## About

### Biography

João Santos Silva graduated in Economics from the Technical University of Lisbon in 1985, and he received a masters degree in Applied Mathematics in 1988 from the same institution. In 1992, he completed his PhD in Economics at the University of Bristol. He taught at the Technical University of Lisbon and at the University of Essex, before joining the School of Economics in 2015. João's research focuses on theoretical and applied microeconometrics, and he has published in a variety of academic journals, including the *Review of Economic Studies*, *Journal of the American Statistical Association*, *Review of Economics and Statistics*, *Journal of Econometrics*, and the *Journal of Business and Economics Statistics*.

## Research

### Research interests

#### Areas of research interest include:

- Mode regression
- Quantile regression
- Count Data Models
- Gravity equation for trade

### Indicators of esteem

"Log of Gravity" by Joao Santos Silva and Silvana Tenreyro acknowledged as a Classic paper in Economics.

## Supervision

### Postgraduate research supervision

## Teaching

**Semester 1:**

**Semester 2:**

## Publications

### Highlights

"Log of Gravity" by Joao Santos Silva and Silvana Tenreyro acknowledged as a Classic paper in Economics.

#### Refereed Publications

- Santos Silva, J.M.C. and Winkelmann, Rainer (2026), Misspecified Exponential Regressions: Estimation, Interpretation, and Average Marginal Effects,
*The Review of Economics and Statistics*, forthcoming.

- Breinlich, H., Novy, D., and Santos Silva, J.M.C. (2024), Trade, Gravity and Aggregation,
*The Review of Economics and Statistics*, 106, 1418–1426.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2022), The Log of Gravity at 15,
*Portuguese Economic Journal*, 21, 423–437.

- Kemp, G.C.R., Parente, P.M.D.C., and Santos Silva, J.M.C. (2020), Dynamic Vector Mode Regression,
*Journal of Business & Economic Statistics*, 38(3), pp. 647–661.

- Machado, J.A.F. and Santos Silva, J.M.C. (2019), Quantiles via Moments,
*Journal of Econometrics*, 213(1), pp. 145–173.**The estimator for quantile regression with fixed effects is available in Stata: type "ssc install xtqreg".****An example of how to implement the jackknife correction with clustered standard errors is available****here****.****The estimator of the structural quantile function is available in Stata: type "ssc install ivqreg2".**

- Machado, J.A.F., Santos Silva, J.M.C., and Wei, K. (2016), Quantiles, Corners, and the Extensive Margin of Trade,
*European Economic Review*, 89, pp. 73–84.**The estimator is available in Stata: type "ssc install fqreg"**.

- Parente, P.M.D.C. and Santos Silva, J.M.C. (2016), Quantile Regression with Clustered Data,
*Journal of Econometric Methods*, 5(1), pp. 1-15.**The covariance estimator and test are available in Stata: type "ssc install qreg2"**.

- Dias, D.; Marques, C.R.; Martins, F. and Santos Silva, J.M.C. (2015), Understanding Price Stickiness: Firm-Level Data Evidence on Price Adjustment Lags and their Asymmetries,
*Oxford Bulletin of Economics and Statistics*, 77(5), pp. 701-718.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2015), Trading Partners and Trading Volumes: Implementing the Helpman-Melitz-Rubinstein Model Empirically,
*Oxford Bulletin of Economics and Statistics*, 77(1), pp. 93-105.**The code and data are available****here****.**

- Santos Silva, J.M.C., Tenreyro, S., and Windmeijer, F. (2015), Testing Competing Models for Non-Negative Data with Many Zeros,
*Journal of Econometric Methods*, 4(1), pp. 29-46.**The test is available in Stata: type "ssc install hpc"; the code and data used in the applications are available****here**.

- Santos Silva, J.M.C., Tenreyro, S., and Wei, K. (2014), Estimating the Extensive Margin of Trade,
*Journal of International Economics*, 93(1), pp. 67-75.**The Flex is available in Stata: type "ssc install flex"; an example using it is available****here****.**

- Kemp, G.C.R. and Santos Silva, J.M.C. (2012), Regression Towards the Mode,
*Journal of Econometrics*, 170(1), pp. 92-101.

- Papadopoulos, G. and Santos Silva, J.M.C. (2012), Identification Issues in Some Double-Index Models for Non-Negative Data,
*Economics Letters*, 117(1), pp. 365-367.

