variable you may want to add to your model. Adjusted Rsq is = 100*[1 - {(regSS/regDF)/(totalSS/totalDF)}]

To assume that other variable do not change in order to allow for an evaluation of partial variation in a dependent variable due to variation in the only independent while other variables do not change

Stata, Eviews and R can do time series measurement well. You need to know how to implement event study using these software from the literature review of other similar studies.

Dear Prof. Raymond,

My aim is to see what happens to returns of stocks when they join a certain stock exchange index, do they generate abnormal returns?

I’m trying to study that for the last 3 years.

So the event is “joining the index” which happens with 2 dates (1) announcement date (AD), on which stock exchange announces the news of those stocks will join the index, and (2) change date (CD), which is the date for really including those stocks in the index, this CD is is decided and announced by the stock exchange during the AD.

I have attached a similar work for your kind reference.

Thanks for your reply.

You can consider using the country's stock market index as a proxy for market portfolio.

Thanks to all of you for providing clear concept about SUR model.

Am not sure Santiago I follow what you said. Elasticity can be used and Beta weights can be used. If I understand you? I will interpret elasticity as I % increase in the RHS variable changes the regressand by the estimated sign and coefficient of the RHS eg LnY= 2 -0.5Ln(X) -- Here a percent increase in X decreases y by .5 on the avg

"I don't have the theory to include more control variables that may me important for this model." -- so this is a statement. You know the field and the arguments why or why not a variable might have to be considered. You state that, at the best of your knowledge. So you can defend it and clearly point the advantages and limitations of your model. If reviewers (and, later, readers) have different ideas, they are invited to discuss it.

Now I understand. Please look at the definition of dummy variable. What you mean seems to me to be a categorical variable. BTW Actually I am not. I just answer these questions because I enjoy the enlightened repartee. If you want to know my background you are welcome to click on my name where a number of my papers, affiliations, my degrees, etc are included. May the force be with you. D. B.

Thank you Paul!

And yes, David. What can you say about the question if you re-read it changing the word variable with "coefficient of the variable"?

Hello Santiago and Calleagues,

A t -test for one variable is identical to an F-test, in a simple regression model (with one explanatory variable); as a matter of fact in this case the square of the t-statistic value is exactly equal to the F statistic value (t^2 =F).

Once you include additional independent variables the F-test is the one that you rely to report the results. If you have significant F- test then you report the regression results and you look which explanatory variables are significant using the t-test. However if the F-test is insignificant you stop there and you do not report the regression.You need to find another model that at the minimum passes the F-test.This is a specification issue.

Kind regards,

George K Zestos

Yes. Your model can be overfitted. You can think of overfitting in several ways, but let us take two different avenues. First, number of relevant variables. Imagine that the truly correct model has only 30 of the total of 50 variables that you happen to have. Whatever method you use to identify the correct variables in your model can lead you to "false discoveries". This is closely related to the type I error in statistical inference. You can be very strict with the type I error, but this will never be zero. So, you are admitting the possibility of false discoveries. These false discoveries have more chances to occur, the more variables and transformations of variables you try over the same sample. You mention that you have 50 variables...but what about using the squares of these variables, or logs of them or product of pairwise combinations of them. The more combinations you try over the same sample, the more likely is that you end up with false disvoveries: variables that are not in the model...but your statistical method is unable to detect that they are not....

Second, imagine that the true share of variance that can be explained in your model is 50%. So, this is the best R2 you can get if you could identify the correct model. Now, because you are trying to find the correct variables using the same sample over and over again, you end up with a sample R2 of 75%. You again have an overfitting issue induced by the data mining process.

Large N helps but a lot of the overfitting problem relies on the repeated use of the same sample to find a correct model.

This is a key topic....hope it helps!

Mr. Valdivieso. I think the Multicollinearity is almost definitely the problem. Try the simple VIF test. Then try to change the way you measure the variables Area & Access. Good luck.

Hi Santiago,

I believe that what you write is correct, there might be a problem of endogeneity. As you seem to be dealing with subjective indicators, there might be self-reporting biases involved. For instance, respondents who tend to be more optimistic would report a higher score with overall life satisfaction but also with the different dimensions that you look at. Further, those scores might beaffected by the current mood of the respondent etc.

I think this problem becomes worst if you include these self reported variables as predictors and outcomes in your model. Maybe addressing these two elements in separate models might be a solution (one model with overall life satisfaction and your 40 dependent variables and one model looking at the different dimensions of life satisfaction and their impact on overall satisfaction).

I had a quick glance at the literature. Pachecho & Lange adress this question of endogeneity: https://www.emerald.com/insight/content/doi/10.1108/03068291011062489/full/html

You have many independent variables: To check the multicollinearity among the variables use the Variance Inflation factors.

STATA 14 is very good to estimate the panel threshold model.

Hi, I have a related question to this topic. Currently I'm working in a time series anylsis, the first ADF test with raw data I didn't consider any lag and all the results where nonstationarity. After this I runt eADF test for the first difference and the are stationarity, but I also run the test with lags according to the varsoc test and the first difference and they also non stationarity. Wich should be the right process. Thanks

Mohamed R. Abonazel

We compute Fama-MacBeth betas in this paper which is available on line.

