7

You can do anything you want, especially if it's a term paper or something of that nature. To obtain useful results you can't use nonstationary data with OLS and time series. There are other more advanced methods where nonstationarity is a non issue. With OLS you have to difference real GDP and indices, and also apply log transform in many cases. UPDATE: ...


5

You are interested in why countries are "stagnating"; stagnation is about a lack of growth, so, GDP growth seems logical. A couple notes: 1. You will need data on countries that are growing at different rates. 2. If you are using data from different years for the same countries (e.g Ghana in 2011, Ghana in 2012, Ghana in 2013...) then a regular regression ...


5

Going from real to nominal will cause you to lose out on a lot of the legitimacy of your (probably intended) theory, because many of the changes in nominal gdp are not production-related, they are inflation-related. Note that GDP and other macro variables are likely cointegrated. This is going to represent a problem if you are trying to publish or draw ...


5

I have a graduate degree in econometrics specializing in times eries and survival analyis. I'll try to give you short undergrad advice instad of a proof. You should never use OLS for time-series data (the only exception is SOMETIMES it is appropriate to use this technique for panel data). OLS results will be garbage - it will result in a spurious regression ...


4

Remember that OLS is linear on parameters. This is, regression estimates the parameters of each regressor in the following equation: $$ \Delta ln I = \beta_{1}\Delta lnY + \beta_{2}\Delta lnY(-1) + \beta_{3}\Delta lnR + \beta_{4}\Delta lnR(-1) + \beta_{5}\frac{lnI(-1)}{Y(-1)} + \beta_{6}lnR(-1) + \beta_{7}i(-1) + \epsilon $$ However, the ECM has parameters ...


4

Basically, there's no ambiguity here: you must use the differences in the regression. There could be some discussion whether it's a simple difference or a log difference, but the latter is more common in the literature. If you had a cross-section, then this wouldn't matter. For a short period of time it probably doesn't matter that much either, but you're ...


3

No, you can't. If you have just two variables, and they have different integration orders, they will not be cointegrated, and thus your regression is spurious. For example, say your population model (or data generating process, DGP) is: $$ GDP_{i} = \beta FDI_{i} + e_{i} $$ Given your setting, $GDP_{i} \sim I(2)$ and $FDI_{i} \sim I(1)$, where $I(n)$ is ...


3

Some general comments. You may think about omitted variable bias. If there are other variables influencing/determining the GDP growth, and those variables are correlated with the change in the working-age population, you will have a biased and inconsistent estimate of $\beta_1$, and hence poor forecasts. If you are using quarterly (rather than yearly) data,...


3

Endogeneity The macroeconomic variables you are studying are likely to affect each other. In particular, the variables on the right hand side of your model might be affected by the variable on the left hand side. That is known as the problem of endogeneity, which results in inconsistent estimates of model parameters and problems in interpreting the model. A ...


3

The excellent textbook by Barro and Sala-i-Martin (Economic Growth, MIT press, 2004), can help you to choose your model. However, as Peter Flom said, be careful with cross-section regression, it can be misleading; you might need to apply a panel data methodology (see the paper by Islam, 1995, on The Quarterly Journal of Economics 110(4), 1127-1170). Again, ...


3

I would strongly encourage you to read a an introduction in VAR estimation, e.g. Lütkepohl. The visual impulse response analysis is quite simple: The columns always indicate the reaction to one shock. The first column gives the reaction to an one time expansive fiscal policy (GS-Shock). We see that GS increases up to 45 in period 0 and then decreases slowly ...


2

There are a number of papers that provide significant detail on the methodology behind various economic indices. Examples/Case Studies Constructing socio-economic status indices: how to use principal components analysis The Composite Index of Leading Economic Indicators Creating a sustainable national index for social, environmental and economic ...


2

A very important question is availability of data. Example, you can get the data from wto.org. A very realistic answer to your question is that you should build your model in both ways and compare the accuracy prediction parameters e.g. $R^2$ , adjusted $R^2$, and residual graphs. Then start validating your hypotheses for which form of GDP you should take. ...


2

The question is actually more generic than just VAR models and Granger causality. In statistical modelling, you need a minimum sample size to be technically able to estimate model parameters. Once the minimum is passed, you can estimate the model and examine the parameter estimates and their confidence bounds. The larger your sample, the narrower the ...


