48

Structural estimation is a term coined by the Cowles commission which at the time seems to have been dominated by Haavelmo, Koopmans and a few others. The motto of the Cowles commission (after 1965) was: "Theory and Measurement". The phrase represents the underlying rationale of structural modelling, that measurement cannot be done without some kind of ...


15

Natural experiments are usually a setting for causal inference rather than a causal inference tool per se. You often need to employ something like difference-in-difference or instrumental variables anyway even when you have a natural experiment. Here a list of statistical causal inference approaches (Approach: Lay description) Instrumental Variables: ...


12

Some related studies: Al-Marhubi, F. A. (2000). Corruption and inflation. Economics Letters, 66(2), 199-202. The analysis is based on cross-country data consisting of 41 countries from Asia and Latin America for which data is available on four alternative indices of corruption (two from Transparency International, one is the Business International index, ...


12

The answer to the question is yes, it is indeed meaningful (at least mathematically speaking). If you estimate the linear equation $$ W = \beta_0 + \beta_1 PTR, $$ then $\beta_1=\frac{\partial W }{\partial PTR}$, meaning that $\beta_1$ represents the marginal change of $PTR$ over $W$. Now, if you estimate $$ log(W) = \beta_0 + \beta_1 log(PTR), $$ then $\...


12

For a shorter proof, here are a few things we need to know before we start: $X_1, X_2 , ..., X_n$ are independent observations from a population with mean $\mu$ and variance $\sigma^{2}$ $\mathbb E(X_i) = \mu$ , $\mathbb{Var}(X_i)= \sigma^{2}$ $\mathbb E(X^2) = \sigma^{2} + \mu^{2}$ $\mathbb{Var}(X)=\mathbb E(X^2)-\mathbb [E(X)]^2$ $\mathbb E(\bar{X}^2) ...


12

The meaning of the words first Some people use the word "IV estimator" to refer to any estimator that uses instrumental variables. To them, IV estimators contain 2SLS, LIML, k-class estimators, and others, so 2SLS is a special case of IV. For example, the title of Bekker's (1994, Econometrica) paper is "Alternative approximations to the distribution of ...


10

"But if any of these control variables are endogenous to some omitted variable, doesn't this contaminate the unbiasedness of ALL the independent variables?" I don't want to emphasize this too much, but it's worth mentioning that this is not true in general. The following derivation will hopefully provide some understanding of the "contamination" you mention....


10

Personally, for choice analysis, I like Discrete Choice Methods with Simulation by Ken Train (pdf) Applied Choice Analysis: A Primer by Hensher and Greene (2nd edition, book) Modeling Ordered Choices by Hensher and Greene (pdf) Regression Models for Categorical Dependent Variables Using Stata by Long and Freese (3rd edition, book) (1) is a fairly short, ...


9

I know that during my university time I had similar problems to find a complete proof, which shows exactly step by step why the estimator of the sample variance is unbiased. The proof I used can be found under http://economictheoryblog.wordpress.com/2012/06/28/latexlatexs2/ The proof itself is not very complicated but rather long. That also the reason why ...


9

Under the assumption of i.i.d. Normal characteristics, the situation described is taken care by separate Welch's t-tests that account for possibly different sample sizes and different variances. Denote the statistics of these tests $t_j, j=1,...,K$. The p-value associated with each is $$p_j = \Pr\big(|t_j|\geq t(\alpha)\mid H_0\big) $$ where $H_0$ is the ...


9

Welcome to the wonderful world of econometrics! Most introductory econometrics courses will extend Ordinary Least Squares (OLS) by considering binary outcomes models such as the logit and probit. Whilst OLS is typically restricted to modelling continuous outcomes bound between $-\infty$ and $\infty$, in research one will often come across data where this is ...


9

I recommended familiarity with the following topics: partial differentiation and optimization of multivariate functions study fixed point theorems. Kakutani and Brower are good ideas. Set theory is very important analysis (especially sequences, sub-sequences, convergence of sequences, etc.) Topology (basics is good enough. For example, understanding ...


8

Like people have said in the comments, log-log is commonly used. It amounts to estimating a constant elasticity model $Y = \alpha X^\beta$, which is a commonly used functional form within economics. Once you take logs, this becomes $\ln Y = \ln \alpha + \beta \ln X$. You can read more about this here. I guess your question is whether or not using this ...


