Input Impedance of a Bipolar Transistor Bias with Feedback

AoE shows a bipolar transistor bias circuit using feedback from the collector.  AoE2 and AoE3 show the identical circuit, but they differ in the values of the input impedance: AoE2 states 300 Ohms and AoE3 200 Ohms.  We would like to analyze the circuit to see why the value has changed.  Here the base bias is established by a resistor from the collector, which has the effect of negative feedback: a high bias lowers the collector voltage that reduces the base voltage.  

Here we estimate the collector current to be about 1mA.  The input impedance is about 200 Ohms for a beta of 100; it does not exceed 225 Ohms as the beta goes to infinity.  So it seems justified that AoE3 makes the correction.   Even when the temperature varies, the input resistance stays relative constant.  For example, if T = 100C, VT = kT/q = 32mV, but because Vbe decreases with increasing temperature, the emitter current also goes up, Vbe = 0.4V, Ie = 1.34mA, gm is still around 1/25 A/V.