Network effects -- the utility gains from additional consumers of a good -- are widely regarded as critical to the digital economy. Yet recent theory and evidence suggest that local network effects -- the economic value created by specific social network connections -- drive value in networked online platforms. Using incentive-compatible online choice experiments with 19,923 Facebook, Instagram, LinkedIn, and X users in the United States, we provide the first large-scale empirical measurement of local network effects in the digital economy and measure heterogeneity in connection value across platforms. Platform value ranges from \$78 to \$101 per consumer per month, with 8.1-23.7% explained by local network effects. We find that 1) stronger ties are more valuable on Facebook and Instagram, while weaker ties are more valuable on LinkedIn and X; 2) work connections are most valuable on LinkedIn and least on Facebook, and job-seekers value LinkedIn significantly more and Facebook significantly less; 3) men value connections to women significantly more than to other men, particularly on Instagram, Facebook, and X, while women value connections to men and women equally across platforms; 4) consumers value connections on any platform more if they are also connected on other platforms, suggesting that platforms are complements, not substitutes; 5) white consumers disproportionately value same-race connections on Facebook while, on Instagram, connections to alters eighteen or younger are valued significantly more than any other age group -- two patterns not seen on other platforms. Each platform generates between \$53B and \$215B in annual US consumer surplus. These results suggest that social media generates significant value, that local network effects drive a substantial fraction of it, and that the sources and contours of these effects vary across platforms, consumers, and connections.