include": [
    "./**/*"
  ]
}

And a sample.tsx file for a React component that replicates this issue:
import * as React from "react";

export interface HelloProps { compiler: string; framework: string; }

export const Hello = (props: HelloProps) => {
    return <h1>Hello from {props.compiler} and {this.props.framework}!</h1>
};

I also went ahead and created another project replicating this issue and uploaded it to BitBucket for anyone interested. Any help would be greatly appreciated. If this turns out to be an issue with TypeScript itself, I'll make sure to create an Issue on the Github repo.

A: Looks like implicit import does not always work. When I fixed your package.json (removed trailing comma in scripts) and tsconfig.json (added bin to exclude), I'm getting these errors with typescript 2.1.4:
src/greeter.tsx(2,24): error TS2307: Cannot find module'react-modal'.
src/greeter.tsx(19,26): error TS2339: Property'setState' does not exist on type 'Greeter'.

I think I khow the explanation for the first one. In package.json for react-modal, the main property is 
"main": "./lib/index",

but the actual file has.js extension, that is, it's./lib/index.js.
When I change main in node_modules/react-modal/package.json to 
"main": "./lib/index.js",

the first error goes away.
I think it's indeed an issue with TypeScript.

A: try and add you tsconfig and enable and disable noImplicitAny : 
{
  "compilerOptions": {
    "target": "es5",
    "module": "commonjs",
    "moduleResolution": "node",
    "sourceMap": true,
    "emitDecoratorMetadata": true,
    "experimentalDecorators": true,
    "lib": ["es2015", "dom"],
    "noImplicitAny": true,
    "suppressImplicitAnyIndexErrors": true,
    "typeRoots": [
      "../../node_modules/@types/"
    ]
  }      
}

Venture investments grew 69 per cent to USD 16.4 billion in the September quarter on the back of a jump in the number of transactions, a report said on Thursday.
including private equity, infrastructure and real estate.
“With increasing interest from large global pension and sovereign wealth funds combined with the evolution of new investment structures like InvITs and REITs, we continue to project sustained growth in real asset investments in India,” he said.
In a similar report, its rival KPMG also said venture capital investment in India strengthened during the September quarter led by a slew of large deals of over USD 100 million.
However, it was more circumspect on the outlook front.
“VC investment in India is expected to remain strong in the December quarter and the March quarter. However, given the current credit squeeze it might not be as robust as it has been over the past two quarters,” it said.
The EY report said that exits have been subdued as the total number stood at USD 8.1 billion for the first three quarters as against USD 8.5 billion in the same period last year, the data said.
“The Governments step to rationalise corporate tax rate and introduce positive changes to the FPI policy are steps in the right direction, and increase attractiveness of India for long-term capital investment relative to it’s emerging markets peers,” it said.
I wasn't sure whether to post this here or email you as this relates to the website, so I hope I've done it right posting here.
Anyway, when I read through the forums on my iPhone the mobile site version is great and easy to use. But when I try to respond to posts and try to paste web links I've always had a bit of trouble.
What it is, is that the "pinch and drag" on the iPhones screen works great all over the site, but when trying to paste a link, the text edit window comes off the screen making it difficult to paste either in portrait or landscape modes and I'm unable to "drag to reduce" the screen size. I'm currently using an iPhone 5s with iOS 8 and I have provided a couple of screen shots below.
Looking at the pictures it doesn't look particularly bad, but actually using it, I have to keep flipping the phone back and fourth to paste, add a description, then to send. I also tried to paste a link using a Sony Xperia android phone earlier and it was impossible to paste anything.
This is not a criticism, far from it, but I thought you would like to know as I use my iPhone to view and respond to posts, a lot, and it can be a bit of a pain. I don't know if anyone else has faced this, but like I said, I thought you might like to know in case you were unaware of it. I hope you don't mind me mentioning it.
The forum's a good place to tell us about these issues, thanks for letting us know!
You are using the Safari web browser on your phone, right?
And it's specifically the windows that come up for the buttons like "add link", etc? Or is it a problem in the main message box as well?
That's correct. It's the add link, add image, and add YouTube buttons (although YouTube is actually not to bad as its only one text input field). The main message box is absolutely fine.
And it is Saffari that my iPhone is using.
Thanks! I know why that is - because I didn't ever update those popups to be responsive They still use a table layout. D'oh! So basically they aren't designed for phones yet.
Doh :P, oh well that explains it. No problem. Thanks for looking in to it Chrissie.Anderson's of Nottingham Nottingham, Nottinghamshire.
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Van Dusen, owner and principal of LVW Advisors LLC in Pittsford, ranks 42nd among New York advisers. Fischer ranks 68th. The state-by-state rankings were released Feb. 24.
Van Dusen manages assets of $3.1 billion, with typical accounts of $50 million from clients with a typical net worth of $75 million, data compiled by Barron’s shows.
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Fischer is executive director of the Fischer Consulting Group at Linden Oaks. The group is part of Graystone Consulting, the institutional consulting business of Morgan Stanley Smith Barney LLC.ï Requires separate 120 Vac spark generator.
ï S89E has 10-second maximum delay for safe start check before ignition.
ï S89F has 38-second maximum delay for safe start check plus valve on delay before ignition.
ï Available with 4 or 11 second (nominal) lockout timing.
ï 100 percent shutoff for use with all heating gases.
ï Ambient temperature rating is -40 F to +175 F (-40 C to +80 C).
ï Separate electrodes for spark ignition and flame sensing.
ï Uses Honeywell or any other 2A or less dual valve combination gas control designed for Direct Spark Ignition (DSI) applications.
ï Locks out system after trial for ignition if main burner fails to ignite.
ï Flame rectification principle used to monitor flame; false flame signals resulting from short to ground results in safety shutdown.
ï After safety shutdown, S89E and F can be reset from the thermostat.
IMPORTANT The specifications given in this publication do not include normal manufacturing tolerances. Therefore, this unit may not match the listed specifications exactly. Also, this product is tested and calibrated under closely controlled conditions, and some minor differences in performance can be expected if those conditions are changed.
120 Vac Spark Generator with 1.5A or less current draw. Q347 Spark Igniter or equivalent. Q354 Flame Sensor or equivalent. VR845, VR854, VR8450, or VR8305 Combination Gas Controls or any dual valve rated 2A or less and designed for DSI applications.
24 to 30 Vac Thermostat.
HIgh Temperature Limit Controller. 24V Transformer. See Table 1 for VA rating.
Power supply: Requires two power supply connectionsó24 and 120 Vac, 50/60 Hz. Current at 24V input: 2.2A maximum.
Spark Generator Relay