Part of this question is "What is a a reputable economics journal?" There are several rankings.
RePEc was mentioned above. Since this is based on citations and the RePEc database, especially when it comes to citations, is far from comprehensive, I would not rely on this too much.
Thomson Reuters Social Science Citation Index is another source (that itself is not open access).
The above mentioned Elsevier has a service Scopus that ranks journals and also lists open access ones. As you see in the complete list there are many non-English-language open access economics journals and the ranking changes quite a bit according to what score you choose.
2017
Journal CiteScore SJR SNIP
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ClinicoEconomics and Outcomes Research 2.18 0.861 1.003
Theoretical Economics 1.97 5.511 2.203
Judgment and Decision Making 1.89 1.491 1.255
Wine Economics and Policy 1.78 0.539 1.658
Quantitative Economics 1.73 3.742 1.655
Review of Development Finance 1.30 0.452 1.787
Borsa Istanbul Review 1.02 0.372 1.276
Economics and Sociology 1.01 0.617 1.091
International Journal of Energy Economics and Policy 0.98 0.503 0.628
Agricultural and Resource Economics Review 0.93 0.400 1.030
IIMB Management Review 0.90 0.227 1.308
China Journal of Accounting Research 0.90 0.278 0.803
Agricultural Economics (Czech Republic) 0.89 0.553 0.933
Regional Studies, Regional Science 0.82 0.231 0.732
Agris On-line Papers in Economics and Informatics 0.65 0.344 0.916
Panoeconomicus 0.64 0.349 0.936
European Research on Management and Business Economics 0.64 0.236 0.557
SERIEs 0.58 0.304 0.754
REVESCO Revista de Estudios Cooperativos 0.54 0.216 0.643
Latin American Economic Review 0.54 0.258 0.852
Journal of Economics, Finance and Administrative Science 0.54 0.156 0.663
Review of Economic Perspectives 0.50 0.262 0.516
Journal of Economic Education 0.50 0.344 0.782
Croatian Economic Survey 0.50 0.145 0.617
Amfiteatru Economic 0.48 0.250 0.427
Economics 0.46 0.256 0.414
Universia Business Review 0.44 0.169 0.332
South African Journal of Economic and Management Sciences 0.43 0.219 0.403
IZA Journal of Labor Economics 0.43 0.428 0.348
Revista de Economia e Sociologia Rural 0.40 0.227 0.687
Asian Academy of Management Journal of Accounting and Finance 0.40 0.158 0.502
Latin American Journal of Economics 0.39 0.152 0.232
European Journal of Government and Economics 0.38 0.246 0.301
Journal of Applied Economic Sciences 0.37 0.199 0.416
Investigaciones Regionales
0.37 0.159 0.555
Zbornik Radova Ekonomskog Fakultet au Rijeci 0.35 0.157 0.352
IZA Journal of Labor and Development 0.34 0.182 0.510
Economic Annals 0.34 0.167 0.459
Revista de Economia Mundial 0.33 0.170 0.281
IZA Journal of European Labor Studies 0.32 0.200 0.449
IZA Journal of Labor Policy 0.31 0.182 0.213
Economy of Region 0.31 0.260 0.771
Danube 0.31 0.139 0.460
Contemporary Economics 0.31 0.141 0.379
South East European Journal of Economics and Business
0.30 0.169 0.145
Econ Journal Watch 0.30 0.184 0.287
Australasian Accounting, Business and Finance Journal 0.30 0.155 0.224
Revista de Economia Politica/Brazilian Journal of Political Economy 0.29 0.221 0.664
Revista de Metodos Cuantitativos para la Economia y la Empresa 0.28 0.205 0.491
Journal of Current Chinese Affairs 0.28 0.118 1.404
Economics Bulletin 0.27 0.199 0.306
Estudios de Economia 0.21 0.111 0.588
Revista de Analisis Economico 0.20 0.124 0.434
Electronic International Journal of Time Use Research 0.20 0.120 0.202
Economia Aplicada 0.19 0.152 0.552
Journal of Central Banking Theory and Practice 0.18 0.112 0.169
CESifo Forum 0.18 0.165 0.448
America Latina en la Historia Economica 0.17 0.136 0.598
Statistika 0.15 0.121 0.173
Business and Economic Horizons 0.14 0.106 0.163
Revista de Economia del Rosario 0.13 0.128 0.300
Revista Brasileira de Economia 0.12 0.165 0.355
Nova Economia 0.12 0.113 0.325
Estudos Economicos 0.12 0.120 0.398
Investigacion Economica 0.11 0.127 0.329
Cuadernos de Economia (Colombia) 0.11 0.124 0.254
Comparative Economic Research 0.11 0.105 0.116
Revista Contabilidade e Financas 0.10 0.111 0.203
Problemas del Desarrollo 0.10 0.121 0.295
Trimestre Economico 0.09 0.166 0.109
(and some others)
The German Economic Association in 2015 ranked the journals that were mentioned by others above from 0.05 (bottom) to 1 (top): Journal of Economic Perspectives 0.2, Theoretical Economics and Brookings Papers of Economic Activity 0.15, Journal of Economic Education and Economics Bulletin 0.1, and Games, Quantitative Economics and Review of Economic Analysis 0.05. Critical Finance Review was probably too new to be ranked at the time. Journal of Mechanism and Institution Design not included. In 2017 the ranking was updated to reflect changing impact factors over time and is now based on the Scopus SJR. That brought Journal of Economic Perspectives to 0.8 for 2016, Theoretical Economics 0.56, Quantitative Economics 0.54, Brookings Papers of Economic Activity 0.38, Journal of Economic Education 0.2, Games 0.05, Economics Bulletin 0.04, Review of Economic Analysis 0.025 (lowest ranking because not in EconLit), Critical Finance Review and Journal of Mechanism and Institution Design not included.
There are many further rankings, like the French CNRS Journal Ranking in Economics and Management June 2017 (1 top to 4 bottom: Journal of Economic Perspectives, Theoretical Economics, Brookings Papers of Economic Activity, Quantitative Economics all 1, Economics Bulletin 3. Review of Economic Analysis, Critical Finance Review, Games and Journal of Mechanism and Institution Design not included.
If you look at more restrictive rankings you'll not find many open access journals. Tilburg University only includes the Brookings Papers on Economic Activity and the Journal of Economic Perspectives in its 35 journals for the ranking of top economics universities as far as I see.
The Directory of Open Access Journals has 71 entries under "Subject: Economic theory. Demography" but some further economics journals are listed under different categories like Journal of Economic Education" under "Subject: Education: Theory and practice of education", and "Journal of Economic Development, Environment and People" under "Subject: General Works".