- Dhaene, G. and Santos Silva, J.M.C. (2012), Specification and Testing of Models Estimated by Quadrature,
*Journal of Applied Econometrics*, 27(2), pp. 322-332.

- Parente, P.M.D.C. and Santos Silva, J.M.C. (2012), A Cautionary Note on Tests for Overidentifying Restrictions,
*Economics Letters*, 115(2), pp. 314-317.

- Baldauf, Markus and Santos Silva, J.M.C. (2012), On the Use of Robust Regression in Econometrics,
*Economics Letters*, 114(1), pp. 124-127.**Dave Giles wrote about this paper in his****blog****.**

- Santos Silva, J.M.C. and Tenreyro, Silvana (2011), poisson: Some Convergence Issues,
*STATA Journal*, 11(2), pp. 207-212.**The command is available in Stata: type "ssc install ppml".**

- Santos Silva, J.M.C. and Tenreyro, Silvana (2011), Further Simulation Evidence on the Performance of the Poisson Pseudo-Maximum Likelihood Estimator,
*Economics Letters*, 112(2), pp. 220-222.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2010), Currency Unions in Prospect and Retrospect,
*Annual Review of Economics*, 2, pp. 51-74.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2010), On the Existence of the Maximum Likelihood Estimates in Poisson Regression,
*Economics Letters*, 107(2), pp. 310-312.

- Santos Silva, J.M.C. and Murteira, J.M.R. (2009), Estimation of Default Probabilities Using Incomplete Contracts Data,
*Journal of Empirical Finance*, 16(3), pp. 457-465.

- Monfardini, Chiara and Santos Silva, J.M.C. (2008), What Can we Learn About Correlations from Multinomial Probit Estimates?,
*Economics Bulletin*, 3(28), pp. 1-9.

- Dias, D.; Marques, C.R. and Santos Silva, J.M.C. (2007), Time or State Dependent Price Setting Rules? Evidence from micro data,
*European Economic Review*, 51(7), pp. 1589-1613.

- Godfrey, L.G. and Santos Silva, J.M.C. (2007), A Note on Variable Addition Tests for Linear and Log-Linear models,
*Economics Letters*, 95(3), pp. 422-427.

- Dias, D.; Marques, C.R. and Santos Silva, J.M.C. (2007), A Note on Measuring the Importance of the Uniform Nonsynchronization Hypothesis,
*Economics Bulletin*, 4(6) pp. 1-8.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2006), The Log of Gravity,
*The Review of Economics and Statistics*, 88(4), pp. 641-658.**The data and much additional information can be found in****The Log of Gravity page****.**

- Reis, H. and Santos Silva, J.M.C. (2006), Hedonic Prices Indexes for New Passenger Cars in Portugal (1997-2001),
*Economic Modelling*, 23(6), pp. 890-908.

- Santos Silva, J.M.C. (2006), A Note on Influence Assessment in Score Tests,
*Communications in Statistics: Theory and Methods*, 35(7), pp. 1243-1256.

- Machado, J.A.F. and Santos Silva, J.M.C. (2006), A Note on Identification with Averaged Data,
*Econometric Theory*, 22(3), pp. 537-541.

- Godfrey, L.G.; Orme, C.D. and Santos Silva, J.M.C. (2006), Simulation-Based Tests for Heteroskedasticity in Linear Regression Models: Some Further Results,
*Econometrics Journal*, 9(1), pp. 76-97.

- Machado, J.A.F. and Santos Silva, J.M.C. (2005), Quantiles for Counts,
*Journal of the American Statistical Association*, vol. 100, no. 472, pp. 1226-1237.**This estimator is available in Stata (type "ssc install qcount") and in R (see****here****).**

- Dias, D.; Marques, C.R.; Neves, P.D. and Santos Silva, J.M.C. (2005), On the Fisher-Konieczny Index of Price Changes Synchronization,
*Economics Letters*, 87(2), pp. 279-283.

- Godfrey, L.G. and Santos Silva, J.M.C. (2004), Bootstrap Tests of Nonnested Hypotheses: Some Further Results,
*Econometric Reviews*, 23(4), pp. 325-340.

- Santos Silva, J.M.C. (2004), Deriving Welfare Measures in Discrete Choice Experiments: A Comment to Lancsar and Savage (2),
*Health Economics*, 13(9), pp. 913-918.

- Santos Silva, J.M.C. (2003), A Note on the Estimation of Mixture Models under Endogenous Sampling,
*Econometrics Journal*, 6(1), pp. 46-52.

