Motivated by a fundamental question, namely how the Chinese economy is or was working, this thesis studies two puzzles regarding Chinese economic growth and business cycles based on comparative perspectives. Chapter One studies whether the finance-growth relationships in China contradict cross-country findings. This issue is empirically examined with particular emphasis on the role of innovation based on data from 30 Chinese provinces over 1991 to 2014. Our findings suggest that there is an innovation channel through which banking sector development promotes productivity and economic growth while stock market development impedes them. We further investigate if the effects of financial development differ in different development stages. Based on the sub-sample regressions, we show that the effects have dramatic difference across different periods, which is very likely due to multiple reforms. These findings also provide a reconciliation that the Chinese finance-growth nexus is not completely different from cross-country findings. In chapter Two, we build and estimate a DSGE model with endogenous technology creation and extended financial markets to compare the contributing factors behind Chinese and the US profiles for economic activity. Our analysis is motivated by a puzzling contrast in business cycle behaviour between the two countries, which share similar profiles for the path of gross domestic product (GDP) yet contrasting profiles for total factor productivity (TFP). Our findings suggest that government policies through fiscal and investment interventions work well for output smoothing in China, but exacerbate the volatility of TFP. The addition of a stock market in the model reinforces this explanation; the option to switch into equities for US firms has a dampening effect on TFP, with the reverse case for China, meaning that China should develop equity markets, but proceed cautiously.