8

The $\mathbf M = \mathbf I-\mathbf X(\mathbf X'\mathbf X)^{-1}\mathbf X'$ matrix is the "annihilator" or "residual maker" matrix associated with matrix $\mathbf X$. It is called "annihilator" because $\mathbf M\mathbf X =0$ (for its own $X$ matrix of course). Is is called "residual maker" because $\mathbf M \mathbf y =\mathbf {\hat e}$, in the regression $\...


8

Usually, $\hat{\beta_1^{IV}} = \beta_1 + \frac{cov(z,u)}{cov(z,x)}$. The denominator will go to zero. That is true unless there is some correlation between the instrument and the error term, and the nominator is the strength of the relationship between the instrument and the endogenous variable. The smaller the denominator gets, the greater the bias $\...


8

I can recommend this paper as an example: The Colonial Origins of Comparative Development: An Empirical Investigation Daron Acemoglu, Simon Johnson, and James A. Robinson http://economics.mit.edu/faculty/acemoglu/data/ajr2001 (paper and data) This example is famous not only thanks to the creative use of instrumental variables, but also because of the ...


8

An interesting question that leads to a debate among econometricians. Some consider that Econometrics is just statistics applied to economic problems Econometrics is just statistics applied to economic problems—nothing more and nothing less. We should probably call it “statistical economics,” but I guess people feel that the term “econometrics” has ...


7

I repeat part of my answer in the question the OP already mentioned with some additional proposals: Since you have a background in Statistics "Probability Theory and Statistical Inference: Econometric Modeling with Observational Data" 1999, by A. Spanos, provides the statistical foundations of econometrics in a way no other book does. "Econometrics" by ...


7

"Adult" Wooldridge is great intro to various microeconometrics topics. For time series, Hamilton's Time Series and Lutkepohl's Introduction to Multiple Time Series Analysis are both nice, though Hamilton is a bit dated and Lutkepohl is more focused. As far as more foundational, rigorous material, Herman Bierens has a short Introduction to the Mathematical ...


7

The Linear algebra part should not worry you, it is just basic linear algebra plus familiarizing yourself a bit with differentiation of vectors and matrices (and for some chapters, visualizing the Kronecker product). Hayashi goes some length into writing out explicitly large matrices, which is virtually with no-precedent (see eg. pages 267, or 288), ...


7

To (slightly) paraphrase the OP: Economies (Human Bodies) are extremely complex systems with many variables, not to mention the fact that they emerge from the interactions of complex beings (factors). I agree that economies (human bodies) have certain underlying principles, but I remain skeptical of the overall value of econometrics (medicine) as ...


7

Alright, the other respondents have covered the logic behind a log-log regression pretty well, so I'm just going to add some practical tips. If you want to check whether your specification is reasonable, and your problem is the assumption of a constant elasticity, try splitting the sample into groups based on percentiles of $x$ and recalculating $\alpha$ and ...


7

Actual availability of regressors may be an issue here, but if all four mentioned variables are available, the situation is as @Michael mentioned in a comment: Since $X_2$ is correlated with $Y$, it should be included in the regression specification as a "control". $$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + u$$ This is intuitive, but it also takes care ...


7

tl;dr No, it is not possible to have a negative Gini coefficient. The Gini coefficient is the area between the line of equality and the Lorentz curve, and this area cannot be negative. Let the area of equality as in the link be denoted by $A$, and the area under the Lorentz curve be denoted by $B$, then the Gini coefficient is given by $$ G = \frac{A-B}{B}$...


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....


7

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 ...


6

Induced jobs are those created by the spending of those employed directly by the primary source or indirectly by suppliers to the source. For example, you have a project to build a bridge. That project hires a worker. That worker stops at a convenience store every morning and buys a coffee and a bagel. The people responsible for selling the coffee and ...


6

While it´s true that there is no direct relationship between corruption and inflation, there are mechanisms which can lead to corruption acting to influence inflation through the monetary system. Inflation is primarily a direct function of the money supply, and an inverse function of total production. If corruption takes the form of corrupt bank lending, ...


6

To test market efficiency, you always need to specify the market's model of price formation Tests of the efficient markets hypothesis must always include a model of how the market forms prices. One of Fama's big contributions was that you cannot separate these two things in a test. Tests of efficient markets and models of price formations are inherently ...


6

Well, if you believe that treatment is endogenous (which depends on the problem at hand here and is not an inherent feature of the model), then using eligibility as an instrumental variable will help you to get rid of the biases due to the safe selection in treatment. (Incidentally, DID is intended to do the same, but won't do as good a job as a well chosen ...


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