[typescript] tsc throws `TS2307: Cannot find module` for a local file

I've got a simple example project using TypeScript: https://github.com/unindented/ts-webpack-example

Running tsc -p . (with tsc version 1.8.10) throws the following:

app/index.ts(1,21): error TS2307: Cannot find module 'components/counter'.
components/button/index.ts(2,22): error TS2307: Cannot find module 'shared/backbone_base_view'.
components/button/index.ts(3,25): error TS2307: Cannot find module 'shared/backbone_with_default_render'.
components/counter/index.ts(2,22): error TS2307: Cannot find module 'shared/backbone_base_view'.
components/counter/index.ts(3,25): error TS2307: Cannot find module 'shared/backbone_with_default_render'.
components/counter/index.ts(4,27): error TS2307: Cannot find module 'shared/backbone_with_subviews'.
components/counter/index.ts(5,20): error TS2307: Cannot find module 'components/button'.

It complains about all imports of local files, like the following:

import Counter from 'components/counter';

If I change it to a relative path it works, but I don't want to, as it makes my life more difficult when moving files around:

import Counter from '../components/counter';

The vscode codebase does not use relative paths, but everything works fine for them, so I must be missing something in my project: https://github.com/Microsoft/vscode/blob/0e81224179fbb8f6fda18ca7362d8500a263cfef/src/vs/languages/typescript/common/typescript.ts#L7-L14

You can check out my GitHub repo, but in case it helps here's the tsconfig.json file I'm using:

{
  "compilerOptions": {
    "target": "es5",
    "module": "commonjs",
    "noImplicitAny": false,
    "removeComments": false,
    "preserveConstEnums": true,
    "sourceMap": true,
    "outDir": "dist"
  },
  "exclude": [
    "dist",
    "node_modules"
  ]
}

Funny thing is, building the project through webpack using ts-loader works fine, so I'm guessing it's just a configuration issue...