8

If I include $z_1$ in the model, like this: $$ > y = \beta_0 + \beta_1 x + \beta_2 z_1 + e, > $$ Does that mean that $\beta_1$ is predominantly capturing the effect of $z_2$? Yes. This can be seen using the Frish-Waugh-Lovell theorem: If you regress: $$ y = \beta_0 + \beta_1 x + \beta_2 z_1 + e, $$ then $\beta_1$ will be the same as the corresponding ...


8

I'd interact the regressor you are interested in with a dummy for the country being developed and see what happens. Its entirely possible that the mechanisms at play in developed contries are different from those in the rest of the world. Depending on what your goal is you might satisfy yourself with the observation that the effects are different for the two ...


7

Building further on the answer of @1muflon1, the disadvantage of the mean is indeed that it entirely disregards inequality or variation of income. This can be offset (in part) to looking at measures of spread, like the variance or interquartile range. The economic literature on inequality and welfare measurement contains a large number of concepts to ...


7

It can either increase or decrease when clustering, it depends on the covariance structure of the error terms. It is more frequent to observe standard errors increase with clustering.


7

tldr: As the other two answers also indicated, there is not necessarily a problem with your results. It might be the case that the two subgroups have different distributions of the covariates. Alternatively, it might be the case that the within group effects of the law are different from the between group effect. Joint and separate regressions Consider two ...


6

This sounds like a case of Simpson's Paradox. Did you control for fixed effects? You might also have heterogeneity - there may be different results in developing vs developed countries. Generally, it's not wise to ignore something interesting in your data, but I defer to the advisor who's familiar with the area. It may be a known phenomenon that isn't ...


5

Theorem 2.1 in Horowitz (2019) is what you are looking for


5

You are correct. The bootstrap samples with replacement while subsampling samples without replacement. Theoretically, when $m \ll n$, it does not matter if you sample with or without replacement (if you sample with replacement and $m \ll n$ the probability of drawing the same observation twice can be made arbitrarily small as $\frac{m}{n} \to 0$). In ...


4

What does industry * year fixed effect mean? $Industry \cdot year$ fixed effect is just an interaction term between industry and dummy year variables. For example, you can have dummy particular industry, let us say finance where $D=1$ if firm is a finance firm and $0$ otherwise, then you can have a year dummy which will be set to equal $1$ for particular ...


4

Assume that for each observation $i = 1,\ldots, N$, we have $M$ equations: $$ y_{i,j} = x_{i,j}\beta_j + \varepsilon_{i,j} $$ Where $i = 1,\ldots, N$ enumerates individuals and and $j = 1,\ldots, M$ enumerates the equations. here $x$ is of size $1 \times k_j$ and $\beta_j$ is of size $k_j \times 1$ and $k_j$ is the number of covariates for regression $j$. ...


3

What is Error Structure A good explanation on what error structure is, is already provided in this Cross-Validated answer. In short: error structure in this respect is referring to the "element of randomness" in your model. For example, in least squares regression, we often assume that the error term of the model (i.e. residuals) follows a normal ...


3

Based on this definition, why economics relating to social science, and what is other than social science? There is actually no clear cut consensus on where Economics belongs (although it is fair to say most would likely put it into category of social science). Some authors consider it to be science, some social science, some even moral science, and some ...


3

The short answer is yes, you can control for any number of dimensions. However, there are some caveats. In terms of being able to estimate the model, you need at least one observation per cell. In your case, you need to have at least one observation for every firm$\times$year$\times$industry combination. If you have only a single observation per cell, then ...


3

As far as I can see from the discussion there, by unit level they mean the level of the panel variable. What that is depends on your study. It might be firm or individual or country or whatever your panel variable happens to be. The panel variable is the variable that dictates the spatial dimension of your panel data. E.g if your panel consists of ...


3

It depends on a few things. First, if you expect treatment effects change over time, then you want to estimate an event-study style DD specification. If you have a single treatment timing (all treatment starts at the same time), then an event-study will unbiasedly estimate the treatment path. If you have variation in treatment timing, you want to use a ...


3

Averages are always skewed by outliers. There is no good solution to that if you insist on using averages. There is no need for using averages. A common practice when people compare welfare among countries is to use median incomes, wages etc. Median is the value for the person who is literally in the middle so in your example above median in group A would be ...


