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2

The $NR^2$ test is a particular case of an LM test. You can refer to Davidson, R., & MacKinnon, J. G. (1993). Estimation and inference in econometrics, p. 90 for the exact derivation.


0

This can be seen as a time series problem or a general regression problem. If former, you can go for a SARIMAX model for each chain. The seasonal/cyclical/persistence variation across time can be exploited for better predictability. Alternatively, you can convert use past brand1 weekly sale as regressors: y(t), other regressors, chain dummy, y(t-1), y(t-2)......


-1

according to me that would be the Spatial econometrics model Why? The spatial model uses information gathered from different data sets to create models for use in business. The data either results in dependent data pieces or correlated data taken from a larger population of information. Therefore other models are under this one


2

I use Stata and Python heavily. I have dabbled in R, but won't pretend I know it well enough to comment on it. Stata and Python complement each other nicely and I am a big fan of both. You can run Python code in Stata and Stata from Python. The key distinction is the Stata is purpose-built for data management and regressions, it focuses on causal inference, ...


1

Careful, you are not calculating the matrix inverse. The correct inverse is solve((t(W)%*%W)), not (t(W)%*%W)^(-1).


4

Regression discontinuity, IV, diff-in-diff, fixed effects, synthetic control, and MLE, and GMM are the major methods. Fixed Effects example - Zou (2021) Fixed Effects and IV example - Benzell and Cooke (2021) Diff-in-diff example - Gu, Jiang, Zhang, and Zou (2021) Regression discontinuity (fuzzy also) - Ost, Pan and Webber (2018) Regression Kink ...


1

It should be (Nominal Price for Selected Year)*((Index of base year)/(Index of selected))


3

The answer appears to be in your quotes: "The intuition here is that only units that are alike on unobservables and observables would follow a similar trajectory pre-treatment." That intuition isn't necessarily true. There could always be unobserved confounders which hamper the analysis. Nothing renders you immune from that. However, once you are ...


5

My understanding is that the classical test for serial correlation is actually conditional to the validity of the strict exogeneity assumption: $E[u_t|X]=0,$ or, as the requirement applies to any $t$, $E[u_{t-1}|X]=0$. This is a shortcoming, because violations of the strict exogeneity assumption usually generates autocorrelation (we may find evidence for ...


1

My suggestion would be to review the entry on Inflation by Lawrence H. White in the Concise Encyclopedia of Economics, particularly the part where he gets into the dynamic form of the equation and its uses.


4

Surely there is an element of tautology here? It is tautology only in a way that within its logical system it is always true (i.e. following the definition of tautology from pure math). However, it is not a tautology following rhetorical definition of tautology (used in propositional logic) as a statement that refers to itself repetitively (e.g. MV=PY is ...


0

There's an easier way to do this than what's shown above. You can include indicator variables for both male and female. Be warned, however, that since the indicator variables for both of them are in linear combination a unit vector (that is, a vector of all ones), you have to force the constant vector (i.e., $\beta_0$ in your first equation: $income = \...


7

Let us rewrite the two equations in your question like this to avoid using the same symbols for different parameters: $income = \beta_0 + \beta_1 edu + \beta_2 age + \epsilon$, if male = 0 $income = \gamma_0 + \gamma_1 edu + \gamma_2 age + \epsilon$, if male = 1 You can account for the possibility of different coefficients by adding interaction terms for ...


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