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Asymptotically, you should be able to interchange the role of $Y_t$ and $X_t$ and estimate lets say $$X_t =\alpha^* + \beta^* Y+ u^*_t$$ where $\alpha^* = -\alpha/\beta$ and $\beta^*= 1/\beta$ and still get cointegrated relationship. However, crucial caveat here is that this holds only asymptotically and only for $R^2$ close to unity. In finite samples you ...

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I know this is a old post, but since I found it and I know the answer I might as well share it. I would go further than the first component, but it also depends on how much of the variance is actually explained within the component. There is two approaches that I use when determining which components I am using. The rule of thumb is to use and component ...

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The reason for that is that 2SLS does not solve omitted variable bias without its cost. First, for every omitted variable you would have to find suitable instrument. Finding instruments is incredibly hard so why would you purposely create more omitted variable bias? Unless you are trying to challenge yourself for fun or doing it as a practice exercise for ...

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1 - The normal form does not match the word problem. The profit of the DC firm when the other firm plays C is 1, not 2. 2 - Say $p$ is the probability given to C by player 1, then in equilibrium, player 2 is indifferent between his two strategies. Hence, $p - (1-p) = p$ which only has one solution. 3 - You need to specify what you mean by cooperation. ...

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Hint on the non-existence of mixed strategy NE: Suppose the row player uses a mixed strategy that plays C with probability $p$ and DC with probability $1-p$. What's the column player's best response to such a strategy? Does the response depend on the value of $p$? Based on this, what can you say about the optimality of any mixed strategy that assigns ...

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Introductory Econometrics: A modern approach by Wooldridge Econometric Theory and Methods - Davidson and MacKinnon Econometric Analysis of Cross Section and Panel Data. by Jeffrey Wooldridge Mostly Harmless Econometrics Microeconometrics - Trivedi

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This is simply saying that the falling returns are usually correlated with high variance (i.e. sharp movement in prices). This is not very surprising... you can see from the graph of S&P vs VIX below. Whenever the stock market plunges, volatility shoots up. What @heh said was right. You need to compare assets that are more or less substitutable. For ...

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I am tempted to deviate from others' answer and suggest that the best Econometrics textbook for someone with a strong enough mathematical background might not a "mathematically-minded" econometrics textbook, but rather a textbook that focuses on "empirical methods and economics research", the best of which at the moment seems to remain: Mostly Harmless ...

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Depending on the context this is sometimes called Jackknife resampling In statistics, the jackknife is a resampling technique especially useful for variance and bias estimation. The jackknife pre-dates other common resampling methods such as the bootstrap. The jackknife estimator of a parameter is found by systematically leaving out each ...

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\begin{align*} \mathbb{E}\left[ \epsilon_t \vert X \right] &= \mathbb{E}\left[\epsilon_t \vert X_1, \dots, X_t, \dots, X_n \right]\\ &= \mathbb{E} [Y_t - X_t'\beta^0 \, \vert X_1, \dots, X_t, \dots, X_n] \\ &= \mathbb{E} [Y_t - X_t'\beta^0 \, \vert X_t] \quad \text{since $\{Y_t,X_t\}$ is iid.} \\ &=\mathbb{E}\left[ \epsilon_t \vert X_t \right]...

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The ar.ols() function in R defaults to order $10log_{10} (N)$. This implies that, to catch the 30th time lag, you need at least 1000 observations. That seems like a lot, but bear in mind that you are then running OLS on 30 features (lags t-1 to t-30). All else equal, it is not clear why 30 is the magic number for you here, and you can't just drop the more ...

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They will simply be sucked up into one variable. To "fix" this, you could simply drop all of Brazil's characteristics and leave a constant in: $\ln(EXP_D) = c + \beta_1 \ln(GDP_D) + \beta_2 \ln(POP_D) + \ldots$ Edit Just understood the question from the comments below. If you have only a cross-sectional data, you cannot distinguish the effects of GDP, ...

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