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Perfect multicolinearity means that two independent variables are perfectly correlated with their $r^2=1$ multicolinearity technically refers to any non zero correlation between two independent variables but when it is mentioned as a problem it usually implies that the correlation is high. So there is a difference between the two terms perfect ...


3

The $k+1$ parameters are $k+1$ unknowns. In general, you need at least $k+1$ equations (which are observations in the context of OLS estimation) to uniquely pin down those $k+1$ unknowns.


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Reduced form is a regression of dependent variable on instrument directly without using some two stage approach. Consider the following example of endogenous system Second Stage: $$Y = \alpha + \beta X + \epsilon$$ First Stage: $$X = \mu + \gamma Z+ \eta $$ Where $Y$ is dependent variable $X$ endogenous regressor and $Z$ is your instrument. One ...


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FE logit requires the idiosyncratic errors to be IID across $i$ and $t$, quite a strong assumption. Also the regressors should be strictly exogenous, but it's the same for linear FE models. In your application, the fact that FE logit wouldn't converge will make a good argument against FE logit, and will satisfy some referees but not all. An important ...


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Remember that consistency describes how the estimator behaves in the limit as N asymptotically approaches infinity. Assuming no errors in your math up to this point, you need to consider how your error terms $U_i$ behave asymptotically as well.


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I am not an econometrician so this will be a very informal explanation how to get the Instrumental Variable (IV) estimates. Since $S_i$ is endogenous, $$\text{cov}(S_i,\epsilon_i)\neq0$$ We can think of it as having two components: $$S_i = v_i + u_i$$ Suppose, $\text{cov}(u_i,\epsilon_i) =0 $ and $\text{cov}(v_i,\epsilon_i)\neq0$. $v_i$ is the ...


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It’s an indicator but I personally would never decide based on them. $t$- statistics tests the null that individual coefficient $\beta_i$ is 0 against alternative that it is statistically different from 0. $F$-test which is increasing function of $R^2$: $$F=\frac{R^2/k}{(1-R^2)/(n-k-1)}$$ Which tests the hypothesis that all $\beta$ coefficients are 0 ...


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Yes, the data is weighted based on the population size of the area from which it came. The survey designers employ a method called stratified random sampling, which ensures that the prices of goods selected for the sample are distributed across all areas (rather than by chance landing up concentrated in a few areas). Then, the prices in each stratum are ...


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Just to make things simple I'll show how to do it for a simpler case. Let's say you have a regression $Y = \beta_1 X_1 + \beta_2 X_2 + \varepsilon$ and you want to impose $\beta_1 = 2\beta_2$. This is equivalent to saying $Y = 2 \beta_2 X_1 + \beta_2 X_2 + \varepsilon = \beta_2 (2 X_1 + X_2) + \varepsilon$. That is, you can generate a new variable $X_3 = ...


1

As a first pass, I would interpret as with any other dummy variable's coefficient. Assuming a linear model, when two countries share a border, their export similarity index rises, on average, by 0.15 when all other variables are held fixed. If you're writing a report on this model, you'll obviously need to discuss at length what this actually means. The ...


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If GDP is measured (as it usually is) for a period such as a year, then number of hours worked ($h$) should be measured for the same period. Thus $h$ is dimensionless and the dimension of the right hand side is also value / time.


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The "ragged edge" seems to be more centered around the challenge of so-called "now-casting" -- essentially, near-real-time very-short-term fore- and back-casting -- given that information from different sources is released on different schedules. It's not really a new issue. For example, GDP and other macro-level data is routinely lagged for developing ...


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The intuition is that OLS is a linear model and to estimate any linear model you need at least 2 points in 2D space. The reason for that is that with a single point you can’t uniquely identify any line. Adding extra parameter increases the dimensions and in each higher dimension you need one more point to estimate linear model. You can think about it in a ...


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Asymptotically, you should be able to interchange the role of $Y_t$ and $X_t$ and estimate lets say $$X_t =\alpha^* + \beta^* Y_t+u^*_t$$ 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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My problem is: because Brazil is the origin for the exports to all other countries, GDP_O, POP_O and any other variables representing Brazilian data will be equal for all observations and as such there will be perfect multicollinearity. This isn't perfect multicollinearity. It's a lack of time/space variation. Multicollinearity occurs between features, not ...


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In case someone wanted the links for some of the references in the comments. Brookings Institute Peterson Institute for International Economics


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