Yes you can compare it t-crtical values by Pss (2001) or kremers, Ericssan and Dolado (1992)

My apologies for not noticing sooner that this thread continued with a further question. Consider running a random effects panel regression, with each person who is tracked over time as a panel, person-level demographic and other explanators, and dummy variables denoting the group/village each person was in (with no dummy for the comparison group). Run a Hausmann test to assure random effects made sense. To look at the effects of the intervention, initially do not code demographic/geographic differences between the villages as explanators. But in a subsequent run, code those to probe whether differences observed (or lack thereof) resulted from differences between the villages rather than the intervention. Often, the significance of intervention only becomes clear when those village-level controls are added. I'm unsure if ANCOVA also allows a panel formulation.

Dear all, kindly click on the link below to watch video on how to perform the Gregory-Hansen test

Dear SC Thushara,

I'm not sure about your question, but I think I've read about it in:

https://pdfs.semanticscholar.org/b1cd/c8da3b994606ba4f96b8e0577e26f8dccd29.pdf?_ga=2.30146879.1241071524.1551216901-578234132.1551216901

Hi there. Normality is desirable but it is not a requirement for many aspects of time series analysis.

For instance, if your objective is to obtain the best linear forecast for a given variable, simple OLS estimation in a regression model, or an ARDL model, will give you a consistent estimator of the BLP (Best Linear Predictor) irrespective of any assumption about normality.

Basic asymptotic theory for stationary time series does not require normality to hold true. Most of Wald tests, t-tests in traditional time-series regressions will have the "correct" asymptotic distribution even if errors are not normal.

So, my general answer is that normality in error terms is not necessarily a requirement, especially when you have a decent number of observations.

In most financial applications normality is rejected. It is not the end of the world and I would not be extremely concerned about it. I am mostly interested in forecasting, so what is the cost of non normality for your forecast?, confidence intervals will be tipically different than in the Gaussian case, but the forecast will be just fine.

Hope it helps!

It is possible to such a result depends on what you were working on.

Hi. The answer is in the Stata documentation : "When Qt is stationary, the R matrix in (1) is a weighted average of the unconditional covariance matrix of the standardized residuals et, denoted by R, and the unconditional mean of Qt, denoted by Q. Because R is not eaqual to Q, as shown by Aielli (2009), R is neither the unconditional correlation matrix nor the unconditional mean of Qt. For this reason, the parameters in R are known as quasicorrelations; see Aielli (2009) and Engle (2009) for discussions". Type in your favorite search engine "DCC-GARCH STATA quasi correlation matrix" and you will find it on page 5. I used Google.

When asked questions such as this by colleagues my initial reaction would be to ask for more details of the series. Did the user look at the background of the series to see if there was any reasons why there might be discontinuities in the series (changes in method of calculation of data, changes in government policy or other interventions). Was there a deterministic element in the series that should have been removed before ARIMA estimation? Perhaps some transformation of the data might help, Perhaps the heavy tails were caused by an ARCH/GARCH effect.

Note that estimates of an AR(p) process are robust with respect to non-normality.

There also appears to be some confusion in earlier answers to this question. To me white noise is a process that is identically distributed with zero mean, constant variance and is uncorrelated. Independent white noise is a process that is independent identically distributed with zero mean and constant variance. Normal white noise is a white noise that follows a normal distribution.

Some of the proposals in the first paragraph should cure your problem. If they do not I would fear that the heavy tails would make you confidence intervals large and you might have to search for an alternative forecasting methodology.

The exponential smoothing method gives greater weight to the more new observations, while moving average give equal weight to all observations

put the iv list of variables, which are strictly exogenous variables. that is iv (list the exogenous variable names here), and add to what you have already had

I am sorry to have missed the not-gender post.

I suspect that 2SLS with a dummy endogenous explanatory variable is a applied while there is no way to tell the software that X2 is a dummy variable (like with logit or probit). In a way the software assumes that X2 coincidentally has only two values. Then the estimate is computed as if X2 can assume all values. (Admittedly this is not an answer to the original question.)

Hello Heba,

The quick answer is yes, you can use linear regression for such a dependent variable. But, there are things to consider.

Think of a linear probability model with two outcomes (0 or 1). Although a major drawback of such a model is its predicted probabilities (i.e., greater than 1 or less than 0), it is much easier to deal with endogeneity issues when using a linear model. As such, if you are looking to make causal inferences (i.e., zero mean assumption), but have endogeneity issues, a linear problem is a bit easier to tackle. If you take a look at marginal effects of logit or probit and compare to the beta estimates of the linear model, they should be similar. This is telling you that the effect of the variable is approximately the same with either modeling framework.

Ultimately, it comes down to what you trying to do: predict or make causal inference by dealing with endogeneity.

Best,

Jason

An explanation without any theory will likely lead to misspecified equations. A god estimate for such an equation is not a data problem ("weakness of data"). Even if you had a mass of data and, by accident, got good statistical results, these resuts are not acceptable.

Thank you Feroze Sheikh,

I decided to add dummy variable instead.

Best wishes..