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Hot answers tagged econometrics

7

I might be wrong but from what you write, it seems you've been given a "classical" introduction to econometrics: You've covered IVs and Diff-in-diff but apparently only in passing, and causal inference does not look like it was the core of the classes you've taken. If that's correct, then I would recommend reading: Mastering 'Metrics (https://www.amazon....

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Sure you can, just that your interpretation of your variables in your analysis changes however. In this case you are analyzing how investment in differing factors of production affect output. I'd recommend that you may want to estimate a more flexible functional form like the Translog Production Function to check if your function is CES instead of just a ...

5

I will attempt to explain the distinction using the simplest example: the sample mean. Suppose we have an iid sample of random variables $\{X_i\}_{i=1}^n$. Then define the sample mean as $\bar{X}_n$. As the sample size grows, our value of the sample mean changes, hence the subscript $n$ to emphasize that our sample mean depends on the sample size. Noting ...

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Wooldrige - Econometric Analysis of Cross Section and Panel Data Greene - Econometric Analysis, 8th Edition. This is probably the 'bible', i.e. it covers everything, but I find it hard to digest.

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If prices are constant then quantities are proportional to expenditures. Consider : $$Y=AK^{\alpha}L^{\beta} = A(\frac{E_{K}}{r})^{\alpha}(\frac{E_{L}}{w})^{\beta}$$ $$= (\frac{A}{r^\alpha w^\alpha})(E_{K})^{\alpha}(E_{L})^{\beta}$$ $$= \tilde{A}(E_{K})^{\alpha}(E_{L})^{\beta}$$ If prices don't vary too much this may be an acceptable approximation. ...