- Chesher, Andrew and Santos Silva, J.M.C. (2002), Taste Variation in Discrete Choice Models,
*The Review of Economic Studies*, 69(1), pp. 147-168.

- Santos Silva, J.M.C. (2001), A Score Test for Non-nested Hypotheses with Applications to Discrete Data Models,
*Journal of Applied Econometrics*, 16(5), pp. 577-597.

- Santos Silva, J.M.C. and Windmeijer, Frank (2001), Two-Part Multiple Spell Models for Health Care Demand,
*Journal of Econometrics*, 104(1), pp. 67-89.

- Santos Silva, J.M.C. and Cardoso, F.N. (2001), The Chow-Lin Method Using Dynamic Models,
*Economic Modelling*, 18(2), pp. 269-280.**This method is available in Matlab; please contact me for details.**

- Santos Silva, J.M.C. (2001), Influence Diagnostics and Estimation Algorithms for Powell's SCLS,
*Journal of Business and Economics Statistics*, 19(1), pp. 55-62.**This algorithm is available in Stata: type "ssc install scls"**.

- Machado, J.A.F. and Santos Silva, J.M.C. (2000), Glejser's Test Revisited,
*Journal of Econometrics*, 97(1), pp. 189-202.**This test is available in Stata: type "ssc install mss"**.

- Santos Silva, J.M.C. (2000), Does the Link Matter?,
*Econometric Theory*, Solution, 99.5.3, 16(5), pp. 794-795.

- Santos Silva, J.M.C. and Covas, F. (2000), A Modified Hurdle Model for Completed Fertility,
*Journal of Population Economics*, 13(2), pp. 173-188.

- Santos Silva, J.M.C. (1999), Does the Link Matter?,
*Econometric Theory*, Problem 99.5.3, 15(5), p. 778.

- Santos Silva, J.M.C. (1998), A Consistent Estimator for Truncated Poisson Models With Specification Error,
*Econometric Theory*, Solution 97.3.1., 14(3), pp. 382-383.

- Santos Silva, J.M.C. (1997), A Consistent Estimator for Truncated Poisson Models With Specification Error,
*Econometric Theory*, Problem 97.3.1., 13(4), p. 605.

- Santos Silva, J.M.C. (1997), Generalized Poisson Regression for Positive Count Data,
*Communications in Statistics: Simulation and Computation*, 26(3), pp. 1089-1102.

- Santos Silva, J.M.C. (1997), Unobservables in Count Data Models for On-Site Samples,
*Economics Letters*, 54(3), pp. 217-222.

- Windmeijer, F.A.G. and Santos Silva, J.M.C. (1997), Estimation of Count Data Models with Endogenous regressors; An Application to Demand for Health Care,
*Journal of Applied Econometrics*, 12(3), pp. 281-294.**The estimators discussed in the paper are available in Stata: type "help ivpoisson"**.

- Santos Silva, J.M.C. (1993), A Note on the Score Test for Neglected Heterogeneity in the Truncated Normal Regression Model,
*Economics Letters*43(1), pp. 11-14.

#### Other Publications

- Breinlich, H., Corradi, V., Rocha, N., Ruta, M., Santos Silva, J.M.C., Zylkin, T. (2021), Chapter 3 - Using Machine Learning to Assess the Impact of Deep Trade Agreements
*, in*Fernandes, A., Rocha, N., and Ruta, M. (eds.),*The Economics of Deep Trade Agreements*, CEPR Press: London, pp. 25-34.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2013), Chapter 31 - Currency Unions
*, in*Gerard Caprio Jr. (ed.),*The Evidence and Impact of Financial Globalization*, Academic Press: San Diego, Pages 451-461.

Santos Silva, J.M.C. (2011), A Review of Micro-Econometrics: Methods of Moments and Limited Dependent Variables by Myoung-jae Lee,

*Econometrics Journal*, 14(2), pp. B1-B4.Santos Silva, J.M.C. and Tenreyro, Silvana (2010), Has the euro increased trade?,

*CentrePiece*, 15(2), pp. 6-7.Dias, D.; Marques, C.R., Martins, F. and Santos Silva, J.M.C. (2009), Price Adjustment Lags: Evidence from firm-level data,

*Boletim Económico do Banco de Portugal*, 15(4), pp. 51-69.Brito, Paulo and Santos Silva, J.M.C. (2009), Editorial Note,

