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3

It is not a critical result at all. First, the difference is very small. Both round to 0.61 and we don't usually look at further digits. Most importantly though, the R-squared is largely irrelevant to difference-in-difference analysis. You should be most worried about whether your identifying assumptions (e.g. parallel trends) hold. Secondly, you can ...


1

In simplified and intuitive way: Consistency is ability of the estimator to on average uncover true value of the coefficient. For example, if the true value of some coefficient $\beta=2$ then estimator $\hat{\beta}= E[\beta]=\beta=2$ as well. An estimator that in expectations would not give you the true beta coefficient would not be consistent. Efficiency is ...


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I would argue that utility theory is unfortunately meaningless in this context. As you point out, interpersonal utility comparisons don't work, I can always multiply a utility function by 10 and it will represent the same preferences. In some studies they assume quasilinear utilites and say that money has the same value to everyone, but this assumption would ...


1

No, here the correct interpretation would be that on the average the treatment led to 0.5 decrease in number of rich people per million, conditional on all other covariates. Here (I am adding t subscript because I think you must have omitted it): $$-0.5=\beta = E[Y_{it1} -Y_{it0}]$$ There is no per year there, this is one off effect that reduces the amount ...


1

I think the essence of this question is actually asking the difference between statistics and econometrics. You can find some good answers here. Here is my try on a simple - and maybe abstract, but I think useful way of - classification of these things. ML are statistics models. Econometrics are often the combinations of economics models and statistics ...


3

First of all, let me tell you that it is bad statistics to compare $p$-values across different specification. What you certainly should not do is to pick the specification based on the $p$-values that you obtain. Having said this. Assume that the right specification is given by: $$ y_i = \alpha + \beta D_i + \gamma X_{i} + \varepsilon_i $$ Assume you ...


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When you add covariates, $\beta$ is interpreted as "the effect of $D$ on $y$ holding fixed $X$. Adding variables to $X$ can either increase or decrease the p-value depending on the relationship of $X, D,$ and $y$.


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Consider a regression with a dummy variable: $$ y_i = \alpha + \beta D_i + \varepsilon_i. $$ Then $\beta$ will be identified by: $$ \mathbb{E}(y_i|D_i = 1) - \mathbb{E}(y_i| D_i = 0) = \beta $$ Whether I should use log for this outcome variable because I am not sure it is a ratio or actual value (ratio to me normally percent, not per million like that)? It ...


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If I understood correctly the gap is in the middle of the data. In such cases you should not use forecasts that extrapolate the data, but some interpolation method. If there is relatively large amount of variation in the data you would have best results using something like Catmull–Rom spline. Catmull–Rom spline has some nice properties (see here). The main ...


2

As I understand it, the issue is the following: Under the assumption of homogeneous treatment effects, you can estimate long run treatment effects. On the other hand, if treatment effects are heterogeneous, these long run treatment effects are not identified (as eventually everyone gets treated, there are no control group anymore). This means that ...


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As mentioned in tdm’s +1 answer in real life all samples are finite. However, when you theoretically derive some econometric model you can analytically always examine what would happen if the sample you have grows to infinity $(n \rightarrow \infty)$. This allows you to examine asymptotic properties of your estimator, and in real life these asymptotic ...


3

The phrase "finite sample" is somewhat of a pleonams as every sample is (by definition) finite. What they probably refer to with the phrase "finite sample" is a sample that is small or moderate in size. A large part of statistical inference is based on large sample approximations. For example, if the sample size grows very big then the ...


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"From my understanding," treatment is simultaneous" is that all countries passed a law at the same time, is this correct?" Yes. And what is multiple treatment events can happen in the same unit ? The same individual can be treated several times. i.e. suppose treatment is a binary variable for "the minimum wage increased". A ...


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A two-way FE model is: $y_{it} = \beta_0 +\beta_1 x_{it} +\gamma_i + \delta_t +u_{it}$ The $\delta_t$ absorb average time effects, but there may still be unit-specific trends, which could be modelled with: $y_{it} = \beta_0 +\beta_1 x_{it} +\alpha_i t +\gamma_i + \delta_t +u_{it}$ There is not a violation of multicollinearity and it is more general than ...