3

Nerlove and Wallis (1966) result Nerlove and Wallis (1966) have discussed this issue. Their Equation (3) derives the probability limit of the Durbin-Watson statistic as: $$\mathrm{plim}\, d^* = 2 \left[ 1 - \frac{\rho \beta (\beta + \rho)}{1+\beta \rho} \right].$$ (Their notation for $\beta$ is $\alpha$ in the paper.) Nerlove and Wallis's (1966) derivation ...


2

To further elaborate on the answer of @Michael Gmeiner, the difference in the estimate of the variance between the model that takes into account clustering and the model without cluster is usually expressed with what is called, Moulton factor. See also Moulton (1986), Random group effects and the precission of regression estimates. Consider the basic case ...


2

The first model you presented is for a case where the treatment is applied, the effect occurs, and then no further effects from the treatment are observed. The second model imagines that the treatment could be preceded by some sort of anticipation effect (such as investors anticipating that the Fed will change interest rates). The maximum number of periods ...


2

Yes it is important indeed to use precise language to clarify methods and issues, especially in econometrics, a discipline in which fundamental but confusing nuances between different types of variables: some are endogenous, other exogenous, observed, unobserved, random, conditionally random, etc. I did not often encounter such subtleties in mathematics (or ...


2

Suppose we don't have a constant. Including firm and industry fixed effects means including a dummy variable for all firms, and also a dummy variable for all industries. If the set of firms in an industry never changes, there is a multicollinearity violation, as the sum of all dummy variables for firms in an industry is equal to the dummy variable for the ...


2

I'm a little unsure of what "pt" means, but I assume that "pt" is the independent variable of interest. In the regression with the interaction term, the coefficient for "pt" is "the expected value of the dependent variable for undeveloped countries if all other independent variables are 0". The coefficient for the ...


1

And with the result below, how could I conclude? From the output above you can conclude that those laws do not affect the dependent variable in developed countries differently (of course, assuming there are no other issues or methodological problems not mentioned above). Can I compare the law effect between the developed and developing countries or Can I ...


1

We have \begin{align} \frac1n \sum_{i=1}^n Z_i \tilde{e}_i^2 Z_i' &= \frac1n \sum_{i=1}^n Z_i \Big[e_i^2 - 2e_i X_i' (\tilde\beta - \beta) + (\tilde\beta - \beta)' X_i X_i' (\tilde\beta - \beta)\Big] Z_i' \\ &= A_1 - 2A_2 + A_3. \end{align} because $\tilde{e}_i = y_i - X_i'\tilde\beta = (X_i'\beta + e_i) - X_i'\tilde\beta = e_i - X_i' (\tilde\beta - \...


1

$y_t =\alpha+\beta_1s_t+\beta_p p_t +\epsilon_t$ If you don't observe a variable, I don't think you want to "take it to the left-hand side", doing that is just unnecessarily complicated. It would be this: $y_t-s_t =\alpha+(\beta_1-1)s_t+\beta_p p_t +\epsilon_t$ Where $s_t$ is still unobserved on the right-hand side. Rather, if a variable isn't ...


1

"Clustered standard errors/variances with clustering at the unit level are equivalent to robust standard errors/variances." "Unit-level" in this context means "observation-level".


1

Have you ever seen any paper controlling for firm, industry, and year fixed effect at the same time? You literally cite the Dasgupsta et al who does it, so anyone looking at that study seen one, but if you ask other than the Dagsputa study yes for example: Combes, P. P., Duranton, G., & Gobillon, L. (2008). Spatial wage disparities: Sorting matters!. ...


1

Because even if you include in diff-in-diff fixed effects your model can still suffer from omitted variable bias. Fixed individual effects only help to control for time invariant individual effects. For example, IQ or innate ability that is often though to be time invariant can be controlled by fixed effects. However, fixed individual effects do not help to ...


1

First of all, you actually do not need to use clustering specifically in that case. The point of clustering is to correct for heteroskedasticity or/and autocorrelation at some level. You have to correct for heteroskedasticity or/and autocorrelation somehow otherwise your test statistics (base on which you calculate p-values) will be wrong. But you do not ...


1

I'm not trying to be picky, but just in case, there is no such thing as the consistent but inefficient estimator. Perhaps you mean a consistent but inefficient estimator? Your estimator is the OLS estimator. See $X'X$ cancelled. If you only use the moment conditions $E(x_t u_t)=0$, then OLS is the only GMM (or actually MM) estimator that can follow. As the ...


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