Instrument variable estimation in gravity model of trade.

[Ridwan Sheikh]

Dear Joao Santos Silva , Tom Zylkin and Jeff Wooldridge
I am estimating the panel gravity model of trade with endogeneous regressor. The dependent variable (y) is nominal trade values in levels, expressed in exponential model as:

y_ij,t = exp(Xa)epsilon_ij,t (1)

and partioned X = [x^'_1, x^'₂], where x^'₁ is vector of ENDEGENEOUS regressors (in my case, this include just a single ENDEGENEOUS regressor)and x^'₂ is vector of EXOGENEOUS variables and epsilon_ij,t is multiplicative error term. To further elaborate it, let x^'₁ is importer-specific time-variant ENDEGENEOUS regressor (say, index of labor laws). Supose we instrument x₁ with indicator for countrys' colonial status (i.e., dummies for British and French colony). Further x^'₂ = [distance_ij^BB, contiguity_ij^BB, common language_ij^BB, human capital_jt, trade openness_jt, population_jt] is a vector of time-constant GRAVITY specific (distance, contiguity etc.) and time-variant country-specific [human capital_jt, trade openness_jt, population_jt] EXOGENEOUS variables. I am using Baier and Bergstrand (2009) transformation on bilateral variables (denoted by superscript BB) that uses first-order Taylor series expansion to approximate the multilateral resistance. As I mentioned above, I assume the variables in x^'₂ are exogeneous.
Since my model using BB transformation to approximte MRTs and does not not require to include effects, therefore ivpoisson which otherwise is not immune to incidental parameter problem should be fine in my case, since no fixed effects are specified. therefore i tried running

ivpoisson gmm Trade_Value distanceijBB contiguityijBB commonlanguageijBB humancapitaljt tradeopennessjt populationjt  (x1= British French)

Question 1: I specify British and French as an instrument for x₁ . This code worked fine but at the end of output table, it say apart from British and French, it uses all the exogeneous variables as instruments for x₁. The magnitude of coefficient for x₁ is (positive) but above the theoretically acceptable range (it is 5.43). I want to know, what is the problem here, to which I am clueless about. Why the effect of x₁ is large enough to justify ?

Instead of using gmm estimator, I also tried one step control function estimator

ivpoisson cfunction Trade_Value distanceijBB contiguityijBB commonlanguageijBB humancapitaljt tradeopennessjt populationjt (x1= British French)

Question 2: Here I get totally different results compare to gmm estimator as in previous case. The parameter of interest changes sign and is negative with magnitude of coefficient (<1). I am not sure what might be happening here- whether or not ivpoisson work well in case of gravity with panel data or it is using too many instruments for endogenous regressor or is senstive to specifying gmm vs cfunction ?

Apart from that, I also run ivppml (from the log of gravity website), the results throw an error message
Trade_Value has very large values, consider rescaling
model is not identified; there are more parameters, 11, than instruments, 4

ivppml Trade_Value distanceijBB contiguityijBB commonlanguageijBB humancapitaljt tradeopennessjt populationjt, inst(British French)

As suggested by Tom Zylkin , I also tried running ivgravity . The STATA (.ado) file, that compliments this estimation can be found here . My codes are:

ivgravity  Trade_Value distanceijBB contiguityijBB commonlanguageijBB humancapitaljt tradeopennessjt populationjt (x1= British French), indn(iso_j) indm(iso_i)

This throws an error message - moremata- is required; type -ssc install moremata- to obtain it. When I tried

ssc install moremata

It throws an error message:

file http://fmwww.bc.edu/repec/bocode/m/stata.toc not found
server says file temporarily redirected to https://wifilogin.du.ac.in/onboardpo...85&origurl=htt
> p://fmwww.bc.edu/repec/bocode/m/stata.toc
http://fmwww.bc.edu/repec/bocode/m/ either
1) is not a valid URL, or
2) could not be contacted, or
3) is not a Stata download site (has no stata.toc file)

Question 3: I am not sure why ivgravity is not working/or is it specific to cross-section data, while I have panel gravity model. ?

I am sorry for the long query.

PLEASE GET BACK TO ME, I SHALL BE VERY THANKFUL

[Joao Santos Silva]

Dear Ridwan Sheikh,

On Question 2, the syntax of ivppml requires you to list in the option inst all instruments, including the exogenous regressors that instrument themselves.

Best wishes,

Joao

[Ridwan Sheikh]

Than you Joao Santos Silva for your reply.
Sorry for making a coding error in ivppml syntax. I have corrected the code by running

ivppml Trade_Value x1 distanceijBB contiguityijBB commonlanguageijBB humancapitaljt tradeopennessjt populationjt, inst(British French x'2)

where x^'₂ is the vector of exogeneous regressors.

Now the command worked fine and produces the results. But with a minor warning at the end of results table: equation 1 not found.

Question 1: should we be worried about the warning ?

Moreover, ivppml gives almost identical results to that in ivpoisson with gmm estimator. Therefore i want to ask:

Question 2: Is gmm the default estimator in ivppml? that is, is it correct to say the two commands are same in the present context (the way I am using them) ?

However, I am not sure to what extent the instrument exogenity and relevance is satisfied.

Question 3: Would it be right to run a simple OLS estimator of endogeneous variable (x₁ ) on instruments (British, French) and the vector of all exogeneous regressors (x^'₂) to chech whether instrumets used are predictors of endogeneous variable, this may be crude way of testing instrument relevance. That is:

xtreg x1 British French x'2, vce(robust)

Question 4: I also tried testing the overidentifying restiction (Hansen J-statistics) using postestimation estat overid command after ivpoisson. However, the test rejects the null (p-values of 0.002) that instruments and residuals are uncorrelated. This means instrument exogenity might be violated in this case. Does this totally invalidate the instrument variable estimation?

Sorry for posting a long query. Please reply if possible...

Thanks and regards,
(Ridwan)