*Portuguese Economic Journal*, 8(1), pp. 1-2.Reis, H.J. and Santos Silva, J.M.C. (2002), Hedonic Prices Indexes for New Passenger Cars in Portugal (1997-2001),

*Boletim Económico do Banco de Portugal*, 8(4), pp. 21-26.Machado, J.A.F. and Santos Silva, J.M.C. (2002), 50 Anos de Ensino de Econometria em Portugal,

*Economia*, 26, pp. 95-112.Santos Silva, J.M.C. and Windmeijer, Frank (2002), Microeconometrics: Editors' Introduction,

*Portuguese Economic Journal*, 1(2), pp. 89-90.Covas, Francisco and Santos Silva, J.M.C. (1999), Outlet Substitution Bias,

*Boletim Económico do Banco de Portugal*, 5(3), pp. 77-85.Santos Silva, J.M.C. (1989), Função Consumo, Alguns Desenvolvimentos Recentes e Análise do Caso Português,

*Estudos de Economia*IX(4), pp. 353-372.

#### Working Papers

- Breinlich, H., Novy, D., Santos Silva, J.M.C. (2021).
*Trade, Gravity and Aggregation*, School of Economics, University of Surrey, DP 07/21.

- Breinlich, H., Corradi, V., Rocha, N., Ruta, M., Santos Silva, J.M.C., Zylkin, T. (2021).
*Machine Learning in International Trade Research: Evaluating the Impact of Trade Agreements*, Policy Research working paper 9629, Washington (D.C.): World Bank.

- Machado, J.A.F. and Santos Silva, J.M.C. (2008),
*Quantiles for Fractions and Other Mixed Data*, Department of Economics, University of Essex, Discussion Paper No 656.

- Santos Silva, J.M.C. (2006),
*Monthly estimates for the Portuguese unemployment rate*, Eurostat-Euroindicators Working Papers and Studies, General and regional statistics, KS-DT-05-006.

- Proença, Isabel and Santos Silva, J.M.C. (2000),
*Parametric and Semiparametric Specification Tests for Binary Choice Models: A Comparative Simulation Study*, CEMAPRE/ISEG, Documento de trabalho No7-00.

- Santos Silva, J.M.C. and Andrade e Silva, J.M.S. (1997),
*Misspecification in Models for Positive Count Data*, CEMAPRE/ISEG, Documento de trabalho No7-97.

Santos Silva, J.M.C. (1992),

*The Performance of an Approximation to a Random Parameter Multinomial Logit Model*, Institute of Actuarial Science and Econometrics, University of Amsterdam, Report AE 16/92.

#### Stata Code

- Machado, J.A.F. and Santos Silva, J.M.C. (2018),
*IVQREG2: Stata module to estimate structural quantile functions*, Statistical Software Components S458571, Boston College Department of Economics.

- Machado, J.A.F. and Santos Silva, J.M.C. (2018),
*XTQREG: Stata module to compute quantile regressions with fixed effects*, Statistical Software Components S458523, Boston College Department of Economics.

- Santos Silva, J.M.C., Tenreyro, S., and Windmeijer, F. (2015),
*HPC: Specification test to discriminate between models for non-negative data with many zeros*, Statistical Software Components S457963, Boston College Department of Economics.

- Santos Silva, J.M.C., Tenreyro, S., and Wei, K. (2013),
*FLEX: Stata module for flexible pseudo maximum likelihood estimation of models for doubly-bounded data*, Statistical Software Components S457735, Boston College Department of Economics.An example using flex is available here.

- Santos Silva, J.M.C. (2012),
*SCLS: Stata module to perform symmetrically censored least squares*, Statistical Software Components S457402, Boston College Department of Economics.

- Machado, J.A.F. and Santos Silva, J.M.C. (2011),
*MSS: Stata module to perform heteroskedasticity test for quantile and OLS regressions*, Statistical Software Components S457370, Boston College Department of Economics. More information about this module can be found here.

- Machado, J.A.F., Parente, P.M.D.C., and Santos Silva, J.M.C. (2011),
*QREG2: Stata module to perform quantile regression with robust and clustered standard errors*, Statistical Software Components S457369, Boston College Department of Economics.More information about this module can be found here and here.

- Santos Silva, J.M.C. and Tenreyro, Silvana (2011), PPML: Stata module to perform Poisson pseudo-maximum likelihood estimation,
*STATA Journal*, 11(2), pp. 207-212.To install the command please type "net sj 11-2" in Stata and follow the links; please read the help file carefully before using the command.