No.

Before going into the specific case which you mention, it would be useful to understand why recessions (i.e drop in economic output for 2 consecutive quarters) occurs. Recessions in a market economy are caused by the inability of the market to expand as fast the productive forces of the economy. Under a Capitalist market economy, each firm whether it is a State owned enterprise, Private Limited Company or a Co-operative is an individual unit production. Capital needs to constantly keep on expanding and this forces them to keep on using better technology to improve output and extract profit. Under universal competition, the reward of firm is sooner rather than later taken away which further encourages to carry on this process and expand output to it's limit.This leads to development of means of production in general.

Even in a very primitive market economy, this phenomenon was observed and described by Adam Smith in Wealth of Nations. The development of commodity production, large market, extensive trade and most importantly the credit system provided by banks organized as joint stock companies sharpened the process making the boom and bursts increasingly severe. These periods are characterized by sharp appreciation of asset value (well beyond their 'real value'), reckless lending by financial institutions, heavy buildup in corporate and household debt and ultimately resolution in a severe debt deflation throwing the commercial world out of it's joint.

The primary purpose of taxes is to collect sufficient revenue for the Government for spending. The influence of tax rates on economic growth is a controversial topic on which you will find a wide variety of opinions. However, fiscal policy (taxes and spending) is are relatively small part of the entire puzzle piece of public policy. The boom and burst cycles that have been observed with the introduction of market economy (characterized by commodity production) are entirely independent of tax policy.

The 1930's crisis was caused by massive expansion of productivity starting with mechanization of agriculture leading to creation of surplus labour, massive expansion of technology notably in communication systems and in the Automobile Industry which led to rapid improvements in productivity and consequent fast rise in income for a small but growing number of Americans. This was further enhanced by reckless lending and expansion of credit ("over banking") that culminated in the stock market crash and led to large scale crisis. There was growth in number of brokerage houses and investment trusts to take advantage of the boom. People also used margin accounts to purchase stocks with borrowed funds. Purchasers put down a fraction of the price, typically 10 percent, and borrowed the rest. The stocks they bought were served as a collateral for loan. The heavy flow of borrowed money into stock markets sent stock prices higher.

It was also compounded by the fact that the banking system was fragmented as the law made it relatively easy to open a small bank but which was exceptionally difficult to expand. When the market crashed, there was a systematic failure in banking system of the United States as many small banks had lend to agricultural enterprises and the collapse in prices hit them hard.The Federal Reserve did not loosen policy as it was forced to maintain the gold standard which caused very severe deflationary pressure which worsened the crisis leading to further bankruptcies and rapid decline in output.

This had some similarities with the crisis in Britain in late 1860's which was also preceded by a boom period.There was a similar period of rapid growth starting from 1840’s because of repeal in corn laws and other protectionist measures in Britain which led to expansion of markets, domination of steam engines, rapid development of infrastructure, increase in money supply (and consequently credit) because of discovery of gold mines etc. However, the rapid growth and increase in productivity also led to vast bubbles, reckless trading and eventually there was a large crisis. Capitalism tends towards over production and the massive expansion in the 20 year period from 1840’s to late 1860’s was also followed by a big burst. The result was growth in inequality, dumping by export oriented countries on world markets because of low prices, bankruptcies of enterprises, discontent among the people, increase in protectionism and formation of cartels in countries like Germany.

I would suggest that the basic reason which I mentioned above for the crisis can be seen in a number of other such cases in different countries in different periods namely- The mid 1960's bank failures in Hong Kong and the subsequent rescue by the government and the late 1980's banking crisis in Norway.

Notes :

Why do we let Banks Fail by Lee Alston, Wayne Grove, David Wheellock

Banking Panics of 1930 and 1931 by Gary Richardson

Stock Market Crash of 1929 by by Gary Richardson, Alejandro Komai, Michael Gou, and Daniel Park

This is a old question, but I want to respond, just because I don't think the other answer is correct.

Economist have uniformly rejected the idea that the depression is caused by anything that happens in the 1920s, except monetary policy. The waste majority of economist attribute the Great Depression, particularly the early part with a monetary contraction caused by a combination of a badly managed Fed, badly behaved international gold standard and maybe the expand tariffs effect on banking.

You will find almost no modern economist who would agree with /u/Shashank1000 the 'demand not keeping up with supply' story. That is the old marxian story of overproduction and it has been rejected uniformly, both in case of the great depression and in general.

The problem is that if you look back from a recession, you can always observe the past and say that there was overlanding. The problem is that if there was no recession, this credit would have been good. So unless you can actually show a causational link between the lending and the depression the credit would have been good.

He is correct however that banking was very bad and fragmented. These banks could not withstand collapsing export (because of the new tariffs) or other local problems (bad harvest for example). Most economist agree that this made the monetary contraction even worse.

Some economist (Barry Eichengreen) have argued that the gold standard was holding back the Fed. This argument has been attacked because after WW1 the US had lots of gold and the could have easily done their job correct, with the resources they had.

Conclusion, Harding and Coolidge can be blamed for the great depression except if argue that they failed to reform the central bank.