4

Suppose $X$ and $Y$ are iid random variables. The 'identically distributed' part means both random variables have the same distribution function (cdf). Formally this can be stated as $$F_X(z)=F_Y(z),$$ where $F_X(\cdot)$ and $F_Y(\cdot)$ are the marginal cdfs of $X$ and $Y$, respectively. The 'independently distributed' part means the joint cdf of $X$ and $... 4 Disclaimer: this answer comes from a microeconomic research perspective. Time series / macroeconomic specialists will likely have other perspectives. There is no general rule for what's too low across the entire field of economics. Yes, microeconomic models (i.e., individual-level observations) will tend to give low R-squared values (often in single ... 4 Completing the notation with the indices $$\forall j: \sum_{i=1}^{n} X_{i,j}\hat{u}_{i} = 0.$$ As you say, if$X_0$is the constant then $$\forall i: X_{i,0} = 1.$$ Inputing$j = 0into the first equation \begin{align*} \sum_{i=1}^{n} X_{i,0}\hat{u}_{i} & = 0 \\ \\ \sum_{i=1}^{n} 1\hat{u}_{i} & = 0 \\ \\ \sum_{i=1}^{n} \hat{u}_{i} & = 0. \... 4 The simple answer to why the Cobb-Douglas functional form is used is because it is at least a log-linear approximation to some higher-order production function. That is, suppose you take a functional form that looks like this: \log Y_t = f(A, K, L). Then a linear approximation would look like the Cobb-Douglas production function. (For a small 1\% ... 4 Yes it is "allowed". Econometrically it is not a problem. The real question is how useful such a model is for your setting and that will depend on your exact research question, variables and data. 3 I think that the effect of additional bedroom on house price is higher for larger houses. Is this correct? As @emeryville said, if your question is about what the result should look like, different people may have different theories. I think one can make a reasonable argument that going from 1 bedroom (small house) to 2 bedrooms should have a larger impact ... 3 There are cases error serial correlation is a disaster. For example, if your model is y_t = \beta_0 + \beta_1 y_{t-1} + u_t, then serial correlation in u_t means correlation of y_{t-1} and u_t (in general) and your OLS estimator is biased and inconsistent. In other cases, serial correlation does not cause endogeneity and OLS is still consistent. An ... 3 It is a fancy, confusing and indirect way to say that GMM, being a Method-of-Moments estimator, does not require distributional assumptions in order to estimate regression coefficients, just like Ordinary Least Squares, and in contrast to maximum likelihood that needs to make distributional assumptions. The wording is confusing, because "robust to ... 3 When you run a regression you are making the assumptions of the Gauss Markov Theorem, one of which is that the error is uncorrelated with all of the independent variables (exogeneity). If you remove from your regression a variable that is correlated with other explanatory variables then the error term and those explanatory variables will be correlated and ... 3 Thomas Sargent and Lars Peter Hansen have a series of work on "robustness", a theory (and technique) that deals directly with potential model misspecifications in the context of macro. [The term "robustness" derives from robust control theory]. Sargent's website has a page dedicated to this topic. The two also published a book, Robustness, that contains ... 3 Instead of looking at bitcoin like a currency, I think you should look at it like a regular stock. The "return" is the return of your fiat money (USD) that's investing in Bitcoin... so the risk free rate should be the risk free rate of your money, i.e. T-bill, etc. 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. 3 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 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 ... 3 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 $$Where Y is dependent variable X endogenous regressor and Z is your instrument. One ... 3 Actually there is no single agreed upon definition of low middle and high class. For example, Pew research center uses the following definitions: “Pew Research defines middle-income Americans as those whose annual household income is two-thirds to double the national median. For a family of three, that ranges from \42,000 to \126,000 in 2014 dollars. ... 3 The difference is that the first regression is unbiased only if you can assume that high school GPA and ACT score are orthogonal on each other cov(x,z)=0 where x is shortcut for high school GPA and z for ACT score. Or if you can assume the second variable ATC score does not affect the dependent variable at all \beta_2=0. This is because in simple ... 2 Ok, I am far from an econometrician, but my train of thought would be as follows: By using random assignment we have two groups that are on average equal to one another on all aspects. As you rightly point out due to sampling variation there will be differences. My worry would be that if I start "correcting" those after randomization (as per your example ... 2 I hope this meets your idea for intuition, but equation 1 comes from using the Law of Total Expectation with the independence condition (Condition 1). There are four possible values of D_i(z)-D_i(w).$$D_i(z)=D_i(w)=1D_i(z)=D_i(w)=0D_i(z)>D_i(w)D_i(z)<D_i(w)$$. Consider the LHS of (1).$$E[(D_i(z)-D_i(w))*(Y_i(1)-Y_i(0))]$From the ... 2 I know this is a old post, but since I found it and I know the answer I might as well share it. I would go further than the first component, but it also depends on how much of the variance is actually explained within the component. There is two approaches that I use when determining which components I am using. The rule of thumb is to use and component ... 2 First of all, you mentioned that the disasters you are dealing with are "randomly" occurring. So I want to provide the following as food for thought: There is an important question here about what your "disaster" variable actually measures and at what level it was "randomized" (if at all). If it is measured in spatial terms (was an individual at this ... 2 Causality between time-series variables does not require the two to be cointegrated. First, cointegration requires that each series be$I(1)$. It is certainly possible for two$I(0)$series to follow a causal relationship (or two$I(d)$variables for that matter). Second, cointegration implies a long-run equilibrium among the series, which is not ... 2 The coefficient of the interaction effect$\beta_3\$ could be either positive or negative depending on your theory. A positive value for the effect of the interaction term would indeed imply that the larger the house, the greater (more positive) the effect of bedrooms on prices is. Here is a nice reference on Interaction effects between continuous ...

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That is illegal because an I(1) series wanders ( doesn't have a constant mean ) and an I(0) series doesn't so they can't be set equal. In order to obtain a valid time series regression, the order on the LHS has to be the same as the order on the RHS. Note that if both sides are I(1), then a time series regression is okay but only if what is on the RHS is ...

2

Those are some good starting points but I would refrain from using them as the end result. There are some fatal logical jumps in your example. Moving house: A good one to use. If I were to guess, I think the ratio should have decreased due to tech. For example, we don't have those huge t.v. nowadays. No desktops for the most part. However, be careful about ...

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