The US and Europe cannot fight inflation by raising interest rates because their domestic economies are not pushing against full employment. The source of inflation is from the emerging markets. The US and Europe need China and India to raise interest rates and fight inflation. If they get what they need, that means interest rates in emerging economies rising faster than USD and EUR rates. In terms of term structure, USD and EUR yield curves will only flatten if BRL, CNY and INR curves flatten first.
The more likely scenario is that China and India are facing serious inflation. China will act to slow inflation, India is slightly caught between a rapidly cooling economy and together, aggregate demand will slow. The implications for the rest of the world will be an easing off in energy prices, then food prices, albeit to a lesser extent, and thus lower risk of inflation. The US and Europe will find themselves less motivated to combat inflation.
The price of stable prices will be slowing emerging economies and thus demand for US and European exports. Taking the US as an example, consumption is likely to be weak from poorer consumer sentiment, rising unemployment and weaker income, investment is likely to be weak from scarcity of credit, poorer business expectations, weaker corporate profits, the government is broke, any spending might be inflationary. Trade is almost the last hope for any earlier or stronger than expected recovery. That requires export demand from countries other than those in similar financial health or lack thereof: the developing world. If that part of the world is slowing down, it doesn’t leave much hope for a quick recovery.
What could change that is investment in infrastructure in parts of the developing world where inflationary pressures can be addressed by ad hoc and specific measures, i.e. where market prices do not apply wholesale to the economy and there is sufficient central planning, and where balance sheets corporate or sovereign still have the firepower.