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"unrestricted treatment effect heterogeneity" means the effect of treatment can differ for each individual, and there are no assumptions or limitations on how the effect differs. Diff-in-diff models using twoway fixed effects with heterogeneous treatment effects and heterogeneous treatment times are known to be biased. Sun and Abraham 2020 is a ...


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A parameter is "identified" if it can be known from an infinite amount of data. "Underidentified" thus means, "even if we had infinite data, we could never learn the true parameter". "Point identified" contrasts with "set identified" with "point" meaning, "we know the exact value" and &...


1

There's no widely accepted benchmark. The idea is to present as much evidence as you can to convince your audience that the parallel trend is satisfied. The least you can do (and most of the time is done in economics papers) is to plot the trend and see if there's any discernible divergent trend before the intervention. It also depends on your unit of ...


1

There is no universal rule, in principle you could get away even with the joint test showing significant differences at 10% but not at 5%. It all depends on specifics of your research. For example, if you have large sample, coefficients will be estimated with much higher precision so using 10% level would not be reasonable (although when it comes to testing ...


2

0.05 is the standard for significance in economics. In that sense, the difference in pre-trends is insignificant. Nevertheless, you are justified in being concerned. You may consider adding in individual-specific pre-trends to account for this. A concern is that your treatment response may be dynamic, in which case the individual-specific trends will absorb ...


2

Comparing simple or multiple regressions estimates is in itself interesting. There are only two special cases where simple regression of $y$ on $x_1$ will produce the same OLS estimate on $x_1$ as regressing $y$ on $x_1$ and $x_2$. Let's see why. $\tilde{y}=\tilde{\beta_o}+\tilde{\beta_1}x_1$ and the multiple regression analog $\hat{y}=\hat{\beta_o}+\hat{\...


2

There can be several reasons. In case the subsamples are not random, the variable may be significant on a subsample and not on another. This would be a case of omitted variables. The larger a sample, the stronger the statistical strength of the estimate, because the standard error of the estimator goes down with sample size. So it is quite possible that a ...


2

This is because the first coefficient estimate was estimated in the presence of omitted variable bias (OVB), and the effect of omitted variable just previously loaded onto the the $\gamma$ coefficient. OVB can drastically change the value of coefficients, if the true model is given by $$Y_{it}=\alpha_i+β_t+\gamma D_{it} + \theta X_{it} + e_{it}$$ but you ...


1

I have to highlight a flaw in the premise of your question. For the quarterly NIPA statistics published and reported by the Bureau of Economic Statistics (bea.gov) under the U.S. Dept. of Commerce, the real growth rate shown in Table 1.1.1 in an annualized statistic based on the estimate of the QoQ level change in the real/constant-dollar value of the ...


1

You typically use the Kronecker product in multivariate models to write the system of equations in a more compact form and exploit the symmetry (if any) across equations to simplify the derivation of estimators of the parameters of interest. For example in the VAR model you have: $ y_t = \Pi_0 + \Pi_1y_{t-1} + \ldots + \Pi_py_{t-p} + u_t $ where $y_t$ and $\...


1

The use of the Kronecker product is meaningful whenever its application simplifies notation and makes clearer what's going on. (Sorry for that tautology, but your question implied it, too.) It's especially useful whenever there is a need to replicate a matrix structure as substructure of a bigger matrix, such as in partitions (as mentioned in the comment by ...


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From a quick scan, I think what the authors really want to do is see if data they've collected on school quality by state and cohort (table 1) explains returns to education. The point of the interacted cohort/state dummies in equation (1) above is to generate average differences in returns to education by state/cohort (table 2), which they can then use as ...


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See this Github page from David Novgorodsky and Bradley Setzler (University of Chicago) and the companion.


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Kernels can be normalized based on $\int K(u)^2 du$. i.e. one could normalize such that $\int K(u)^2 du =1$, and the only term that affects efficiency is the so-called "roughness" of the kernel, $\int u^2 K(u)^2 du $. Thus, mulitplying by $\int K(u)^2 du$ is just scaling based on the variance of the kernel (which could be normalized).


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