2

There is at least one reason -- the bias-variance trade-off. You might prefer a wrong model as long as it gives you better forecasts. Suppose VECM is the true model. Then VAR in first differences is wrong because it misses a variable, namely, the error correction term*. Suppose also that the loading (the coefficient) on the error correction term cannot be ...


2

This is very much dependent on your context and the purpose for which you might want to apply the logarithmic transformation. You did not provide enough detail to go really in depth with my answer. There are in general two main reasons to do something like this: (1) In your model you believe that the transformation helps you to achieve better fit. For ...


2

Baltagi, B. H. (2006). Panel Data Econometrics Theoretical Contributions and Empirical Applications. Emerald Group Publishing Limited. See https://scholar.harvard.edu/files/stock/files/aea_2015_lecture4_har_rev.pdf and the other lectures in the same series (which you can watch online at https://www.aeaweb.org/conference/cont-ed/2019-webcasts (2019 version) ...


2

Feature Selection Feature selection aka model selection is difficult. By that I mean it is an unsolved problem and there is evidence that it is an NP-hard problem. The title of Maymin (2011) hints at why: "Markets are efficient if and only if P = NP." However, there are a few heuristic tools often used. First, we rest on theory. If theory suggests ...


2

Let’s say that a very low interest rate is of the order of 0.1% and a high interest rate of the order of 10%, so there is a likely range of say two orders of magnitude. Then logarithmic thinking commits you to regarding the difference between 0.1 and 1% as equivalent to that between 1 and 10%. Is that sensible or accurate economically? I know as an ...


1

A common approach to dimensionality reduction is to perform Principal Components Analysis (PCA). Let's say you have some vector $\mathbf{x}$. Instead of a basis $\mathbf{u}_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \\ \cdots \end{bmatrix}$, $\mathbf{u}_2 = \begin{bmatrix} 0 \\ 1 \\ 0 \\ \cdots \end{bmatrix}$, etc..., the idea is to find a new basis: $\hat{\mathbf{u}}...


1

Primiceri (2005) writes on p. 830 bottom that the first 10 years (40 obs.) are used to calibrate the prior distributions. He estimates a constant parameter VAR model on the first 40 obs. and uses these point estimates to calibrate the prior distributions. Note that he calibrates the variance as four times the estimated variance from the constant parameter ...


1

Frank Harrell does not rule out intelligent use of backward elimination. He includes as a possibility (page 97, RMS, 2nd edition): Do limited backwards step-down variable selection if parsimony is more important than accuracy. This, however, is only to be done in the context of an already well-specified model. It is the last step before the "'final' ...


1

When is a statistical test said to be robust? That depends on who is saying it! There are two main things with hypothesis tests -- how they perform under the null and how they perform under the alternative. Many people only consider performance under the null -- impact on the significance level -- i.e. to see if it remains close to the chosen significance ...


1

Note that MANOVA (together with the whole family of linear regressions) does not assume normality of neither the dependent, nor the indepentend variables. The only normality assumption is that the residuals (i.e. the errors) are normally distributed. And that is a thing that you have to check AFTER you fit your model (or perform MANOVA). In regard to your ...


1

If you have regressions of the form $$ y_t = \beta_0 + \beta_1 x_{1,t} + \dotsc + \beta_K x_{K,t} + \varepsilon_t $$ where the $x$s are exogenous and you are interested in $\beta$s* (which could be thought of as structural parameters), then you may try regression with ARMA errors (see e.g. here). This setup preserves the original model (so you obtain $\...


1

What you are referring to are ARIMA models.They consist of AR, MA and Integrated component(first difference). You can read about them in detail. You're allowed to use anything as long as you don't use future data in you model. P.S. If this doesn't answer your question, please guide me about what your query is about.


1

Reverse your data set i.e. set the first observation equal to the most recent (true observation), the second observation to the penultimate one ( next to last most recent true observation) ,... the last observation to the true first observation. Develop a transfer function and forecast. These forecasts can then be used as the "lost values" or "unavailable ...


1

It may not be advisable to choose the model just by using the information criteria; subject-matter knowledge can be very helpful. Sometimes you can rule out some of the candidate models because their shape clearly clashes with reality (despite good in-sample fit which may be due to chance). In your case, consulting macroeconomic theory could be worthwile. ...


1

Transformations are like drugs, some are good for you and some aren't. You should presume neither transformation but rather detect the appropriate solution based upon the data that you are trying to model. My answer to the log issue When (and why) should you take the log of a distribution (of numbers)? suggests that there is a logical procedure to determine ...


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